ML_basics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Based on the [Machine Learning Tutorial Series](https://www.youtube.com/watch?v=gmvvaobm7eQ) by Dhaval Patel\n",
    "---\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Requirements\n",
    "---\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.linear_model import LinearRegression, LogisticRegression, Lasso, Ridge\n",
    "from sklearn import tree, svm\n",
    "from sklearn.ensemble import RandomForestClassifier, BaggingClassifier\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.naive_bayes import MultinomialNB\n",
    "from sklearn.model_selection import train_test_split, cross_val_score, GridSearchCV\n",
    "from sklearn.datasets import load_digits, load_iris, load_breast_cancer\n",
    "from sklearn.metrics import confusion_matrix, classification_report\n",
    "from sklearn.preprocessing import LabelEncoder, MinMaxScaler, StandardScaler\n",
    "from sklearn.feature_extraction.text import CountVectorizer\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression\n",
    "---\n",
    "---\n",
    "Predicting a continous value based on a single input value\n",
    "- Utilises a linear function: $ y = m*x + b $\n",
    "    - `y = target value`\n",
    "    - `m = slope `\n",
    "    - `x = argument` \n",
    "    - `b = interception with y-axis`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>area</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2600</td>\n",
       "      <td>550000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3000</td>\n",
       "      <td>565000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3200</td>\n",
       "      <td>610000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3600</td>\n",
       "      <td>680000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4000</td>\n",
       "      <td>725000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   area   price\n",
       "0  2600  550000\n",
       "1  3000  565000\n",
       "2  3200  610000\n",
       "3  3600  680000\n",
       "4  4000  725000"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = os.path.join(\"data\", \"linear_regression_data.csv\")\n",
    "# loading the data\n",
    "df = pd.read_csv(path)\n",
    "# display the numeric data\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1c6093d3ac0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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bKuLHA4cAW3NXs+XbN5T7RMSrkral9r/PJyhpOjAd4LDDDuvkxzEzs+7o7D6Y89/guscBl0XEMklfB2YC3wS+AkT6/ipwwRvYzh6LiGuBawFKpZKPbszMelBnlyl/UNLbc/NflPSQpDskjexk3c1Ac0QsS/MLgXERsSkidqRnmX2bXafBWoDhuf7DUqy9+LNAfbpPJx/fbV1p+cGpvZmZVUlng/z/THaaC0lnAn9NdrRxB3BNRx0j4mlgg6TRKXQq8JikoblmHwYeSdN3AOemK8BGAqOAXwEPAqPSFWP7kV0IcEcaT7kfODv1nwbcnltX+RLqs4H7PP5iZlZdnY3BRESUrxY7C7iu/IgYSZd0Yf2XATemwrAeOB+YK2kM2SmyJ4BPpA09KukW4DHgVeCTEbEDQNKlwGKgH3B9RDya1v954CZJ/wSsAMrPRLsO+F66UGALWVEyM7MqUkd/2Et6GPhTskuSfwv8RUQ0pmWPRcTR7XauMaVSKRobG3s7DTOzmiJpeUSU2lrW2RHM14CVwPPA6lxxGQts7MEczcxsL9PZVWTXS1oMvA14KLfoabLTXWZmZm3q7IVj43KzYyQF8PuI2NBeHzMzM+j8FNlX24gNSoP250XEyp5PyczM9gadnSJ7b1txSSVgLtmjYMzMzF6ns/tg2pQG+9/cw7mYmdleZI8KjKQhZPexmJmZtamzQf5v8PpCMojs3pi/e30PMzOzTGeD/JV3HgbZM70uj4hniknJzMz2Bp0N8s+vViJmZrZ36expyj9OT1Qe0MaywyVdIalXHrVvZmZ9W2enyC4CLge+JmkL2ZOVDwBGAOuAb0bE7e13NzOzfVVnp8ieBj4HfE7SCGAo0Ar8JveUZTMzs9fpzmXKARyY7t4PSW8pJiUzM9sbdKnASLqI7I2U/55Cw4BFBeVkZmZ7ga4ewXwSOJHssf1ExFqyJyybmZm1qasF5uWIeKU8k95z7zv5zcysXV0tMA9I+gegTtIHgB8CPy4uLTMzq3VdLTAzyS5RXgV8ArgT+MeikjIzs9rX1QJTB1wfER+JiLOB61OsQ5LqJS2U9Lik1ZJOkDQnzT8s6TZJ9antCEmtklamzzW59YyXtEpSk6S5kpTigyQtkbQ2fQ9McaV2TWk749pM0MzMCtPVAnMvuxeUOuBnXej3deDuiDgKOBZYDSwB3hkR7wZ+A8zKtV8XEWPS5+JcfB7ZTZ+j0mdSis8E7o2IUSnHmSl+eq7t9NTfzMyqqKsF5oCIeKE8k6bf1FEHSQeTvZDsutTnlYjYGhH3RMSrqdlSskueO1rPUOCgiFgaEQEsAKakxZOB8vPS5lfEF0RmKVCf1mNmZlXS1QLzYv40k6TxZHf0d2Qk2bjNdyWtkPQdSQdWtLkAuCvfJ7V9QNJJKdYANOfaNKcYwJCI2JimnwaG5PpsaKfPTpKmS2qU1Lh58+ZOfhwzM+uOrhaYTwM/lPQLSf8F3Axc2kmf/sA4YF5EjAVeZNcpLCR9AXgVuDGFNgKHpbaXA9+XdFBXf5B0dNOtS6cj4tqIKEVEafDgwd3pamZmnejsYZcARMSDko4CRqfQmojY3km3ZqA5Ipal+YWkAiPpY8CZwKmpMBARLwMvp+nlktYBRwIt7H4abViKAWySNDQiNqZTYOV31LQAw9vpY2ZmVdDZ4/rfl77PAj5I9g/+kcAHU6xd6UGZGySVi9KpwGOSJpE9QPND+QdmShosqV+aPpxsgH59OgX2vKQJ6eqxqUD5Cc53ANPS9LSK+NR0NdkEYFvuVJqZmVVBZ0cwfwbcR1ZcKgVwayf9LwNulLQfsB44H3gQ2B9Ykq42XpquGDsZuELSduA14OKI2JLWcwlwA9nVa3exa9xmNnCLpAuBJ4FzUvxO4AygCXgpbdfMzKpI6QxV+w2kPwLOjohbqpNS7yiVStHYWPmGaDMz64ik5RFRamtZp4P8EfEa2SktMzOzLuvqVWQ/k/T3koanu+cHSRpUaGZmZlbTunQVGfBRsjGXSyrih/dsOmZmtrfoaoE5mqy4vIes0PwCuKbDHmZmtk/raoGZT/aysblp/i9T7Jx2e5iZ2T6tqwXmnRFxdG7+fkmPFZGQmZntHbo6yP/rdMMiAJKOB3xNr5mZtaurRzDjgf+W9Ls0fxiwRtIqsseAvbuQ7MzMrGZ1tcBM6ryJ2b5r0YoW5ixew1NbWzm0vo4ZE0czZezrHuBttk/p6sMunyw6EbNatWhFC7NuXUXr9h0AtGxtZdatqwBcZGyf1tUxGDNrx5zFa3YWl7LW7TuYs3hNL2Vk1je4wJi9QU9tbfvde+3FzfYVLjBmb9Ch9XXdipvtK1xgzN6gGRNHUzeg326xugH9mDFxdDs9zPYNXb2KzMzaUR7I91VkZrtzgTHrAVPGNrigmFXwKTIzMyuEC4yZmRXCBcbMzApRaIGRVC9poaTHJa2WdEJ6G+YSSWvT98DUVpLmSmqS9LCkcbn1TEvt10qalouPl7Qq9ZkrSSne5jbMzKx6ij6C+Tpwd0QcBRwLrAZmAvdGxCjg3jQPcDowKn2mA/MgKxbAl4DjgeOAL+UKxjzgoly/8jPT2tuGmZlVSWEFRtLBwMnAdQAR8UpEbAUmk72sjPQ9JU1PBhZEZilQL2koMBFYEhFbIuI5YAkwKS07KCKWRkQACyrW1dY2zMysSoo8ghkJbAa+K2mFpO9IOhAYEhEbU5ungSFpugHYkOvfnGIdxZvbiNPBNnYjabqkRkmNmzdv3pOf0czM2lFkgekPjAPmRcRY4EUqTlWlI48oMIcOtxER10ZEKSJKgwcPLjINM7N9TpEFphlojohlaX4hWcHZlE5vkb6fSctbgOG5/sNSrKP4sDbidLANMzOrksIKTEQ8DWyQVH4g06nAY8AdQPlKsGnA7Wn6DmBquppsArAtneZaDJwmaWAa3D8NWJyWPS9pQrp6bGrFutrahpmZVUnRj4q5DLhR0n7AeuB8sqJ2i6QLgSeBc1LbO4EzgCbgpdSWiNgi6SvAg6ndFRGxJU1fAtwA1AF3pQ/A7Ha2YWZmVaJsiMJKpVI0Njb2dhpmZjVF0vKIKLW1zHfym5lZIVxgzMysEC4wZmZWCBcYMzMrhAuMmZkVwgXGzMwK4QJjZmaFcIExM7NCuMCYmVkhXGDMzKwQLjBmZlYIFxgzMyuEC4yZmRXCBcbMzArhAmNmZoVwgTEzs0K4wJiZWSFcYMzMrBAuMGZmVggXGDMzK0ShBUbSE5JWSVopqTHFbk7zK9PylSk+QlJrbtk1ufWMT+tpkjRXklJ8kKQlktam74EprtSuSdLDksYV+XOamdnrVeMI5r0RMSYiSgAR8dE0Pwb4EXBrru268rKIuDgXnwdcBIxKn0kpPhO4NyJGAfemeYDTc22np/5mZlZFvXaKLB2FnAP8oJN2Q4GDImJpRASwAJiSFk8G5qfp+RXxBZFZCtSn9ZiZWZUUXWACuEfScknTK5adBGyKiLW52EhJKyQ9IOmkFGsAmnNtmlMMYEhEbEzTTwNDcn02tNNnJ0nTJTVKaty8eXO3fzgzM2tf/4LX/56IaJH0NmCJpMcj4j/TsvPY/ehlI3BYRDwraTywSNIxXd1QRISk6E5yEXEtcC1AqVTqVl8zM+tYoUcwEdGSvp8BbgOOA5DUHzgLuDnX9uWIeDZNLwfWAUcCLcCw3GqHpRjApvKpr/T9TIq3AMPb6WNmZlVQWIGRdKCkt5SngdOAR9Li9wOPR0Rzrv1gSf3S9OFkA/Tr0ymw5yVNSOM2U4HbU7c7gGlpelpFfGq6mmwCsC13Ks3MzKqgyFNkQ4Db0hXF/YHvR8Tdadm5vH5w/2TgCknbgdeAiyNiS1p2CXADUAfclT4As4FbJF0IPEl20QDAncAZQBPwEnB+j/5kZmbWKWUXZlmpVIrGxsbeTsPMrKZIWl6+DaWS7+Q3M7NCuMCYmVkhir5M2WyPLFrRwpzFa3hqayuH1tcxY+Jopox93a1MZtaHucBYn7NoRQuzbl1F6/YdALRsbWXWrasAXGTMaohPkVmfM2fxmp3Fpax1+w7mLF7TSxmZ2Z5wgbE+56mtrd2Km1nf5AJjfc6h9XXdiptZ3+QCY33OjImjqRvQb7dY3YB+zJg4upcyMrM94UF+63PKA/m+isystrnAWJ80ZWyDC4pZjfMpMjMzK4QLjJmZFcIFxszMCuECY2ZmhXCBMTOzQrjAmJlZIVxgzMysEC4wZmZWCBcYMzMrRKEFRtITklZJWimpMcW+LKklxVZKOiPXfpakJklrJE3MxSelWJOkmbn4SEnLUvxmSful+P5pviktH1HEz7doRQsnzr6PkTN/yomz72PRipYiNmNmVpOqcQTz3ogYExGlXOyqFBsTEXcCSDoaOBc4BpgEXC2pn6R+wLeA04GjgfNSW4B/Tes6AngOuDDFLwSeS/GrUrseVX4pVsvWVoJdL8VykTEzy/SlU2STgZsi4uWI+C3QBByXPk0RsT4iXgFuAiZLEvA+YGHqPx+YklvX/DS9EDg1te8xfimWmVnHii4wAdwjabmk6bn4pZIelnS9pIEp1gBsyLVpTrH24ocAWyPi1Yr4butKy7el9ruRNF1So6TGzZs3d+sH80uxzMw6VnSBeU9EjCM7vfVJSScD84B3AGOAjcBXC86hXRFxbUSUIqI0ePDgbvX1S7HMzDpWaIGJiJb0/QxwG3BcRGyKiB0R8RrwbbJTYAAtwPBc92Ep1l78WaBeUv+K+G7rSssPTu17jF+KZWbWscIKjKQDJb2lPA2cBjwiaWiu2YeBR9L0HcC56QqwkcAo4FfAg8CodMXYfmQXAtwREQHcD5yd+k8Dbs+ta1qaPhu4L7XvMVPGNnDlWe+iob4OAQ31dVx51rv8DhMzs6TIF44NAW5LY+v9ge9HxN2SvidpDNn4zBPAJwAi4lFJtwCPAa8Cn4yIHQCSLgUWA/2A6yPi0bSNzwM3SfonYAVwXYpfB3xPUhOwhawo9Ti/FMvMrH3q4T/sa1apVIrGxsbeTsPMrKZIWl5xG8pOfekyZTMz24u4wJiZWSFcYMzMrBAuMGZmVggP8ieSNgNP7mH3twK/78F0ilZL+dZSrlBb+dZSrlBb+dZSrvDG8n17RLR5p7oLTA+Q1NjeVRR9US3lW0u5Qm3lW0u5Qm3lW0u5QnH5+hSZmZkVwgXGzMwK4QLTM67t7QS6qZbyraVcobbyraVcobbyraVcoaB8PQZjZmaF8BGMmZkVwgXGzMwK4QLTBknDJd0v6TFJj0r6u9yyyyQ9nuL/JxefJalJ0hpJE3PxSSnWJGlmNfOVNEbSUkkr05s7j0txSZqbcnpY0rjcuqZJWps+09rb5hvI9QBJv5L0UMr1f6f4SEnLUk43p1czkF7fcHOKL5M0IreuNvd5lfK9MW33kfRm1gEp3uf2bW75XEkv5Ob76r6VpH+W9BtJqyV9KhfvU/tW0qmSfp1+x/5L0hEp3qv7NretfpJWSPpJmq/u71lE+FPxAYYC49L0W4DfAEcD7wV+Buyflr0tfR8NPATsD4wE1pG9WqBfmj4c2C+1ObqK+d4DnJ7iZwA/z03fBQiYACxL8UHA+vQ9ME0P7OFcBbw5TQ8AlqUcbgHOTfFrgL9N05cA16Tpc4GbO9rnBezb9vI9Iy0T8INcvn1u36b5EvA94IVc+766b88HFgB/VPF71uf2bfpd++Pc/ryhL+zbXN6XA98HfpLmq/p75iOYNkTExoj4dZr+A7AaaAD+FpgdES+nZc+kLpOBmyLi5Yj4LdBE9qbO44CmiFgfEa8AN6W21co3gINSs4OBp3L5LojMUrI3gw4FJgJLImJLRDwHLAEm9XCuERHlv6IHpE8A7wMWpvh8YEou1/lpeiFwqiTR/j7vUe3lGxF3pmVB9mK8Ybl8+9S+ldQPmAN8rqJLn9y3ZL9nV0T21tvK37M+tW/p+Hes1/YtgKRhwJ8D30nzosq/Zy4wnUiHimPJ/mI5EjgpHUI+IOlPUrMGYEOuW3OKtRevVr6fBuZI2gD8GzCrL+SbDttXAs+Q/WOwDtgaEa+2sd2dOaXl24BDqpVrW/lGxLLcsgHA3wB3V+ZbkVev7NuU66Vkb4HdWNG8r+7bdwAfVXZa9y5JoyrzrcirN/ftx4E7JTWT/X8wuzLX3tq3wNfI/qh4Lc0fQpV/z1xgOiDpzcCPgE9HxPNkb+YcRHZoPAO4JVX5PqGNfP8W+ExEDAc+w643fvaqiNgREWPI/uo/DjiqdzPqWGW+kt6ZW3w18J8R8YteSa5CG7meDHwE+EavJtaOdvbt/sD/RPbokm8D1/diiju1k+tngDMiYhjwXeD/9mKKO0k6E3gmIpb3Zh4uMO1If5n+CLgxIm5N4Wbg1nS4/CuyvwzeCrQAw3Pdh6VYe/Fq5TsNKE//kF2Htr2eL0BEbAXuB04gO91RfoV3frs7c0rLDwaerXauFflOSvl8CRhMdp67rK/t2/cCRwBNkp4A3qTsVeK75drH9m0zu/6/vQ14d2W+FXn11r49HTg2d0R7M/Cnlbn20r49EfhQ+m9+E9mpsa9T7d+zrg7W7EsfsgG9BcDXKuIXk50bhux02YbU9hh2HwhbTzbA3z9Nj2TXIP8xVcx3NXBKmj4VWJ6m/5zdB0t/leKDgN+SDZQOTNODejjXwUB9mq4DfgGcSVYA84OPl6TpT7L74OMtabrNfV7Avm0v348D/w3UVbTvc/u2ok1+kL+v7tvZwAUpfgrwYF/dt2RPID4yxS8EftQX9m1F7qewa5C/qr9nhf1QtfwB3kM2ePcwsDJ9ziArEv8BPAL8Gnhfrs8XyMYS1pCu3ErxM8iuNFkHfKHK+b4HWJ7+B1kGjE/tBXwr5bQKKOXWdQHZQF4TcH4Bub4bWJFyfQT4YoofTjZY3pR+CcpX6h2Q5pvS8sM72+dVyvfVtO3y/i7H+9y+rWiTLzB9dd/WAz9N+++XZEcJfXLfAh9OuTwE/Ly8D3t731bkfgq7CkxVf8/8qBgzMyuEx2DMzKwQLjBmZlYIFxgzMyuEC4yZmRXCBcbMzArhAmNWQyQtlHR4mv5Ietrw/ZJOkfSnuXbfkPQ9Sf+S5i+VdEFv5W37JhcYs16QHkDZ3T7HkN3ktj6FLgQuioj3kt3rsLPARMRlwN+T3fcA2eNWLnsjOZt1lwuMWQEkLZK0PL07ZHqKvSDpq5IeAk6Q9NfpHSMrJf17uehImpce9Fj5Tpe/Am5Pbb5IdiPtdZJ+SPaUic+kdZ0k6TCyO+IvAYiIl4AnlN4JZFYNLjBmxbggIsaTvYflU5IOAQ4ke4fJsWTPefoocGJkD1DcQVZAIHviQ4ns7vE/k1R+FteJZE9mICKuABqBv4qIj5A99uOqtK5fps9+ZHdhlzUCJxXz45q9Xv/Om5jZHviUpA+n6eHAKLIi8qMUOxUYDzyYHshdR/YYeIBz0lFPf7KXyR1N9oiSocDmzjYc2ePW23qk+jP08SdX297FBcash0k6BXg/cEJEvCTp52TPevqfiNhRbgbMj4hZFX1Hko2d/ElEPCfphtQXoDU3vScOSOswqwqfIjPreQcDz6XichTZk38r3QucLeltAJIGSXo72dsRXwS2SRpC9kj4stVkj95vyx/IXpfdkSPJHtRoVhUuMGY9726gv6TVZAPtSysbRMRjwD8C90h6mOzNnkMj4iGyp/Y+TvYu9f+X6/ZTsqvF2vJj4MPlQf522pyYtmNWFX6aslmNkFRH9qKrE3On2rradyxweUT8TSHJmbXBBcashkiaCKyOiN91s98HgLUR8UQhiZm1wQXGzMwK4TEYMzMrhAuMmZkVwgXGzMwK4QJjZmaFcIExM7NC/H91Fdckah+pdQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# explore data visually\n",
    "# %matplotlib inline\n",
    "plt.xlabel(\"area(ft²)\")\n",
    "plt.ylabel(\"price(USD)\")\n",
    "plt.title(\"House Prices\")\n",
    "plt.scatter(df.area, df.price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 316404.10958904,  452191.78082192, 1402841.26712329])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# initializing the model\n",
    "model = LinearRegression()\n",
    "# pass data and train the mode, NOTE: first argument is expected to be a column vector, hence the different approaches to value retrieval, \n",
    "# the \"values\" method omits the header of the dataframe\n",
    "model.fit(df[[\"area\"]].values, df.price)\n",
    "# use model to predict price (y) for a list of arguments (area (X))\n",
    "X = np.array([[1000], [2000], [9001]])\n",
    "model.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = f(x)\n",
      "y = m * x + b \n",
      "y = 135.78767123287673 * x + 180616.43835616432\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c6094e8f10>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xp+C4gAOAm+q4zxpA+4gYFxEBjAT2zYf3ASqHlIyoUj4yknFAx3wfM2uOuneH886rNsF8/HEaB7DTTlBRARtvnOYUu+ii1GVjpVPMGsw6wEzgWkkTJV0taaWC49sDH0TEW4XX5HMfl7R9LlsLmFpwztRcBtAlIt7P29OBLgXXTKnhmm9IGiypXFL5zJkzl+RnNLMSuuuuNPT4yith2WXh//4v9b9stVWpIzMoboJpC/QBhkbE5sBnfNuEBXAwi9Ze3gfWzueeBNwoqX19PyzXbmJxAoyIKyOiLCLKOnfuvDiXmlkJffABHHgg7LtvGsncr18aXHbOObDccqWOzioVM8FMBaZGRF6uh1GkhIOktsBPgVsqT46ILyNiVt6eALwNbABMA7oW3LdrLgP4oLLpK7/np7GYBnSr4Roza6Yi0nOWPXumIccrrZQWAXvqqdQ0Zk1L0RJMREwHpkjaMBf1B17N27sAr0fEN01fkjpLapO31yV10E/OTWBzJfXL/TaHAHfly+4GBubtgVXKD8mjyfoBHxc0pZlZM/TOOzBgQBpy/NFHsPvuadXJ3/wG2rQpdXRWnWI/yX8ccIOk5YDJwGG5/CC+27m/A3C+pK+AhcBRETE7HzsGGA60A0bnF8AQ4FZJg4B3SYMGAO4H9gQqgHkFn2tmzcyCBfCPf8CZZ6aH+FddFS6+GH75Sz/T0tQpdV1YWVlZlJeXlzoMMyvwyitphcnxuaH9wANTk1iXLrVfZ41H0oSIKKvumJ/kN7Mm58sv06jkzTdPyWXNNdOIsZtvdnJpTjzZpZk1KePGpVrLq7nH9sgj03otXrq4+XENxsyahE8/heOPh222ScmlR4/0dP4VVzi5NFdOMGZWcg89BJtsApdemqYbO/10eOEF+NGPSh2ZLQ03kZlZycyaBSedBCNHpv3NN4dhw7x0cUvhGoyZNboIuOWWNM3LyJGwwgpp7ZZnn3VyaUlcgzGzRjV1KhxzTFq6GFIz2FVXeenilsg1GDNrFAsXwj//maZ0ueceaN8+7T/yiJNLS+UajJkV3ZtvwuDB8PjjaX/vveHyy710cUvnGoyZFc1XX6W+lU03Tcll9dVT38uddzq5tAauwZhZUUycmB6YnDgx7R9yCFx4Iay2WmnjssbjGoyZNajPP0/PsWyxRUouP/gBPPBAmmbfyaV1cQ3GzBrM44/DEUfAW2+lmY6PPx5+/3svXdxaOcGY2VL7+GM47bQ0KgzS8y3DhqWVJq31chOZmS2Vu+9OCeWf/4Rll4Vzz4Xnn3dyMddgzGwJffBBWk3y1lvT/lZbpVqLly62Sq7BmNliiUjTu/TqlZLLiiumFSafftrJxRZV7wQjqZOkjSWtK6le10nqKGmUpNclvSZpa0nnSZomaVJ+7Vlw/hmSKiS9IWn3gvIBuaxC0ukF5etIGp/Lb8lLMyNp+bxfkY93r+/PaWY1e+cdGDAABg6E2bNh113h5ZdTZ36bNqWOzpqaWhOFpA6SzpT0EjAO+CdwK/CupH9J2qmO+18CPBARGwGbAa/l8osiond+3Z8/qxdwELAxMAC4XFIbSW2Ay4A9gF7AwflcgD/ne60PfAQMyuWDgI9y+UX5PDNbQgsWpKWKN9kkTa3fqRMMHw4PPgjrrFPq6KypqqsmMgqYAmwfERtGxHYRURYR3YAhwD6SBlV3oaQOwA7AMICImB8Rc2r5rH2AmyPiy4j4D1ABbJlfFRExOSLmAzfnzxWwc44RYASwb8G9RhT8DP3z+Wa2mF55BbbbDk44AT77DA44AF57LdVi/Ftltam1kz8idq3l2ARgQi2XrwPMBK6VtFk+9/h87NeSDgHKgZMj4iNgLVItqdLUXAYpyRWWbwWsBsyJiK+rOX+tymsi4mtJH+fzPywMUNJgYDDA2muvXcuPYtb6zJ8Pf/oT/OEPacqXNdeEoUPTPGJm9VFnX4qktpJ+IunU/NpLUn1Gn7UF+gBDI2Jz4DPgdGAosB7QG3gf+NsSR7+UIuLKXCMr69y5c6nCMGtyxo+HPn3gvPNSchk8OC1j7ORii6OuPpi1gFeAk4E1STWDU4FXJK1Zx72nAlMjYnzeHwX0iYgPImJBRCwEriI1gQFMA7oVXN81l9VUPgvoWJDsKssXuVc+3iGfb2a1+OwzOPFE2Hrr1DS2/vrw2GPpGZcOHUodnTU3ddVg/kCqgewYESdGxAkR8SNSp/ufarswIqYDUyRtmIv6A69KWqPgtP2Al/P23cBBeQTYOkAP4FngOaBHHjG2HGkgwN0REcCjwP75+oHAXQX3Gpi39wceyeebWQ0eeih14l98MSyzTHoy/8UX04JgZkuirqaufhFxaNXCiLhU0hv1uP9xwA05MUwGDgMuldQbCOAd4Mh8z1ck3Qq8CnwNHBsRCwAk/Rp4EGgDXBMRr+T7nwbcLOn3wETygIL8fp2kCmA2KSmZWTVmz4aTTkqTUQL07p0emOzTp6RhWQug2v6wlzQx958s1rHmqKysLMrLy0sdhlmjiYBRo+DXv4YZM2D55VOfy8knpylfzOpD0oSIKKvuWF01mA6SflrdPYH2Sx2ZmZXEtGlw7LFwV25U3mEHuOoq2GCD0sZlLUtdCeZx4Cc1HHuigWMxsyJbuBCuvhpOPRXmzoX27eEvf0lT7C/jiaOsgdX1HMxhjRWImRXXW2+lRPL442n/Jz+Byy+Hrl1LG5e1XHUNU/6JpB8U7J8j6QVJd+eRXmbWxH39daqlbLppSi6dO8PNN6fmMScXK6b6DFOeCSBpL+CXwOGkYcBXFDc0M1takyalafRPOw2++AIOOSRN83LggZ7mxYqvrgQTETEvb/8UGBYREyLiasCPvps1UZ9/DmecAWVlafGvtdeGBx5IQ5FXW63U0VlrUVeCkaSV8/T8/YGxBcdWKF5YZraknngCNtsMhgxJnfq/+U16Kn/33eu+1qwh1TWK7GJgEjAXeC0iygEkbU6aR8zMmoi5c1NT2BW58bpXrzRibOutSxuXtV51jSK7RtKDwOrACwWHppOeyjezJuCee+Doo9PzLcsuC2eemZrIll++1JFZa1ZrgpFUOFlEb0kBfBgRU2q6xswaz4wZqQnsllvS/pZbpmleNtmktHGZQd1NZNVNpb9qnlvs4IiY1PAhmVldIuD669MiYLNnw4orpnVbjjvOSxdb01FXE1m1SyJLKgMuJa1YaWaN6N134cgj03LFALvumqbT99LF1tQs0eQQubN/5QaOxcxqsWABXHopbLxxSi6dOsHw4WnbycWaovqsTPkdkrqQpts3s0bw6qswaBCMy4uK/+xn8Pe/Q5cupY3LrDZ1dfL/ne8mklWBbYDjixWUmSXz56fnWX7/+7R08ZprpvnD9tmn1JGZ1a2uGkzVBVKCtPTwSRExozghmRnA+PHwq1/By3nN18GD4c9/ho4dSxqWWb3V1ck/YmluLqkjcDWwCSk5HU6acuYnwHzgbeCwiJgjqTvwGlC5Uua4iDgq36cvMBxoB9wPHB8RIWlV4BagO2l1zAMi4iNJAi4B9gTmAYdGxPNL87OYNZbPPoOzz4ZLLkmjxdZfP63VsuOOpY7MbPHUNZvyPXlG5e+sbydpXUnnSzq8lltcAjwQERsBm5ESyBhgk4jYFHgTOKPg/Lcjond+HVVQPhQ4AuiRXwNy+enA2IjoQZrG5vRcvkfBuYPz9WZN3pgx6RmWiy9O67P89rfw4otOLtY81TWK7Ahge+B1Sc9Jul/SI5ImA/8EJkTENdVdKKkDaRjzMICImB8RcyLioYj4Op82Dqh1wnBJawDtI2JcpPWdRwL75sP7AJW1rBFVykdGMg7omO9j1iTNng2HHQa77QbvvAO9e8Ozz6YmsXbtSh2d2ZKpq4lsOvBb4Le5CWsN4HPgzYJZlmuyDmmq/2slbQZMIDVtfVZwzuGkJq5vrpE0kTT32dkR8SSwFjC14JypuQygS0RUzok2HagcU7MWMKWaazx/mjUpETBqVHpA8oMP0tQu554Lp5ySpnwxa84W5zmYAFbKT++HpFXqOL8t0AcYGhGbA5/xbRMWks4CvgZuyEXvA2vnc08CbpTUvt7BpdrNYg2dljRYUrmk8pkzZy7OpWZL7b33YL/94IADUnLZfnt44YU0h5iTi7UE9Uowko4ARpGaxSA1a91Zx2VTgakRMT7vjyIlHCQdCuwF/CInBiLiy4iYlbcnkAYAbABMY9FmtK65DOCDyqav/F45sm0a0K2Ga74REVdGRFlElHXu7OVtrHEsXAhXXgk9e6ZVJVdZBYYOhccegw03LHV0Zg2nvjWYY4FtSU1XRMRbpBmWa5Sb16ZIqvyV6Q+8KmkAqdlt78JmNkmdJbXJ2+uSOugn5yawuZL65dFhhwB35cvuBgbm7YFVyg9R0g/4uKApzaxkKiqgf/801cvcubDXXukhyqOOSp36Zi1JfZ/k/zIi5iuvsSqpLfVrjjoOuCFPjjmZNMX/c8DywJh8v8rhyDsA50v6ClgIHBURs/N9juHbYcqj8wtgCHCrpEHAu8ABufx+0hDlCtIwZS8tYCX19ddw4YWpf+WLL6Bz5zTti5cutpZMuYWq9pOkvwBzSLWH40j/4L8aEWcVNbpGVFZWFuXlVZ8rNVt6kyalaV6ez09i/e//wkUXeeliaxkkTYiIsuqO1bdSfjppRNhLwJGkGsLZDROeWcv0xRdp4a+yspRc1l4bRo+GkSOdXKx1qG8TWTvgmoi4CiD3lbQjNT+ZWRVPPpmmeXnzzdQEdtxxab2WVeoae2nWgtS3BjOWlFAqtQMebvhwzJq3uXPT0sU77JCSS8+e8PTTqb/FycVam/ommBUi4tPKnby9YnFCMmue7r03rdVyxRXQti2ccw5MnAhbb13qyMxKo75NZJ9J6lM5YWSefPLz4oVl1nzMmAHHHw8335z2t9wSrr4afvjD0sZlVmr1TTAnAP+S9B4g4PvAgcUKyqw5iIDrr4cTT4RZs2DFFdO6Lb/5DbRpU+rozEqvXgkmIp6TtBFQ+dDkGxHxVfHCMmva3n03PRz5wANpf5dd0tP5XrrY7Ft1rWi5c0Q8IumnVQ5tIImIuL2IsZk1OQsWpBUlzzgjrdvSsWN6gPLQQ/3ApFlVddVgfgQ8QlogrKoAnGCs1Xj11TT0+Jln0v7++8Pf/w7f/z4wYgTssQesvnrqlBk9GgYOrPV+Zi1dXdP1nytpGWB0RNzaSDGZNSnz58OQIek5lvnzYY01Ui1m333zCe+9lyYXW3HFtJDLpEkwbx7suiusuWbpAjcrsTqHKUfEQtLklGatzrPPQt++aQ6x+fPhiCNSTeab5AIpiUycCCuvDI8+mt4nTnRysVavvs/BPCzpFEndJK1a+SpqZGYl9NlncNJJ6RmWl1+G9daDRx5JHfkdO1ZzQc+eMHx42h4+PO2btXL1HaZ8IKnP5Zgq5es2bDhmpffwwzB4MPznP2kK/VNPhfPOSy1gtaqcb9/z7psB9U8wvUjJZTtSonkSuKJYQZmVwkcfwcknw7XXpv3NNoNhw1ITWb10757a0rp3L1KEZs1LfRPMCNJiY5fm/Z/nsgNqvMKsmYiA226DX/86LV28/PJpmpdTT13MpYu7d09VHTMD6p9gNomIXgX7j0p6tRgBmTWm996DY4+FO+9M+9ttl6Z58dLFZkuvvo3Fz+elhwGQtBXg1bms2YqAq66CXr1ScllllTT0+PHHnVzMGkp9E0xf4N+S3pH0DvAMsIWklyS9WNNFkjpKGiXpdUmvSdo6j0AbI+mt/N4pnytJl0qqkPSipD4F9xmYz39L0sCC8r45hop8rXJ5tZ9hBlBRAf37p478jz+GH/8YXnklTbPv/nmzhlPfX6cBwDqkJ/t/lLcHAHtR/VP+lS4BHoiIjYDNgNdIq2OOjYgepHVmTs/n7gH0yK/BwFBIyQI4F9gK2BI4tyBhDAWOKLhuQC6v6TOsFfv6a7jggjTL8aOPwve+BzfeCPfcA926lTo6s5anvpNdvru4N5bUAdgBODTfYz4wX9I+wI75tBHAY8BpwD7AyIgIYFyu/ayRzx0TEbPzfccAAyQ9BrSPiHG5fCSwLzA636u6z7BWatKkNM3LhAlp/5e/hIsuSknGzIqjmA0C6wAzgWslTZR0taSVgC4R8X4+ZzrQJW+vBUwpuH5qLqutfGo15dTyGYuQNFhSuaTymTNnLsnPaE3cF1/AmWdCWVlKLt26wf33w3XXObmYFVsxE0xboA8wNCI2Bz6jSlNVrq1EEWOo9TMi4sqIKIuIss6dOxczDCuBJ59Mz7L86U+wcGEahvzKK2lOSjMrvmImmKnA1IgYn/dHkRLOB7npi/w+Ix+fBhS2hHfNZbWVd62mnFo+w1qBuXPhmGNghx3gzTdho43gqafSzMerrFLq6Mxaj6IlmIiYDkyRVDnosz/wKnA3UDkSbCBwV96+GzgkjybrB3ycm7keBHaT1Cl37u8GPJiPzZXUL48eO6TKvar7DGvh7r0XNt4Yhg6Ftm3h//2/1P+yzTaljsys9anvg5ZL6jjgBknLAZOBw0hJ7VZJg4B3+XY2gPuBPYEKYF4+l4iYLel3wHP5vPMrO/xJ09cMB9qROvdH5/IhNXyGtVAzZsDxx8PNN6f9LbZID0xuumlp4zJrzZS6KKysrCzKy/3saHMTATfcACecALNmQbt28Pvfp2TTpk2pozNr+SRNiIiy6o4VuwZjVjTvvpsejhyd6639+6fp9Nf1HN9mTYKfW7ZmZ+HC1GG/8cYpuXTsCNdcA2PGOLmYNSWuwViz8uqr6YHJZ55J+//zPynZrLFGaeMys+9yDcaahfnz4Xe/g803T8nl+9+H22+HUaOcXMyaKtdgrMl79tlUa3nppbQ/aFCaU6yTpzA1a9Jcg7Em67PP0gqTW2+dksu668LYsWn4sZOLWdPnBGNN0sMPp1mPL7ww7Z9ySkoyO+9c2rjMrP7cRGZNykcfpVrLtdem/U03hWHD0mSVZta8uAZjTcZtt0HPnim5LLdcemCyvNzJxay5cg3GSu6999JMx3fckfa33Tb1s2y0UWnjMrOl4xqMlUxESiS9eqXksvLKcNll8MQTTi5mLYFrMFYSFRUweHBauhhgzz3TDMhrr13auMys4bgGY43q66/hr39NnfePPppWlbzhhjTNvpOLWcviGow1mhdeSA9JTpiQ9n/xC7joIvBiomYtk2swVnRffAFnnZVGg02YAN26wX33wfXXO7mYtWSuwVhRPfVUmubljTdAgmOPhT/9yUsXm7UGTjBWFHPnwhlnwOWXp/2NNkojxrbdtrRxmVnjKWoTmaR3JL0kaZKk8lx2S96flI9PyuXdJX1ecOyKgvv0zfepkHSpJOXyVSWNkfRWfu+Uy5XPq5D0oqQ+xfw5bVH33ZfWarn8cmjbNjWPTZzo5GLW2jRGDWaniPiwciciDqzclvQ34OOCc9+OiN7V3GMocAQwHrgfGACMBk4HxkbEEEmn5/3TgD2AHvm1Vb5+qwb8mawaM2empYpvuintl5WlaV423bS0cZlZaZSskz/XQg4AbqrjvDWA9hExLiICGAnsmw/vA4zI2yOqlI+MZBzQMd/HiiAiDTXu2TMll3bt0lDkZ55xcjFrzYqdYAJ4SNIESYOrHNse+CAi3iooW0fSREmPS9o+l60FTC04Z2ouA+gSEe/n7elAl4JrptRwzTckDZZULql85syZi/3DGfz3v/DjH8MvfwmzZqXZjl96KU1Y2dY9fGatWrETzHYR0YfUZHWspB0Kjh3MorWX94G1I2Jz4CTgRknt6/tBuXYTixNcRFwZEWURUdbZ42UXy8KF8I9/pL6W0aOhQ4fUif/ww7DeeqWOzsyagqL+jRkR0/L7DEl3AFsCT0hqC/wU6Ftw7pfAl3l7gqS3gQ2AaUDXgtt2zWUAH0haIyLez01gM3L5NKBbDdfYUnrttTT0+N//Tvs//WlKNl662MwKFa0GI2klSatUbgO7AS/nw7sAr0fE1ILzO0tqk7fXJXXQT85NYHMl9cv9NocAd+XL7gYG5u2BVcoPyaPJ+gEfFzSl2RKaPz9Nod+7d0ou3/9+mmL/ttucXMzsu4pZg+kC3JFHFLcFboyIB/Kxg/hu5/4OwPmSvgIWAkdFxOx87BhgONCONHpsdC4fAtwqaRDwLmnQAKSRZnsCFcA84LAG/claoeeeS9O8vPRS2h80CC64wEsXm1nNlLourKysLMrLy0sdRpPz2Wdwzjlw8cWp32XddeHKK6F//1JHZmZNgaQJEVHtsoCei8xqNHYs/PCHcOGFaf/kk1MNxsnFzOrDA0ntOz76CE45Ba65Ju1vumkaIbbFFqWNy8yaF9dgbBG33ZZWmLzmGlhuudSpX17u5GJmi88JxgB4/334n/+B/feH6dPTvGGTJqV5xJZdtgQBjRgBM/Ko8xkz0r6ZNStuImvlIlJt5ZRTYM4cWHllGDIEjj4alinVnx/vvQdHHgkrrpjGRE+aBPPmwa67wpprligoM1tcrsG0Ym+/Dbvskh6anDMH9twTXnklrdlSsuQCKYlMnJiy3aOPpveJE51czJoZJ5hW6Ouv02SUP/whPPIIrLZamqzy3nth7bVLHV3WsycMH562hw9P+2bWrLiJrJV58cX0kGTlIz8//3l6xqVJTsVWWY0qaXXKzJaUf3NbiS++gLPPhr59U3Lp1i3VWG64oYkmF4Du3eHcc9O7mTU7rsG0Ak89BUccAa+/nvaPPRb+9CdYZZXSxlWn7t3hvPNKHYWZLSEnmBbsk0/gjDPgssvS/oYbpgcmt9uutHGZWevgJrIW6v7701otl12WFv4666w02tfJxcwai2swLczMmXDCCXDjjWm/rCzVWjbbrKRhmVkr5BpMCxGROux79UrJpV27NBT5mWecXMysNFyDaQGmTIGjjkrNYgA77QRXXeWli82stFyDacYWLkx9LL16peTSoUNqDhs71snFzErPNZhm6vXX0xQvTz+d9n/6U/jHP7x0sZk1HUWtwUh6R9JLkiZJKs9l50malssmSdqz4PwzJFVIekPS7gXlA3JZhaTTC8rXkTQ+l98iablcvnzer8jHuxfz52xMX30Ff/hD6ld5+mn4/vdh1Kg0zb6Ti5k1JY3RRLZTRPSusqTmRbmsd0TcDyCpF3AQsDEwALhcUhtJbYDLgD2AXsDB+VyAP+d7rQ98BAzK5YOAj3L5Rfm8htfIU8qXl6dRYWefDfPnw+GHw6uvpmn2zcyamqbUB7MPcHNEfBkR/wEqgC3zqyIiJkfEfOBmYB9JAnYGRuXrRwD7Ftyr8l/7UUD/fH7DqZxSfqONYOed0/uRR6byBjZvXppOf6ut0lxi664LDz8Mw4ZBp04N/nFmZg2i2AkmgIckTZA0uKD815JelHSNpMp/ItcCphScMzWX1VS+GjAnIr6uUr7IvfLxj/P5i5A0WFK5pPKZM2cu3k/WSFPKP/JImvX4b39L+yedlJJM//4N+jFmZg2u2Almu4joQ2reOlbSDsBQYD2gN/A+8Lcix1CjiLgyIsoioqzzksz4WMQp5efMSZ34/fvD5MkpyYwblxLNSis12MeYmRVNURNMREzL7zOAO4AtI+KDiFgQEQuBq0hNYADTgG4Fl3fNZTWVzwI6SmpbpXyRe+XjHfL5Da8IU8rffnvKVcOGwXLLwe9+l/pfttiiwT7CzKzoipZgJK0kaZXKbWA34GVJhWOd9gNeztt3AwflEWDrAD2AZ4HngB55xNhypIEAd0dEAI8C++frBwJ3FdxrYN7eH3gkn9/wGnBK+enTYf/9U6f99OmwzTZp/rCzz06JxsysOSnmczBdgDty33pb4MaIeEDSdZJ6k/pn3gGOBIiIVyTdCrwKfA0cGxELACT9GngQaANcExGv5M84DbhZ0u+BicCwXD4MuE5SBTCblJSKowGmlI+Aa6+Fk09OTWMrr5ym0z/mGK+1ZWbNl4r1h31zU1ZWFuWVyzw2osmTYfDg9PQ9wB57wBVXNKGli83MaiFpQpXHUL7hv49LZMECuPBC2GSTlFxWWw2uvx7uu8/JxcxaBk8VUwIvvphGiD33XNo/+GC45JImvHSxmdkScA2mEX35Jfy//wd9+6bk0rUr3Htvml7fycXMWhrXYBrJ00+nWsvrr6f9Y45JHfnt25c2LjOzYnGCKbJPPoEzz0zT6kfAhhumKfW9dLGZtXRuIiui0aNh443TNPpt2qREM2mSk4uZtQ6uwRTBhx/CCSekJYwh9bkMG+ali82sdXENpgFFwE03pWlebrgB2rWDCy5Ic4g5uZhZa+MaTAOZMgWOPjo9xwKw005w1VVeutjMWi/XYJbSwoVw+eWpr+W++6BDh5RYxo51cjGz1s01mKWwYAHsumtaDgZgv/1Sh34DLwljZtYsuQazFNq0gX79oEsXGDUqTbPv5GJmlniyy2xJJ7v84gv4/HMvXWxmrVNtk126iWwprbBCepmZ2aLcRGZmZkXhBGNmZkXhBGNmZkVR1AQj6R1JL0maJKk8l10g6XVJL0q6Q1LHXN5d0uf53EmSrii4T998nwpJlyqvwyxpVUljJL2V3zvlcuXzKvLn9Cnmz2lmZt/VGDWYnSKid8EogzHAJhGxKfAmcEbBuW/nc3tHxFEF5UOBI4Ae+TUgl58OjI2IHsDYvA+wR8G5g/P1ZmbWiBq9iSwiHoqIr/PuOKBrbedLWgNoHxHjIo2pHgnsmw/vA4zI2yOqlI+MZBzQMd/HzMwaSbETTAAPSZogaXA1xw8HRhfsryNpoqTHJW2fy9YCphacMzWXAXSJiPfz9nSgS8E1U2q45huSBksql1Q+c+bMxfrBzMysdsV+Dma7iJgmaXVgjKTXI+IJAElnAV8DeVJ73gfWjohZkvoCd0rauL4fFBEhabGeGo2IK4ErczwzJb27ONcX+B7w4RJeWwrNKd7mFCs0r3ibU6zQvOJtTrHC0sX7g5oOFDXBRMS0/D5D0h3AlsATkg4F9gL652YvIuJL4Mu8PUHS28AGwDQWbUbrmssAPpC0RkS8n5vAZuTyaUC3Gq6pKdbOS/pzSiqv6UnWpqg5xducYoXmFW9zihWaV7zNKVYoXrxFayKTtJKkVSq3gd2AlyUNAH4L7B0R8wrO7yypTd5el9RBPzk3gc2V1C+PHjsEuCtfdjcwMG8PrFJ+SB5N1g/4uKApzczMGkExazBdgDvyiOK2wI0R8YCkCmB5UpMZwLg8YmwH4HxJXwELgaMiYna+1zHAcKAdqc+mst9mCHCrpEHAu8ABufx+YE+gApgHHFbEn9PMzKpRtAQTEZOB76zjGBHr13D+bcBtNRwrBzappnwW0L+a8gCOXcyQl8aVjfhZDaE5xducYoXmFW9zihWaV7zNKVYoUryeTdnMzIrCU8WYmVlROMGYmVlROMFUQ1I3SY9KelXSK5KOLzh2XJ5L7RVJfykoPyPPffaGpN0LygfksgpJp1f9rGLGK6m3pHGVc8FJ2jKX1zhXm6SBeW63tyQNrOkzlyLWFSQ9K+mFHOv/5fJ1JI3PMd0iablcvnzer8jHuxfcq9rvvJHivSF/7suSrpG0bC5vct9twfFLJX1asN9Uv1tJ+oOkNyW9Juk3BeVN6ruV1F/S8/l37ClJ6+fykn63BZ/VRunh9XvzfuP+nkWEX1VewBpAn7y9CmnOtF7ATsDDwPL52Or5vRfwAml03DrA20Cb/HobWBdYLp/TqxHjfQjYI5fvCTxWsD0aENAPGJ/LVwUm5/dOebtTA8cqYOW8vSwwPsdwK3BQLr8CODpvHwNckbcPAm6p7TsvwndbU7x75mMCbiqIt8l9t3m/DLgO+LTg/Kb63R5GmhJqmSq/Z03uu82/az0Lvs/hTeG7LYj7JOBG4N6836i/Z67BVCMi3o+I5/P2J8BrpKlmjgaGRHoolIiofLBzH+DmiPgyIv5DGh69ZX5VRMTkiJgP3JzPbax4A2ifT+sAvFcQb3Vzte0OjImI2RHxEWli0gE0oPyZlX9FL5tfAewMjMrlVeeVq5xvbhTQX5Ko+TtvUDXFGxH352MBPMu3DwM3ue9W6fmyC0jPnxVqkt8t6ffs/IhYmM8r/D1rUt8ttf+Oley7BZDUFfgxcHXeF438e+YEU4dcVdyc9BfLBsD2uQr5uKQt8mk1zX1WrznRihjvCcAFkqYAf+XbmatLGm+utk8izbwwhvRX0Zz4dhLUws/9JqZ8/GNgtcaKtbp4I2J8wbFlgf8FHqgab5W4SvLd5lh/Ddwd333YuKl+t+sBByo1646W1KNqvFXiKuV3+yvgfklTSf8fDKkaa6m+W+Bi0h8VC/P+ajTy75kTTC0krUx6NueEiJhLem5oVVLV+FTSQ54qYYiLqCbeo4ETI6IbcCIwrJTxVYqIBRHRm/RX/5bARqWNqHZV45VU+EzW5cATEfFkSYKroppYdwB+Bvy9pIHVoIbvdnngi0hTl1wFXFPCEL9RQ6wnAntGRFfgWuDCEob4DUl7ATMiYkIp43CCqUH+y/Q24IaIuD0XTwVuz9XlZ0l/GXyPmuc+W+w50Ro43oFA5fa/+LZqW/J4ASJiDvAosDWpuaPywd/Cz/0mpny8AzCrsWOtEu+AHM+5QGdSO3elpvbd7gSsD1RIegdYUWk2jUVibWLf7VS+/f/2DmDTqvFWiatU3+0ewGYFNdpbgG2qxlqi73ZbYO/83/xmUtPYJTT271l9O2ta04vUoTcSuLhK+VGktmFIzWVT8rkbs2hH2GRSB3/bvL0O33byb9yI8b4G7Ji3+wMT8vaPWbSz9NlcvirwH1JHaae8vWoDx9oZ6Ji32wFPkiY+/ReLdj4ek7ePZdHOx1vzdrXfeRG+25ri/RXwb6BdlfOb3Hdb5ZzCTv6m+t0OAQ7P5TsCzzXV75Y0A/EGuXwQcFtT+G6rxL4j33byN+rvWdF+qOb8ArYjdd69CEzKrz1JSeJ64GXgeWDngmvOIvUlvEEeuZXL9ySNNHkbOKuR490OmJD/BxkP9M3nC7gsx/QSUFZwr8NJHXkVwGFFiHVTYGKO9WXgnFy+LqmzvCL/ElSO1Fsh71fk4+vW9Z03Urxf58+u/L4ry5vcd1vlnMIE01S/247Affn7e4ZUS2iS3y2wX47lBeCxyu+w1N9tldh35NsE06i/Z54qxszMisJ9MGZmVhROMGZmVhROMGZmVhROMGZmVhROMGZmVhROMGbNiKRRktbN2z/Lsw0/KmlHSdsUnPd3SddJ+mPe/7Wkw0sVt7VOTjBmJZAnoFzcazYmPeQ2ORcNAo6IiJ1Izzp8k2Ai4jjgFNJzD5CmWzluaWI2W1xOMGZFIOlOSRPy2iGDc9mnkv4m6QVga0m/zGuMTJL0z8qkI2lonuix6pouvwDuyuecQ3qQdpikf5FmmTgx32t7SWuTnog/BiAi5gHvKK8JZNYYnGDMiuPwiOhLWoflN5JWA1YirWGyGWmepwOBbSNNoLiAlEAgzfhQRnp6/EeSKufi2pY0MwMRcT5QDvwiIn5GmvbjonyvZ/JrOdJT2JXKge2L8+OafVfbuk8xsyXwG0n75e1uQA9SErktl/UH+gLP5Qm525GmgQc4INd62pIWk+tFmqJkDWBmXR8cabr16qZUn0ETn7naWhYnGLMGJmlHYBdg64iYJ+kx0lxPX0TEgsrTgBERcUaVa9ch9Z1sEREfSRqerwX4vGB7SayQ72HWKNxEZtbwOgAf5eSyEWnm36rGAvtLWh1A0qqSfkBaHfEz4GNJXUhTwld6jTT1fnU+IS2XXZsNSBM1mjUKJxizhvcA0FbSa6SO9nFVT4iIV4GzgYckvUha2XONiHiBNGvv66S11J8uuOw+0mix6twD7FfZyV/DOdvmzzFrFJ5N2ayZkNSOtNDVtgVNbfW9dnPgpIj436IEZ1YNJxizZkTS7sBrEfHfxbxuV+CtiHinKIGZVcMJxszMisJ9MGZmVhROMGZmVhROMGZmVhROMGZmVhROMGZmVhT/HxWV4wjVnIY9AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# display function graph (y = m*x + b) with the minimal distance to all samples, \n",
    "print(\"y = f(x)\")\n",
    "print(\"y = m * x + b\", \"\\ny =\", model.coef_[0], \"* x +\", model.intercept_)\n",
    "plt.xlabel(\"area(ft²)\")\n",
    "plt.ylabel(\"price(USD)\")\n",
    "plt.title(\"House Prices\")\n",
    "plt.scatter(df.area, df.price, color = \"red\", marker = \"1\")\n",
    "plt.plot(df.area, model.predict(df[[\"area\"]].values), color = \"blue\", linewidth = 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multivariable Linear Regression\n",
    "---\n",
    "---\n",
    "Predicting a continous value based on multiple input values\n",
    "- Utilises a function of this shape: $ y = m1*x1 + m2*x2 + m3*x3 + ... + b $\n",
    "    - `y = target value`\n",
    "    - `m = factors`\n",
    "    - `x = arguments` \n",
    "    - `b = interception with y-axis`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>area</th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>age</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2600</td>\n",
       "      <td>3.0</td>\n",
       "      <td>20</td>\n",
       "      <td>550000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3000</td>\n",
       "      <td>4.0</td>\n",
       "      <td>15</td>\n",
       "      <td>565000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3200</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18</td>\n",
       "      <td>610000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3600</td>\n",
       "      <td>3.0</td>\n",
       "      <td>30</td>\n",
       "      <td>596000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>8</td>\n",
       "      <td>760000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   area  bedrooms  age   price\n",
       "0  2600       3.0   20  550000\n",
       "1  3000       4.0   15  565000\n",
       "2  3200       NaN   18  610000\n",
       "3  3600       3.0   30  596000\n",
       "4  4000       5.0    8  760000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = os.path.join(\"data\", \"multivariate_regression_data.csv\")\n",
    "# loading the data\n",
    "df = pd.read_csv(path)\n",
    "# display the numeric data\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>area</th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>age</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2600</td>\n",
       "      <td>3.0</td>\n",
       "      <td>20</td>\n",
       "      <td>550000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3000</td>\n",
       "      <td>4.0</td>\n",
       "      <td>15</td>\n",
       "      <td>565000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3200</td>\n",
       "      <td>3.5</td>\n",
       "      <td>18</td>\n",
       "      <td>610000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3600</td>\n",
       "      <td>3.0</td>\n",
       "      <td>30</td>\n",
       "      <td>596000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>8</td>\n",
       "      <td>760000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   area  bedrooms  age   price\n",
       "0  2600       3.0   20  550000\n",
       "1  3000       4.0   15  565000\n",
       "2  3200       3.5   18  610000\n",
       "3  3600       3.0   30  596000\n",
       "4  4000       5.0    8  760000"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# handling NaN by averaging present values\n",
    "df.bedrooms = df.bedrooms.fillna(df.bedrooms.median())\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# initializing the model\n",
    "model = LinearRegression()\n",
    "# passing the independent variables (factors of m1, m2, m3) to the model and start training \n",
    "# price (dependent variable) = m1*area + m2*bedrooms + m3*age + b\n",
    "# b = interception with y-axis \n",
    "model.fit(df[[\"area\", \"bedrooms\", \"age\"]].values, df.price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[    198.56145032 -116060.587035    -14172.18646994] 652276.4087270447\n"
     ]
    }
   ],
   "source": [
    "# displaying m1, m2, m3 and interception with y-axis\n",
    "print(model.coef_, model.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "332891"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# use model to predict price (y) for an array of arguments\n",
    "area = 3000\n",
    "bedrooms = 3\n",
    "age = 40\n",
    "features = np.array([[area, bedrooms, age]])\n",
    "int(model.predict(features)[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic Regression\n",
    "---\n",
    "---\n",
    "Used for binary classification\n",
    "\n",
    "- Utilises the logit function (aka sigmoid function): $ y = \\frac{1}{1 + e^{-x}} $\n",
    "    - `y = target value`\n",
    "    - `e = Euler's number (2.71828...) -> base of natural logarithm`\n",
    "    - `x = arguments` <br><br>\n",
    "- Passes linear function into sigmoid function: $y = \\frac{1}{1 + e^{-(m*x + b)}} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>bought_insurance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>22</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>25</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>47</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>52</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>46</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age  bought_insurance\n",
       "0   22                 0\n",
       "1   25                 0\n",
       "2   47                 1\n",
       "3   52                 0\n",
       "4   46                 1"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = os.path.join(\"data\", \"logistic_regression_data.csv\")\n",
    "# loading the data\n",
    "df = pd.read_csv(path)\n",
    "# display some of the numeric data\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1c60b576130>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# explore data visually\n",
    "plt.xlabel(\"age(years)\")\n",
    "plt.ylabel(\"bought an insurance\")\n",
    "plt.title(\"Age/Insurance distribution\")\n",
    "plt.scatter(df.age, df.bought_insurance, marker=\"1\", color= \"red\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# splitting Data into Training and test sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(df[['age']], df.bought_insurance, train_size = 0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3333333333333333"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# initializing the model\n",
    "model = LogisticRegression()\n",
    "# pass data and train the model\n",
    "model.fit(X_train, y_train)\n",
    "# get prediction accuracy\n",
    "model.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Customer data yet unpredicted:\n",
      "    age\n",
      "3   52\n",
      "0   22\n",
      "6   55 \n",
      "\n",
      "Prediction: [1 0 1] \n",
      "\n",
      "Probability for given predictions:\n",
      " [[1.70320845e-03 9.98296792e-01]\n",
      " [9.59919944e-01 4.00800562e-02]\n",
      " [6.56135025e-04 9.99343865e-01]]\n"
     ]
    }
   ],
   "source": [
    "# shape = Customer-ID, age\n",
    "print(\"Customer data yet unpredicted:\\n\", X_test, \"\\n\")\n",
    "# predict values for unknown data\n",
    "print(\"Prediction:\", model.predict(X_test), \"\\n\")\n",
    "# display probability for predicted value\n",
    "print(\"Probability for given predictions:\\n\", model.predict_proba(X_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\pompom\\AppData\\Local\\Programs\\Python\\Python39\\lib\\site-packages\\sklearn\\base.py:445: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c6094c1bb0>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display the models internal sigmoid function together with data points\n",
    "plt.yticks([0.0, 0.5, 1.0])  \n",
    "plt.axhline(y=0.5, color='grey', linestyle='--', lw = 0.4)\n",
    "plt.xlabel(\"age(years)\")\n",
    "plt.ylabel(\"bought an insurance\")\n",
    "plt.title(\"Age/Insurance distribution\")\n",
    "plt.scatter(df.age, df.bought_insurance, marker=\"1\", color= \"red\")\n",
    "plt.plot(\n",
    "    # x values\n",
    "    np.arange(0, 100, 1), \n",
    "    # using the models prediction on every age from 0 to 100 to plot the internal sigmoid function\n",
    "    [y[1] for y in model.predict_proba(np.arange(0,100,1).reshape(100,1))]\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic Regression\n",
    "---\n",
    "---\n",
    "Used for multiclass classification (handwritten digits in this case)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['DESCR', 'data', 'feature_names', 'frame', 'images', 'target', 'target_names']\n",
      "<class 'sklearn.utils.Bunch'>\n",
      "[ 0.  0.  5. 13.  9.  1.  0.  0.  0.  0. 13. 15. 10. 15.  5.  0.  0.  3.\n",
      " 15.  2.  0. 11.  8.  0.  0.  4. 12.  0.  0.  8.  8.  0.  0.  5.  8.  0.\n",
      "  0.  9.  8.  0.  0.  4. 11.  0.  1. 12.  7.  0.  0.  2. 14.  5. 10. 12.\n",
      "  0.  0.  0.  0.  6. 13. 10.  0.  0.  0.]\n"
     ]
    }
   ],
   "source": [
    "# load data (1797 samples, representing handwritten digits of 8x8 pixel as arrays of size 64)\n",
    "digits = load_digits()\n",
    "# get some info about the data format \n",
    "print(dir(digits))\n",
    "print(type(digits))\n",
    "# print first array\n",
    "print(digits.data[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# display some digits\n",
    "plt.gray()\n",
    "for i in range(3):\n",
    "    plt.matshow(digits.images[i])\n",
    "# print corresponding labels\n",
    "digits.target[:3]    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# splitting data into Training and Test sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(digits.data, digits.target, train_size = 0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "347 / 360 samples correctly predicted\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\pompom\\AppData\\Local\\Programs\\Python\\Python39\\lib\\site-packages\\sklearn\\linear_model\\_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
      "\n",
      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
      "Please also refer to the documentation for alternative solver options:\n",
      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
      "  n_iter_i = _check_optimize_result(\n"
     ]
    }
   ],
   "source": [
    "# initializing the model, to fix warning about convergence increase number of iterations (default is max_iter = 100)\n",
    "model = LogisticRegression(max_iter=200)\n",
    "# pass data and train the model\n",
    "model.fit(X_train, y_train)\n",
    "# make a prediction on test set\n",
    "predictions = model.predict(X_test)\n",
    "print((predictions == y_test).sum(), \"/\", len(y_test), \"samples correctly predicted\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(69.0, 0.5, 'Truth')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# print confusion matrix\n",
    "cm = confusion_matrix(y_test, predictions)\n",
    "plt.figure(figsize = (10,7))\n",
    "sns.heatmap(cm, annot=True)\n",
    "plt.xlabel(\"Prediction\")\n",
    "plt.ylabel(\"Truth\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Decision Tree\n",
    "---\n",
    "---\n",
    "Used for classification\n",
    "\n",
    "- Gains information by splitting data into mutual exclusive subsets based on feature (low entropy within a subset = high information gain)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PassengerId</th>\n",
       "      <th>Survived</th>\n",
       "      <th>Pclass</th>\n",
       "      <th>Name</th>\n",
       "      <th>Sex</th>\n",
       "      <th>Age</th>\n",
       "      <th>SibSp</th>\n",
       "      <th>Parch</th>\n",
       "      <th>Ticket</th>\n",
       "      <th>Fare</th>\n",
       "      <th>Cabin</th>\n",
       "      <th>Embarked</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>Braund, Mr. Owen Harris</td>\n",
       "      <td>male</td>\n",
       "      <td>22.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>A/5 21171</td>\n",
       "      <td>7.2500</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Cumings, Mrs. John Bradley (Florence Briggs Th...</td>\n",
       "      <td>female</td>\n",
       "      <td>38.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>PC 17599</td>\n",
       "      <td>71.2833</td>\n",
       "      <td>C85</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>Heikkinen, Miss. Laina</td>\n",
       "      <td>female</td>\n",
       "      <td>26.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>STON/O2. 3101282</td>\n",
       "      <td>7.9250</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Futrelle, Mrs. Jacques Heath (Lily May Peel)</td>\n",
       "      <td>female</td>\n",
       "      <td>35.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>113803</td>\n",
       "      <td>53.1000</td>\n",
       "      <td>C123</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>Allen, Mr. William Henry</td>\n",
       "      <td>male</td>\n",
       "      <td>35.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>373450</td>\n",
       "      <td>8.0500</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   PassengerId  Survived  Pclass  \\\n",
       "0            1         0       3   \n",
       "1            2         1       1   \n",
       "2            3         1       3   \n",
       "3            4         1       1   \n",
       "4            5         0       3   \n",
       "\n",
       "                                                Name     Sex   Age  SibSp  \\\n",
       "0                            Braund, Mr. Owen Harris    male  22.0      1   \n",
       "1  Cumings, Mrs. John Bradley (Florence Briggs Th...  female  38.0      1   \n",
       "2                             Heikkinen, Miss. Laina  female  26.0      0   \n",
       "3       Futrelle, Mrs. Jacques Heath (Lily May Peel)  female  35.0      1   \n",
       "4                           Allen, Mr. William Henry    male  35.0      0   \n",
       "\n",
       "   Parch            Ticket     Fare Cabin Embarked  \n",
       "0      0         A/5 21171   7.2500   NaN        S  \n",
       "1      0          PC 17599  71.2833   C85        C  \n",
       "2      0  STON/O2. 3101282   7.9250   NaN        S  \n",
       "3      0            113803  53.1000  C123        S  \n",
       "4      0            373450   8.0500   NaN        S  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = os.path.join(\"data\", \"titanic.csv\")\n",
    "# loading the data\n",
    "df = pd.read_csv(path)\n",
    "# display some of the numeric data\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Survived</th>\n",
       "      <th>Pclass</th>\n",
       "      <th>Sex</th>\n",
       "      <th>Age</th>\n",
       "      <th>Fare</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>male</td>\n",
       "      <td>22.0</td>\n",
       "      <td>7.2500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>female</td>\n",
       "      <td>38.0</td>\n",
       "      <td>71.2833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>female</td>\n",
       "      <td>26.0</td>\n",
       "      <td>7.9250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>female</td>\n",
       "      <td>35.0</td>\n",
       "      <td>53.1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>male</td>\n",
       "      <td>35.0</td>\n",
       "      <td>8.0500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>male</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8.4583</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>male</td>\n",
       "      <td>54.0</td>\n",
       "      <td>51.8625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>male</td>\n",
       "      <td>2.0</td>\n",
       "      <td>21.0750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>female</td>\n",
       "      <td>27.0</td>\n",
       "      <td>11.1333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>female</td>\n",
       "      <td>14.0</td>\n",
       "      <td>30.0708</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Survived  Pclass     Sex   Age     Fare\n",
       "0         0       3    male  22.0   7.2500\n",
       "1         1       1  female  38.0  71.2833\n",
       "2         1       3  female  26.0   7.9250\n",
       "3         1       1  female  35.0  53.1000\n",
       "4         0       3    male  35.0   8.0500\n",
       "5         0       3    male   NaN   8.4583\n",
       "6         0       1    male  54.0  51.8625\n",
       "7         0       3    male   2.0  21.0750\n",
       "8         1       3  female  27.0  11.1333\n",
       "9         1       2  female  14.0  30.0708"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# discard unneeded data by creating a new dataframe\n",
    "input_data = df.drop([\n",
    "    \"PassengerId\", \n",
    "    \"Name\", \n",
    "    \"Ticket\", \n",
    "    \"SibSp\",\n",
    "    \"Parch\",\n",
    "    \"Cabin\",\n",
    "    \"Embarked\"\n",
    "    ], axis = \"columns\")\n",
    "input_data.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "177 entries in this dataframe contained NaN, now replaced with age average\n"
     ]
    }
   ],
   "source": [
    "# cleaning the data of NaN\n",
    "print(input_data[input_data[\"Age\"].isna()].shape[0], \"entries in this dataframe contained NaN, now replaced with age average\")\n",
    "input_data = input_data.fillna(input_data.Age.median())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# encode nominal features into numeric values; \n",
    "# NOTE: an alternative way would be to introduce dummy variables usind pd.get_dummies([\"Sex\"], axis = \"columns\") and replace the nominal values\n",
    "sex_encoder = LabelEncoder()\n",
    "input_data[\"Sex\"] = sex_encoder.fit_transform(input_data[\"Sex\"])\n",
    "# separating data and targets\n",
    "targets, features = np.split(input_data, [1], axis = 1)\n",
    "# converting targets from float into integer to avoid \"Unknown label type: 'continuous-multioutput'\" error\n",
    "targets = targets.astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# splitting data into Training and Test sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(features, targets, train_size = 0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.770949720670391"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# initializing the model\n",
    "model = tree.DecisionTreeClassifier()\n",
    "# pass data and train the model\n",
    "model.fit(X_train, y_train)\n",
    "# get prediction accuracy\n",
    "model.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Support Vector Machine (SVM)\n",
    "---\n",
    "---\n",
    "- can be used for classification & regression; highly effective in high vector spaces (samples with many features)<br><br>\n",
    "- data points close to a separating margin (line, (hyper-)plane) are called *support vectors*<br><br>\n",
    "- **NOTE**: \"The fit time scales at least quadratically with the number of samples and may be impractical beyond tens of thousands of samples.\" \n",
    "    - [src](https://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html) (accessed: 14.01.22)<br><br>\n",
    "---\n",
    "some terminology:\n",
    "- if data points are inseparable using a linear graph, new features can be introduced by transforming the existing data\n",
    "    - e.g. if `x`, `y` are given features, `z = x² + y²` is a new dimension that could be used to separate the data, the function used for such a transformation is references as **kernel**<br><br>\n",
    "- **gamma**: \"[...] controls the distance of influence of a single training point. Low values of gamma indicates a large similarity radius which results in more points being grouped together. For high values of gamma, the points need to be very close to each other in order to be considered in the same group (or class). Therefore, models with very large gamma values tend to overfit.\" [src](https://towardsdatascience.com/hyperparameter-tuning-for-support-vector-machines-c-and-gamma-parameters-6a5097416167) (accessed: 21.01.22)<br><br>\n",
    "- **Regularization (C)**: \"`C` parameter adds a penalty for each misclassified data point. If c is small, the penalty for misclassified points is low so a decision boundary with a large margin is chosen at the expense of a greater number of misclassifications. If `C` is large, SVM tries to minimize the number of misclassified examples due to high penalty which results in a decision boundary with a smaller margin.\" src: see above "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['DESCR', 'data', 'data_module', 'feature_names', 'filename', 'frame', 'target', 'target_names']\n",
      "['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']\n"
     ]
    }
   ],
   "source": [
    "# load data\n",
    "iris = load_iris()\n",
    "# get information about the data format \n",
    "print(dir(iris))\n",
    "print(iris.feature_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "      <th>target</th>\n",
       "      <th>name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)  \\\n",
       "0                5.1               3.5                1.4               0.2   \n",
       "1                4.9               3.0                1.4               0.2   \n",
       "2                4.7               3.2                1.3               0.2   \n",
       "3                4.6               3.1                1.5               0.2   \n",
       "4                5.0               3.6                1.4               0.2   \n",
       "\n",
       "   target    name  \n",
       "0       0  setosa  \n",
       "1       0  setosa  \n",
       "2       0  setosa  \n",
       "3       0  setosa  \n",
       "4       0  setosa  "
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# converting data set into pandas DataFrame\n",
    "df = pd.DataFrame(iris.data, columns=iris.feature_names)\n",
    "# appending DataFrame with target and -names as well\n",
    "df[\"target\"] = iris.target\n",
    "df[\"name\"] = df.target.apply(lambda x: iris.target_names[x])\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1c60b8dfac0>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\" explore data visually \"\"\"\n",
    "# split data accordingly to class\n",
    "df0 = df[df.target == 0]\n",
    "df1 = df[df.target == 1]\n",
    "df2 = df[df.target == 2]\n",
    "# display different classes using two of the four attributes\n",
    "plt.xlabel(\"sepal length (cm)\")\n",
    "plt.ylabel(\"sepal width (cm)\")\n",
    "plt.scatter(df0[\"sepal length (cm)\"], df0[\"sepal width (cm)\"], color=\"green\", marker=\"+\")\n",
    "plt.scatter(df1[\"sepal length (cm)\"], df1[\"sepal width (cm)\"], color=\"blue\", marker=\".\")\n",
    "plt.scatter(df2[\"sepal length (cm)\"], df2[\"sepal width (cm)\"], color=\"red\", marker=\"1\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1c60b93f310>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# display different classes using the two remaining attributes (other combinations are possible of course)\n",
    "plt.xlabel(\"petal length (cm)\")\n",
    "plt.ylabel(\"petal width (cm)\")\n",
    "plt.scatter(df0[\"petal length (cm)\"], df0[\"petal width (cm)\"], color=\"green\", marker=\"+\")\n",
    "plt.scatter(df1[\"petal length (cm)\"], df1[\"petal width (cm)\"], color=\"blue\", marker=\".\")\n",
    "plt.scatter(df2[\"petal length (cm)\"], df2[\"petal width (cm)\"], color=\"red\", marker=\"1\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# splitting data into Training and Test sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(iris.data, iris.target, test_size=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9666666666666667"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# initializing the model\n",
    "model = svm.SVC()\n",
    "# pass data and train the model\n",
    "model.fit(X_train, y_train)\n",
    "# get prediction accuracy\n",
    "model.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.975\n",
      "0.975\n",
      "0.975\n"
     ]
    }
   ],
   "source": [
    "# K-fold Cross Validation to manually explore different model configurations\n",
    "print(np.average(cross_val_score(svm.SVC(kernel = \"linear\", C = 10, gamma = \"auto\"), X_train, y_train, cv = 5)))\n",
    "print(np.average(cross_val_score(svm.SVC(kernel = \"rbf\", C = 10, gamma = \"auto\"), X_train, y_train, cv = 5)))\n",
    "print(np.average(cross_val_score(svm.SVC(kernel = \"linear\", C = 20, gamma = \"auto\"), X_train, y_train, cv = 5)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>param_C</th>\n",
       "      <th>param_kernel</th>\n",
       "      <th>mean_test_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>rbf</td>\n",
       "      <td>0.966667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>linear</td>\n",
       "      <td>0.980000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10</td>\n",
       "      <td>rbf</td>\n",
       "      <td>0.980000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>10</td>\n",
       "      <td>linear</td>\n",
       "      <td>0.973333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20</td>\n",
       "      <td>rbf</td>\n",
       "      <td>0.980000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>20</td>\n",
       "      <td>linear</td>\n",
       "      <td>0.966667</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  param_C param_kernel  mean_test_score\n",
       "0       1          rbf         0.966667\n",
       "1       1       linear         0.980000\n",
       "2      10          rbf         0.980000\n",
       "3      10       linear         0.973333\n",
       "4      20          rbf         0.980000\n",
       "5      20       linear         0.966667"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Exhaustive Hyperparameter Tuning using GridSearchCV\n",
    "clf = GridSearchCV(\n",
    "    # providing the model architecture\n",
    "    svm.SVC(),\n",
    "    # defining the parameter grid to test upon\n",
    "    {\n",
    "        \"C\" : [1, 10, 20],\n",
    "        \"kernel\" : [\"rbf\", \"linear\"]\n",
    "    },\n",
    "    # number of cross validations\n",
    "    cv = 5, \n",
    "    return_train_score = True\n",
    ")\n",
    "\n",
    "clf.fit(iris.data, iris.target)\n",
    "results = pd.DataFrame(clf.cv_results_)\n",
    "# discard most of the additional information obtained during this process\n",
    "results[[\"param_C\", \"param_kernel\", \"mean_test_score\"]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random Forest Classifier\n",
    "---\n",
    "---\n",
    "\n",
    "- Group of `n` decision trees, each with a different, random subset of given data<br><br>\n",
    "- For classification a majority vote approach is used (greatest number of trees rooting for a certain class will result in classification) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['DESCR', 'data', 'data_module', 'feature_names', 'filename', 'frame', 'target', 'target_names']\n",
      "(569, 30)\n"
     ]
    }
   ],
   "source": [
    "# load data\n",
    "breast_cancer_dataset = load_breast_cancer()\n",
    "# get information about the data format \n",
    "print(dir(breast_cancer_dataset))\n",
    "print(breast_cancer_dataset.data.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean radius</th>\n",
       "      <th>mean texture</th>\n",
       "      <th>mean perimeter</th>\n",
       "      <th>mean area</th>\n",
       "      <th>mean smoothness</th>\n",
       "      <th>mean compactness</th>\n",
       "      <th>mean concavity</th>\n",
       "      <th>mean concave points</th>\n",
       "      <th>mean symmetry</th>\n",
       "      <th>mean fractal dimension</th>\n",
       "      <th>...</th>\n",
       "      <th>worst radius</th>\n",
       "      <th>worst texture</th>\n",
       "      <th>worst perimeter</th>\n",
       "      <th>worst area</th>\n",
       "      <th>worst smoothness</th>\n",
       "      <th>worst compactness</th>\n",
       "      <th>worst concavity</th>\n",
       "      <th>worst concave points</th>\n",
       "      <th>worst symmetry</th>\n",
       "      <th>worst fractal dimension</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>17.99</td>\n",
       "      <td>10.38</td>\n",
       "      <td>122.80</td>\n",
       "      <td>1001.0</td>\n",
       "      <td>0.11840</td>\n",
       "      <td>0.27760</td>\n",
       "      <td>0.30010</td>\n",
       "      <td>0.14710</td>\n",
       "      <td>0.2419</td>\n",
       "      <td>0.07871</td>\n",
       "      <td>...</td>\n",
       "      <td>25.380</td>\n",
       "      <td>17.33</td>\n",
       "      <td>184.60</td>\n",
       "      <td>2019.0</td>\n",
       "      <td>0.16220</td>\n",
       "      <td>0.66560</td>\n",
       "      <td>0.7119</td>\n",
       "      <td>0.2654</td>\n",
       "      <td>0.4601</td>\n",
       "      <td>0.11890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>20.57</td>\n",
       "      <td>17.77</td>\n",
       "      <td>132.90</td>\n",
       "      <td>1326.0</td>\n",
       "      <td>0.08474</td>\n",
       "      <td>0.07864</td>\n",
       "      <td>0.08690</td>\n",
       "      <td>0.07017</td>\n",
       "      <td>0.1812</td>\n",
       "      <td>0.05667</td>\n",
       "      <td>...</td>\n",
       "      <td>24.990</td>\n",
       "      <td>23.41</td>\n",
       "      <td>158.80</td>\n",
       "      <td>1956.0</td>\n",
       "      <td>0.12380</td>\n",
       "      <td>0.18660</td>\n",
       "      <td>0.2416</td>\n",
       "      <td>0.1860</td>\n",
       "      <td>0.2750</td>\n",
       "      <td>0.08902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>19.69</td>\n",
       "      <td>21.25</td>\n",
       "      <td>130.00</td>\n",
       "      <td>1203.0</td>\n",
       "      <td>0.10960</td>\n",
       "      <td>0.15990</td>\n",
       "      <td>0.19740</td>\n",
       "      <td>0.12790</td>\n",
       "      <td>0.2069</td>\n",
       "      <td>0.05999</td>\n",
       "      <td>...</td>\n",
       "      <td>23.570</td>\n",
       "      <td>25.53</td>\n",
       "      <td>152.50</td>\n",
       "      <td>1709.0</td>\n",
       "      <td>0.14440</td>\n",
       "      <td>0.42450</td>\n",
       "      <td>0.4504</td>\n",
       "      <td>0.2430</td>\n",
       "      <td>0.3613</td>\n",
       "      <td>0.08758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11.42</td>\n",
       "      <td>20.38</td>\n",
       "      <td>77.58</td>\n",
       "      <td>386.1</td>\n",
       "      <td>0.14250</td>\n",
       "      <td>0.28390</td>\n",
       "      <td>0.24140</td>\n",
       "      <td>0.10520</td>\n",
       "      <td>0.2597</td>\n",
       "      <td>0.09744</td>\n",
       "      <td>...</td>\n",
       "      <td>14.910</td>\n",
       "      <td>26.50</td>\n",
       "      <td>98.87</td>\n",
       "      <td>567.7</td>\n",
       "      <td>0.20980</td>\n",
       "      <td>0.86630</td>\n",
       "      <td>0.6869</td>\n",
       "      <td>0.2575</td>\n",
       "      <td>0.6638</td>\n",
       "      <td>0.17300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20.29</td>\n",
       "      <td>14.34</td>\n",
       "      <td>135.10</td>\n",
       "      <td>1297.0</td>\n",
       "      <td>0.10030</td>\n",
       "      <td>0.13280</td>\n",
       "      <td>0.19800</td>\n",
       "      <td>0.10430</td>\n",
       "      <td>0.1809</td>\n",
       "      <td>0.05883</td>\n",
       "      <td>...</td>\n",
       "      <td>22.540</td>\n",
       "      <td>16.67</td>\n",
       "      <td>152.20</td>\n",
       "      <td>1575.0</td>\n",
       "      <td>0.13740</td>\n",
       "      <td>0.20500</td>\n",
       "      <td>0.4000</td>\n",
       "      <td>0.1625</td>\n",
       "      <td>0.2364</td>\n",
       "      <td>0.07678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>564</th>\n",
       "      <td>21.56</td>\n",
       "      <td>22.39</td>\n",
       "      <td>142.00</td>\n",
       "      <td>1479.0</td>\n",
       "      <td>0.11100</td>\n",
       "      <td>0.11590</td>\n",
       "      <td>0.24390</td>\n",
       "      <td>0.13890</td>\n",
       "      <td>0.1726</td>\n",
       "      <td>0.05623</td>\n",
       "      <td>...</td>\n",
       "      <td>25.450</td>\n",
       "      <td>26.40</td>\n",
       "      <td>166.10</td>\n",
       "      <td>2027.0</td>\n",
       "      <td>0.14100</td>\n",
       "      <td>0.21130</td>\n",
       "      <td>0.4107</td>\n",
       "      <td>0.2216</td>\n",
       "      <td>0.2060</td>\n",
       "      <td>0.07115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>565</th>\n",
       "      <td>20.13</td>\n",
       "      <td>28.25</td>\n",
       "      <td>131.20</td>\n",
       "      <td>1261.0</td>\n",
       "      <td>0.09780</td>\n",
       "      <td>0.10340</td>\n",
       "      <td>0.14400</td>\n",
       "      <td>0.09791</td>\n",
       "      <td>0.1752</td>\n",
       "      <td>0.05533</td>\n",
       "      <td>...</td>\n",
       "      <td>23.690</td>\n",
       "      <td>38.25</td>\n",
       "      <td>155.00</td>\n",
       "      <td>1731.0</td>\n",
       "      <td>0.11660</td>\n",
       "      <td>0.19220</td>\n",
       "      <td>0.3215</td>\n",
       "      <td>0.1628</td>\n",
       "      <td>0.2572</td>\n",
       "      <td>0.06637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>566</th>\n",
       "      <td>16.60</td>\n",
       "      <td>28.08</td>\n",
       "      <td>108.30</td>\n",
       "      <td>858.1</td>\n",
       "      <td>0.08455</td>\n",
       "      <td>0.10230</td>\n",
       "      <td>0.09251</td>\n",
       "      <td>0.05302</td>\n",
       "      <td>0.1590</td>\n",
       "      <td>0.05648</td>\n",
       "      <td>...</td>\n",
       "      <td>18.980</td>\n",
       "      <td>34.12</td>\n",
       "      <td>126.70</td>\n",
       "      <td>1124.0</td>\n",
       "      <td>0.11390</td>\n",
       "      <td>0.30940</td>\n",
       "      <td>0.3403</td>\n",
       "      <td>0.1418</td>\n",
       "      <td>0.2218</td>\n",
       "      <td>0.07820</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>567</th>\n",
       "      <td>20.60</td>\n",
       "      <td>29.33</td>\n",
       "      <td>140.10</td>\n",
       "      <td>1265.0</td>\n",
       "      <td>0.11780</td>\n",
       "      <td>0.27700</td>\n",
       "      <td>0.35140</td>\n",
       "      <td>0.15200</td>\n",
       "      <td>0.2397</td>\n",
       "      <td>0.07016</td>\n",
       "      <td>...</td>\n",
       "      <td>25.740</td>\n",
       "      <td>39.42</td>\n",
       "      <td>184.60</td>\n",
       "      <td>1821.0</td>\n",
       "      <td>0.16500</td>\n",
       "      <td>0.86810</td>\n",
       "      <td>0.9387</td>\n",
       "      <td>0.2650</td>\n",
       "      <td>0.4087</td>\n",
       "      <td>0.12400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>568</th>\n",
       "      <td>7.76</td>\n",
       "      <td>24.54</td>\n",
       "      <td>47.92</td>\n",
       "      <td>181.0</td>\n",
       "      <td>0.05263</td>\n",
       "      <td>0.04362</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.1587</td>\n",
       "      <td>0.05884</td>\n",
       "      <td>...</td>\n",
       "      <td>9.456</td>\n",
       "      <td>30.37</td>\n",
       "      <td>59.16</td>\n",
       "      <td>268.6</td>\n",
       "      <td>0.08996</td>\n",
       "      <td>0.06444</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.2871</td>\n",
       "      <td>0.07039</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>569 rows × 30 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     mean radius  mean texture  mean perimeter  mean area  mean smoothness  \\\n",
       "0          17.99         10.38          122.80     1001.0          0.11840   \n",
       "1          20.57         17.77          132.90     1326.0          0.08474   \n",
       "2          19.69         21.25          130.00     1203.0          0.10960   \n",
       "3          11.42         20.38           77.58      386.1          0.14250   \n",
       "4          20.29         14.34          135.10     1297.0          0.10030   \n",
       "..           ...           ...             ...        ...              ...   \n",
       "564        21.56         22.39          142.00     1479.0          0.11100   \n",
       "565        20.13         28.25          131.20     1261.0          0.09780   \n",
       "566        16.60         28.08          108.30      858.1          0.08455   \n",
       "567        20.60         29.33          140.10     1265.0          0.11780   \n",
       "568         7.76         24.54           47.92      181.0          0.05263   \n",
       "\n",
       "     mean compactness  mean concavity  mean concave points  mean symmetry  \\\n",
       "0             0.27760         0.30010              0.14710         0.2419   \n",
       "1             0.07864         0.08690              0.07017         0.1812   \n",
       "2             0.15990         0.19740              0.12790         0.2069   \n",
       "3             0.28390         0.24140              0.10520         0.2597   \n",
       "4             0.13280         0.19800              0.10430         0.1809   \n",
       "..                ...             ...                  ...            ...   \n",
       "564           0.11590         0.24390              0.13890         0.1726   \n",
       "565           0.10340         0.14400              0.09791         0.1752   \n",
       "566           0.10230         0.09251              0.05302         0.1590   \n",
       "567           0.27700         0.35140              0.15200         0.2397   \n",
       "568           0.04362         0.00000              0.00000         0.1587   \n",
       "\n",
       "     mean fractal dimension  ...  worst radius  worst texture  \\\n",
       "0                   0.07871  ...        25.380          17.33   \n",
       "1                   0.05667  ...        24.990          23.41   \n",
       "2                   0.05999  ...        23.570          25.53   \n",
       "3                   0.09744  ...        14.910          26.50   \n",
       "4                   0.05883  ...        22.540          16.67   \n",
       "..                      ...  ...           ...            ...   \n",
       "564                 0.05623  ...        25.450          26.40   \n",
       "565                 0.05533  ...        23.690          38.25   \n",
       "566                 0.05648  ...        18.980          34.12   \n",
       "567                 0.07016  ...        25.740          39.42   \n",
       "568                 0.05884  ...         9.456          30.37   \n",
       "\n",
       "     worst perimeter  worst area  worst smoothness  worst compactness  \\\n",
       "0             184.60      2019.0           0.16220            0.66560   \n",
       "1             158.80      1956.0           0.12380            0.18660   \n",
       "2             152.50      1709.0           0.14440            0.42450   \n",
       "3              98.87       567.7           0.20980            0.86630   \n",
       "4             152.20      1575.0           0.13740            0.20500   \n",
       "..               ...         ...               ...                ...   \n",
       "564           166.10      2027.0           0.14100            0.21130   \n",
       "565           155.00      1731.0           0.11660            0.19220   \n",
       "566           126.70      1124.0           0.11390            0.30940   \n",
       "567           184.60      1821.0           0.16500            0.86810   \n",
       "568            59.16       268.6           0.08996            0.06444   \n",
       "\n",
       "     worst concavity  worst concave points  worst symmetry  \\\n",
       "0             0.7119                0.2654          0.4601   \n",
       "1             0.2416                0.1860          0.2750   \n",
       "2             0.4504                0.2430          0.3613   \n",
       "3             0.6869                0.2575          0.6638   \n",
       "4             0.4000                0.1625          0.2364   \n",
       "..               ...                   ...             ...   \n",
       "564           0.4107                0.2216          0.2060   \n",
       "565           0.3215                0.1628          0.2572   \n",
       "566           0.3403                0.1418          0.2218   \n",
       "567           0.9387                0.2650          0.4087   \n",
       "568           0.0000                0.0000          0.2871   \n",
       "\n",
       "     worst fractal dimension  \n",
       "0                    0.11890  \n",
       "1                    0.08902  \n",
       "2                    0.08758  \n",
       "3                    0.17300  \n",
       "4                    0.07678  \n",
       "..                       ...  \n",
       "564                  0.07115  \n",
       "565                  0.06637  \n",
       "566                  0.07820  \n",
       "567                  0.12400  \n",
       "568                  0.07039  \n",
       "\n",
       "[569 rows x 30 columns]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# display numeric data\n",
    "pd.DataFrame(breast_cancer_dataset.data, columns = breast_cancer_dataset.feature_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>param_n_estimators</th>\n",
       "      <th>param_criterion</th>\n",
       "      <th>mean_test_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>10</td>\n",
       "      <td>gini</td>\n",
       "      <td>0.950815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>20</td>\n",
       "      <td>gini</td>\n",
       "      <td>0.961357</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>50</td>\n",
       "      <td>gini</td>\n",
       "      <td>0.959587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>100</td>\n",
       "      <td>gini</td>\n",
       "      <td>0.963111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>250</td>\n",
       "      <td>gini</td>\n",
       "      <td>0.959603</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>500</td>\n",
       "      <td>gini</td>\n",
       "      <td>0.961357</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>10</td>\n",
       "      <td>entropy</td>\n",
       "      <td>0.950800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>20</td>\n",
       "      <td>entropy</td>\n",
       "      <td>0.964850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>50</td>\n",
       "      <td>entropy</td>\n",
       "      <td>0.968390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>100</td>\n",
       "      <td>entropy</td>\n",
       "      <td>0.961357</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>250</td>\n",
       "      <td>entropy</td>\n",
       "      <td>0.964866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>500</td>\n",
       "      <td>entropy</td>\n",
       "      <td>0.964866</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   param_n_estimators param_criterion  mean_test_score\n",
       "0                  10            gini         0.950815\n",
       "1                  20            gini         0.961357\n",
       "2                  50            gini         0.959587\n",
       "3                 100            gini         0.963111\n",
       "4                 250            gini         0.959603\n",
       "5                 500            gini         0.961357\n",
       "6                  10         entropy         0.950800\n",
       "7                  20         entropy         0.964850\n",
       "8                  50         entropy         0.968390\n",
       "9                 100         entropy         0.961357\n",
       "10                250         entropy         0.964866\n",
       "11                500         entropy         0.964866"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Exploring different hyperparameter configurations of Random Forest via GridSearchCV\n",
    "clf = GridSearchCV(\n",
    "    # providing the model architecture\n",
    "    RandomForestClassifier(),\n",
    "    # defining the parameter grid to test upon\n",
    "    {\n",
    "        \"n_estimators\" : [10, 20, 50, 100, 250, 500],\n",
    "        \"criterion\" : [\"gini\", \"entropy\"]\n",
    "    },\n",
    "    # number of cross validations\n",
    "    cv = 5, \n",
    "    return_train_score = True\n",
    ")\n",
    "# pass data to models\n",
    "clf.fit(breast_cancer_dataset.data, breast_cancer_dataset.target)\n",
    "results = pd.DataFrame(clf.cv_results_)\n",
    "# discard most of the additional information obtained during this process\n",
    "results[[\"param_n_estimators\", \"param_criterion\", \"mean_test_score\"]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## K-Means Clustering\n",
    "---\n",
    "---\n",
    "- unsupervised machine learning algorithm for clusterization\n",
    "##### Approach \n",
    "1) place `k` *centroids* into data at a randomly choosen location<br><br>\n",
    "2) assign data points to their closest *centroid* (clustering)<br><br>\n",
    "3) relocate *centroids* to assigned data samples *center of gravity* and repeat process until composition of cluster does not change anymore or a treshold of iterations it reached<br><br>\n",
    "---\n",
    "**Determine the optimal number of clusters**\n",
    "\n",
    "1) calculate the **sum of squared errors** (SSE) for all *clusters* and sum them up\n",
    "$ SSE = \\sum_{i=0}^{n}dist(x_{i} - c)²$\n",
    "    - `i` = iterator, current index\n",
    "    - `n` = total number of data points within cluster\n",
    "    - `x` = data point within cluster\n",
    "    - `c` = centroid<br><br>\n",
    "2) increment `k` (number of total clusters)<br><br>\n",
    "\n",
    "3) use *elbow* method to determine optimal `k` value\n",
    "    - if plotted the *elbow point* shows the greatest change in slope with respect to the previous `k` value from steep to shallow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Name</th>\n",
       "      <th>Age</th>\n",
       "      <th>Income($)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Rob</td>\n",
       "      <td>27</td>\n",
       "      <td>70000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Michael</td>\n",
       "      <td>29</td>\n",
       "      <td>90000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Mohan</td>\n",
       "      <td>29</td>\n",
       "      <td>61000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Ismail</td>\n",
       "      <td>28</td>\n",
       "      <td>60000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Kory</td>\n",
       "      <td>42</td>\n",
       "      <td>150000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Name  Age  Income($)\n",
       "0      Rob   27      70000\n",
       "1  Michael   29      90000\n",
       "2    Mohan   29      61000\n",
       "3   Ismail   28      60000\n",
       "4     Kory   42     150000"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = os.path.join(\"data\", \"income.csv\")\n",
    "# loading the data\n",
    "df = pd.read_csv(path)\n",
    "# display some of the data\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1c60ca3adf0>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# explore data visually\n",
    "plt.xlabel(\"Age\")\n",
    "plt.ylabel(\"Income($)\")\n",
    "plt.title(\"Age/Income Distribution\")\n",
    "plt.scatter(df[\"Age\"], df[\"Income($)\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>income</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>27</td>\n",
       "      <td>70000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>29</td>\n",
       "      <td>90000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>29</td>\n",
       "      <td>61000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>28</td>\n",
       "      <td>60000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>42</td>\n",
       "      <td>150000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age  income\n",
       "0   27   70000\n",
       "1   29   90000\n",
       "2   29   61000\n",
       "3   28   60000\n",
       "4   42  150000"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"modifying the data\"\"\"\n",
    "# drop nominal values and rename colums for workflow optimization\n",
    "df = df.drop([\"Name\"], axis = \"columns\")\n",
    "df = df.rename(columns = {\"Age\" : \"age\", \"Income($)\": \"income\"})\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1c60cad4e50>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# init model\n",
    "model = KMeans(n_clusters = 3)\n",
    "# NOTE: due to features are unscaled yet, the clustering would not be sufficient\n",
    "# scaling the features in a range from 0 to 1\n",
    "scalar = MinMaxScaler()\n",
    "df.income = scalar.fit_transform(df.income.values.reshape(-1, 1))\n",
    "df.age = scalar.fit_transform(df.age.values.reshape(-1, 1))\n",
    "df.head()\n",
    "# pass data and make prediction and assign it to DataFrame\n",
    "df[\"prediction\"] = model.fit_predict(df)\n",
    "# before visualization data is split based on prediction\n",
    "c0 = df[df.prediction == 0]\n",
    "c1 = df[df.prediction == 1]\n",
    "c2 = df[df.prediction == 2]\n",
    "\n",
    "plt.xlabel(\"Age\")\n",
    "plt.ylabel(\"Income($)\")\n",
    "plt.title(\"Age/Income Distribution\")\n",
    "plt.scatter(c0.age, c0.income, color = \"red\")\n",
    "plt.scatter(c1.age, c1.income, color = \"blue\")\n",
    "plt.scatter(c2.age, c2.income, color = \"orange\")\n",
    "plt.scatter(model.cluster_centers_[:,0], model.cluster_centers_[:,1], c=\"black\", marker = \"x\", label = \"centroid\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c60cb5ef70>]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# check if k = 3 is the optimal value for clusterization of this data set\n",
    "sse = []\n",
    "for k in range(1, 11):\n",
    "    kmeans = KMeans(n_clusters = k)\n",
    "    kmeans.fit(df)\n",
    "    # inertia_ = sum of squared errors\n",
    "    sse.append(kmeans.inertia_)\n",
    "\n",
    "plt.xlabel(\"k\")\n",
    "plt.ylabel(\"sum of squared error\")\n",
    "plt.title(\"Elbow method\")\n",
    "plt.axvline(x=3, color='grey', linestyle='--', lw = 0.4)\n",
    "plt.plot(range(1, 11), sse)    \n",
    "plt.plot(3, sse[2], \"s\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Naive Bayes Classifier \n",
    "---\n",
    "---\n",
    "- uses the (naive) assumption that all featured considered during classification process are independent in order to reduce calculation<br><br>\n",
    "\n",
    "- Bayes Theorem: $P(A|B) = \\frac{P(B|A)*P(A)}{P(B)}$ <br><br>\n",
    "\n",
    "- For classification this can be understood the following way: \n",
    "    - What is the probability of a class for a given set of features? $P(\\text{class probability yet to be calculated}|\\text{some given features})$<br><br>\n",
    "\n",
    "- suppose `X = {x1, x2, x3, ..., xn}` are given features and `y` is a binary classification problem\n",
    "{0 = features do not belong to class y, 1 = features do belong to class y}<br><br>\n",
    "\n",
    "- $P(y|X) = P(y|x1, x2, x3, ..., xn) = \\frac{P(x_1|y)*P(x_2|y)*P(x_3|y)*...*P(x_n|y)*P(y)}{P(x_1)*P(x_2)*P(x_3)*...*P(x_n)} = \\frac{P(y)*\\prod_{i=1}^{n}P(x_i|y)}{P(X)}$ <br><br> \n",
    "- Bayes Classifier: $y = argmax(\\frac{P(y)*\\prod_{i=1}^{n}P(x_i|y)}{P(X)})$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Category</th>\n",
       "      <th>Message</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>ham</td>\n",
       "      <td>Go until jurong point, crazy.. Available only ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>ham</td>\n",
       "      <td>Ok lar... Joking wif u oni...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>spam</td>\n",
       "      <td>Free entry in 2 a wkly comp to win FA Cup fina...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>ham</td>\n",
       "      <td>U dun say so early hor... U c already then say...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>ham</td>\n",
       "      <td>Nah I don't think he goes to usf, he lives aro...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Category                                            Message\n",
       "0      ham  Go until jurong point, crazy.. Available only ...\n",
       "1      ham                      Ok lar... Joking wif u oni...\n",
       "2     spam  Free entry in 2 a wkly comp to win FA Cup fina...\n",
       "3      ham  U dun say so early hor... U c already then say...\n",
       "4      ham  Nah I don't think he goes to usf, he lives aro..."
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = os.path.join(\"data\", \"spam.csv\")\n",
    "# loading the data\n",
    "df = pd.read_csv(path)\n",
    "# display some of the data\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "\n",
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       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"4\" halign=\"left\">Message</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>unique</th>\n",
       "      <th>top</th>\n",
       "      <th>freq</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Category</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ham</th>\n",
       "      <td>4825</td>\n",
       "      <td>4516</td>\n",
       "      <td>Sorry, I'll call later</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>spam</th>\n",
       "      <td>747</td>\n",
       "      <td>641</td>\n",
       "      <td>Please call our customer service representativ...</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Message                                                            \\\n",
       "           count unique                                                top   \n",
       "Category                                                                     \n",
       "ham         4825   4516                             Sorry, I'll call later   \n",
       "spam         747    641  Please call our customer service representativ...   \n",
       "\n",
       "               \n",
       "         freq  \n",
       "Category       \n",
       "ham        30  \n",
       "spam        4  "
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get some information about the data to be used for building a spam-mail classifier\n",
    "df.groupby(\"Category\").describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# replace nominal with numeric values (spam = 1, ham = 0)\n",
    "targets = df[\"Category\"].apply(lambda x: 1 if x == \"spam\" else 0)\n",
    "# using CountVectorize to assign a unique number to each word derived from a the index in a set of words of the entire data\n",
    "vectorizer = CountVectorizer()\n",
    "corpus_as_vectors = vectorizer.fit_transform(df.Message.values)\n",
    "features = corpus_as_vectors.toarray()\n",
    "# splitting data into Training and Test sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(features, targets, test_size = 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9755922469490309"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# initializing the model \n",
    "# NOTE: there are other Naive Bayes Classifier available (see: https://scikit-learn.org/stable/modules/classes.html?highlight=bayes#module-sklearn.naive_bayes), e.g.\n",
    "# -> Bernoulli NB (assumes that all features are binary), \n",
    "# -> Gaussian NB (assumes a normal distribution of features, operates on continous values)\n",
    "# -> Multinomial NB is used when there is discrete data and frequency of occurence\n",
    "model = MultinomialNB()\n",
    "# pass data and train the model\n",
    "model.fit(X_train, y_train)\n",
    "# get prediction accuracy\n",
    "model.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0], dtype=int64)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# live demo\n",
    "unseen_data = [\n",
    "    \"Million Dollar Win, click here for free money, this is an exclusive offer.\",\n",
    "    \"Can you pick up the kids today? Love you ♥\"\n",
    "]\n",
    "unseen_data_count_vector = vectorizer.transform(unseen_data)\n",
    "model.predict(unseen_data_count_vector)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.38559859e-02, 9.86144014e-01],\n",
       "       [9.99998807e-01, 1.19250707e-06]])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# building a pipeline for convenience regarding the usage, this way transforming the data manually can be ommitted\n",
    "# splitting data into Training and Test sets, using the previously binary encoded labels and raw text messages as features\n",
    "X_train, X_test, y_train, y_test = train_test_split(df.Message, targets, test_size=0.25)\n",
    "\n",
    "nb_classifier = Pipeline([\n",
    "    (\"vectorizer\", CountVectorizer()),\n",
    "    (\"naive_Bayes_multinomial_classifier\", MultinomialNB())\n",
    "])\n",
    "\n",
    "nb_classifier.fit(X_train, y_train)\n",
    "nb_classifier.predict_proba(unseen_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## L1, L2 Regularization aka Lasso, Ridge Regression\n",
    "---\n",
    "---\n",
    "- adding a scalable penalty to loss-function to reduce *overfitting*\n",
    "\n",
    "**mse** : $\\frac{1}{n}\\sum_{i=1}^{n}(y_{i}-y_{predicted})²$<br><br>\n",
    "**L1** : $ mse = \\frac{1}{n}\\sum_{i=1}^{n}(y_{i}-h_{\\theta}(x_{i}))² + \\lambda\\sum_{i=1}^{n}|\\theta_{i}|$<br><br>\n",
    "**L2** : $ mse = \\frac{1}{n}\\sum_{i=1}^{n}(y_{i}-h_{\\theta}(x_{i}))² + \\lambda\\sum_{i=1}^{n}\\theta_{i}^{2}$\n",
    "- `mse` = mean squared error\n",
    "- `n` = total number of data points\n",
    "- `i` = iterator\n",
    "- `y` = label\n",
    "- `h` = hypothesis\n",
    "    - e.g. when using linear regression <center> $f(x) = \\text{slope}*x + \\text{interception with y-axis} =$ <br> $y = mx + n$ </center> \n",
    "    it can be rewritten as <center> $h_{\\theta}(x) = \\theta_{0}x + \\theta_{1}$ </center> \n",
    "- `θ` = weight assigned to features (sensitivity)\n",
    "- `x` = feature\n",
    "- `λ` = scalar for penality (small value results in great penalty, and vice versa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Suburb</th>\n",
       "      <th>Address</th>\n",
       "      <th>Rooms</th>\n",
       "      <th>Type</th>\n",
       "      <th>Price</th>\n",
       "      <th>Method</th>\n",
       "      <th>SellerG</th>\n",
       "      <th>Date</th>\n",
       "      <th>Distance</th>\n",
       "      <th>Postcode</th>\n",
       "      <th>...</th>\n",
       "      <th>Bathroom</th>\n",
       "      <th>Car</th>\n",
       "      <th>Landsize</th>\n",
       "      <th>BuildingArea</th>\n",
       "      <th>YearBuilt</th>\n",
       "      <th>CouncilArea</th>\n",
       "      <th>Lattitude</th>\n",
       "      <th>Longtitude</th>\n",
       "      <th>Regionname</th>\n",
       "      <th>Propertycount</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Abbotsford</td>\n",
       "      <td>68 Studley St</td>\n",
       "      <td>2</td>\n",
       "      <td>h</td>\n",
       "      <td>NaN</td>\n",
       "      <td>SS</td>\n",
       "      <td>Jellis</td>\n",
       "      <td>3/09/2016</td>\n",
       "      <td>2.5</td>\n",
       "      <td>3067.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>126.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Yarra City Council</td>\n",
       "      <td>-37.8014</td>\n",
       "      <td>144.9958</td>\n",
       "      <td>Northern Metropolitan</td>\n",
       "      <td>4019.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Abbotsford</td>\n",
       "      <td>85 Turner St</td>\n",
       "      <td>2</td>\n",
       "      <td>h</td>\n",
       "      <td>1480000.0</td>\n",
       "      <td>S</td>\n",
       "      <td>Biggin</td>\n",
       "      <td>3/12/2016</td>\n",
       "      <td>2.5</td>\n",
       "      <td>3067.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>202.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Yarra City Council</td>\n",
       "      <td>-37.7996</td>\n",
       "      <td>144.9984</td>\n",
       "      <td>Northern Metropolitan</td>\n",
       "      <td>4019.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Abbotsford</td>\n",
       "      <td>25 Bloomburg St</td>\n",
       "      <td>2</td>\n",
       "      <td>h</td>\n",
       "      <td>1035000.0</td>\n",
       "      <td>S</td>\n",
       "      <td>Biggin</td>\n",
       "      <td>4/02/2016</td>\n",
       "      <td>2.5</td>\n",
       "      <td>3067.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>156.0</td>\n",
       "      <td>79.0</td>\n",
       "      <td>1900.0</td>\n",
       "      <td>Yarra City Council</td>\n",
       "      <td>-37.8079</td>\n",
       "      <td>144.9934</td>\n",
       "      <td>Northern Metropolitan</td>\n",
       "      <td>4019.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Abbotsford</td>\n",
       "      <td>18/659 Victoria St</td>\n",
       "      <td>3</td>\n",
       "      <td>u</td>\n",
       "      <td>NaN</td>\n",
       "      <td>VB</td>\n",
       "      <td>Rounds</td>\n",
       "      <td>4/02/2016</td>\n",
       "      <td>2.5</td>\n",
       "      <td>3067.0</td>\n",
       "      <td>...</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Yarra City Council</td>\n",
       "      <td>-37.8114</td>\n",
       "      <td>145.0116</td>\n",
       "      <td>Northern Metropolitan</td>\n",
       "      <td>4019.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Abbotsford</td>\n",
       "      <td>5 Charles St</td>\n",
       "      <td>3</td>\n",
       "      <td>h</td>\n",
       "      <td>1465000.0</td>\n",
       "      <td>SP</td>\n",
       "      <td>Biggin</td>\n",
       "      <td>4/03/2017</td>\n",
       "      <td>2.5</td>\n",
       "      <td>3067.0</td>\n",
       "      <td>...</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>134.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>1900.0</td>\n",
       "      <td>Yarra City Council</td>\n",
       "      <td>-37.8093</td>\n",
       "      <td>144.9944</td>\n",
       "      <td>Northern Metropolitan</td>\n",
       "      <td>4019.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       Suburb             Address  Rooms Type      Price Method SellerG  \\\n",
       "0  Abbotsford       68 Studley St      2    h        NaN     SS  Jellis   \n",
       "1  Abbotsford        85 Turner St      2    h  1480000.0      S  Biggin   \n",
       "2  Abbotsford     25 Bloomburg St      2    h  1035000.0      S  Biggin   \n",
       "3  Abbotsford  18/659 Victoria St      3    u        NaN     VB  Rounds   \n",
       "4  Abbotsford        5 Charles St      3    h  1465000.0     SP  Biggin   \n",
       "\n",
       "        Date  Distance  Postcode  ...  Bathroom  Car  Landsize  BuildingArea  \\\n",
       "0  3/09/2016       2.5    3067.0  ...       1.0  1.0     126.0           NaN   \n",
       "1  3/12/2016       2.5    3067.0  ...       1.0  1.0     202.0           NaN   \n",
       "2  4/02/2016       2.5    3067.0  ...       1.0  0.0     156.0          79.0   \n",
       "3  4/02/2016       2.5    3067.0  ...       2.0  1.0       0.0           NaN   \n",
       "4  4/03/2017       2.5    3067.0  ...       2.0  0.0     134.0         150.0   \n",
       "\n",
       "   YearBuilt         CouncilArea Lattitude  Longtitude             Regionname  \\\n",
       "0        NaN  Yarra City Council  -37.8014    144.9958  Northern Metropolitan   \n",
       "1        NaN  Yarra City Council  -37.7996    144.9984  Northern Metropolitan   \n",
       "2     1900.0  Yarra City Council  -37.8079    144.9934  Northern Metropolitan   \n",
       "3        NaN  Yarra City Council  -37.8114    145.0116  Northern Metropolitan   \n",
       "4     1900.0  Yarra City Council  -37.8093    144.9944  Northern Metropolitan   \n",
       "\n",
       "  Propertycount  \n",
       "0        4019.0  \n",
       "1        4019.0  \n",
       "2        4019.0  \n",
       "3        4019.0  \n",
       "4        4019.0  \n",
       "\n",
       "[5 rows x 21 columns]"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = os.path.join(\"data\", \"Melbourne_housing_FULL.csv\")\n",
    "# loading the data\n",
    "df = pd.read_csv(path)\n",
    "# display data\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Suburb             351\n",
      "Address          34009\n",
      "Rooms               12\n",
      "Type                 3\n",
      "Price             2871\n",
      "Method               9\n",
      "SellerG            388\n",
      "Date                78\n",
      "Distance           215\n",
      "Postcode           211\n",
      "Bedroom2            15\n",
      "Bathroom            11\n",
      "Car                 15\n",
      "Landsize          1684\n",
      "BuildingArea       740\n",
      "YearBuilt          160\n",
      "CouncilArea         33\n",
      "Lattitude        13402\n",
      "Longtitude       14524\n",
      "Regionname           8\n",
      "Propertycount      342\n",
      "dtype: int64\n",
      "(34857, 21)\n"
     ]
    }
   ],
   "source": [
    "# explore dataset\n",
    "print(df.nunique())\n",
    "print(df.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Suburb</th>\n",
       "      <th>Rooms</th>\n",
       "      <th>Type</th>\n",
       "      <th>Method</th>\n",
       "      <th>SellerG</th>\n",
       "      <th>Regionname</th>\n",
       "      <th>Propertycount</th>\n",
       "      <th>Distance</th>\n",
       "      <th>CouncilArea</th>\n",
       "      <th>Bedroom2</th>\n",
       "      <th>Bathroom</th>\n",
       "      <th>Car</th>\n",
       "      <th>Landsize</th>\n",
       "      <th>BuildingArea</th>\n",
       "      <th>Price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Abbotsford</td>\n",
       "      <td>2</td>\n",
       "      <td>h</td>\n",
       "      <td>SS</td>\n",
       "      <td>Jellis</td>\n",
       "      <td>Northern Metropolitan</td>\n",
       "      <td>4019.0</td>\n",
       "      <td>2.5</td>\n",
       "      <td>Yarra City Council</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>126.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Abbotsford</td>\n",
       "      <td>2</td>\n",
       "      <td>h</td>\n",
       "      <td>S</td>\n",
       "      <td>Biggin</td>\n",
       "      <td>Northern Metropolitan</td>\n",
       "      <td>4019.0</td>\n",
       "      <td>2.5</td>\n",
       "      <td>Yarra City Council</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>202.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1480000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Abbotsford</td>\n",
       "      <td>2</td>\n",
       "      <td>h</td>\n",
       "      <td>S</td>\n",
       "      <td>Biggin</td>\n",
       "      <td>Northern Metropolitan</td>\n",
       "      <td>4019.0</td>\n",
       "      <td>2.5</td>\n",
       "      <td>Yarra City Council</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>156.0</td>\n",
       "      <td>79.0</td>\n",
       "      <td>1035000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Abbotsford</td>\n",
       "      <td>3</td>\n",
       "      <td>u</td>\n",
       "      <td>VB</td>\n",
       "      <td>Rounds</td>\n",
       "      <td>Northern Metropolitan</td>\n",
       "      <td>4019.0</td>\n",
       "      <td>2.5</td>\n",
       "      <td>Yarra City Council</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Abbotsford</td>\n",
       "      <td>3</td>\n",
       "      <td>h</td>\n",
       "      <td>SP</td>\n",
       "      <td>Biggin</td>\n",
       "      <td>Northern Metropolitan</td>\n",
       "      <td>4019.0</td>\n",
       "      <td>2.5</td>\n",
       "      <td>Yarra City Council</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>134.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>1465000.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Suburb  Rooms Type Method SellerG             Regionname  \\\n",
       "0  Abbotsford      2    h     SS  Jellis  Northern Metropolitan   \n",
       "1  Abbotsford      2    h      S  Biggin  Northern Metropolitan   \n",
       "2  Abbotsford      2    h      S  Biggin  Northern Metropolitan   \n",
       "3  Abbotsford      3    u     VB  Rounds  Northern Metropolitan   \n",
       "4  Abbotsford      3    h     SP  Biggin  Northern Metropolitan   \n",
       "\n",
       "   Propertycount  Distance         CouncilArea  Bedroom2  Bathroom  Car  \\\n",
       "0         4019.0       2.5  Yarra City Council       2.0       1.0  1.0   \n",
       "1         4019.0       2.5  Yarra City Council       2.0       1.0  1.0   \n",
       "2         4019.0       2.5  Yarra City Council       2.0       1.0  0.0   \n",
       "3         4019.0       2.5  Yarra City Council       3.0       2.0  1.0   \n",
       "4         4019.0       2.5  Yarra City Council       3.0       2.0  0.0   \n",
       "\n",
       "   Landsize  BuildingArea      Price  \n",
       "0     126.0           NaN        NaN  \n",
       "1     202.0           NaN  1480000.0  \n",
       "2     156.0          79.0  1035000.0  \n",
       "3       0.0           NaN        NaN  \n",
       "4     134.0         150.0  1465000.0  "
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# discard unneeded data by creating a new dataframe\n",
    "df_reduced = df[[\n",
    "    \"Suburb\", \n",
    "    \"Rooms\", \n",
    "    \"Type\", \n",
    "    \"Method\",\n",
    "    \"SellerG\",\n",
    "    \"Regionname\",\n",
    "    \"Propertycount\",\n",
    "    \"Distance\",\n",
    "    \"CouncilArea\",\n",
    "    \"Bedroom2\",\n",
    "    \"Bathroom\",\n",
    "    \"Car\",\n",
    "    \"Landsize\",\n",
    "    \"BuildingArea\",\n",
    "    \"Price\",\n",
    "    ]]\n",
    "df_reduced.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "# option to supress warnings about working on a copy of a slice of a DataFrame in upcoming cell\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Suburb               0\n",
      "Rooms                0\n",
      "Type                 0\n",
      "Method               0\n",
      "SellerG              0\n",
      "Regionname           3\n",
      "Propertycount        3\n",
      "Distance             1\n",
      "CouncilArea          3\n",
      "Bedroom2          8217\n",
      "Bathroom          8226\n",
      "Car               8728\n",
      "Landsize         11810\n",
      "BuildingArea     21115\n",
      "Price             7610\n",
      "dtype: int64\n"
     ]
    }
   ],
   "source": [
    "# check for missing values\n",
    "print(df_reduced.isna().sum())\n",
    "# fill listed columns with zero\n",
    "cols_to_be_zero_filled = [\"Propertycount\", \"Distance\", \"Bedroom2\", \"Bathroom\", \"Car\"]\n",
    "df_reduced[cols_to_be_zero_filled] = df_reduced[cols_to_be_zero_filled].fillna(0)\n",
    "# fill specified columns with mean values\n",
    "df_reduced.Landsize = df_reduced.Landsize.fillna(df_reduced.Landsize.mean())\n",
    "df_reduced.BuildingArea = df_reduced.BuildingArea.fillna(df_reduced.BuildingArea.mean())\n",
    "# drop nominal features with values not available\n",
    "df_reduced.dropna(inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Suburb           0\n",
      "Rooms            0\n",
      "Type             0\n",
      "Method           0\n",
      "SellerG          0\n",
      "Regionname       0\n",
      "Propertycount    0\n",
      "Distance         0\n",
      "CouncilArea      0\n",
      "Bedroom2         0\n",
      "Bathroom         0\n",
      "Car              0\n",
      "Landsize         0\n",
      "BuildingArea     0\n",
      "Price            0\n",
      "dtype: int64\n"
     ]
    }
   ],
   "source": [
    "# display cleaned DataFrame\n",
    "print(df_reduced.isna().sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "# use dummies to one-hot-encode categorical features, use drop_first to avoid dummy variable trap\n",
    "df_reduced = pd.get_dummies(df_reduced, drop_first = True)\n",
    "# split data into Training and Testing set\n",
    "X = df_reduced.drop(\"Price\", axis = 1)\n",
    "y = df_reduced.Price\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.3, random_state = 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.13853683161492103"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# initializing and training the model\n",
    "model = LinearRegression().fit(X_train, y_train)\n",
    "# evaluate model -> massive overfitting\n",
    "model.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6636111369404488"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# using L1-regularized model instead\n",
    "model_lasso = Lasso(\n",
    "    # constant that multiplies the L1 term - synonym to lambda (see above)\n",
    "    alpha = 50, \n",
    "    max_iter = 100,\n",
    "    # tolerance for the optimization\n",
    "    tol = 0.1\n",
    ")\n",
    "model_lasso.fit(X_train, y_train)\n",
    "model_lasso.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6670848945194959"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# using L2-regularized model instead\n",
    "model_ridge = Ridge(alpha = 50, max_iter = 100, tol = 0.1)\n",
    "model_ridge.fit(X_train, y_train)\n",
    "model_ridge.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## K-Nearest Neighbours (KNN)\n",
    "---\n",
    "---\n",
    "- can be used for classification & regression\n",
    "- `k` = natural number constant; represents the count of points that will be taken into consideration during classification (majority => class, best to use an odd number)\n",
    "    - e.g. `k` = 15, consider the **nearest** (eucledian distance) 15 datapoints to determine the class of the sample (optimal value for `k` depends on size of given data)\n",
    "- *weights* parameter:\n",
    "    - uniform -> only consider count of nearest neighbours\n",
    "    - distance -> closer points are assigned a greater importance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load data, for a visual representation see code above (SVM)\n",
    "iris = load_iris()\n",
    "df = pd.DataFrame(iris.data, columns=iris.feature_names)\n",
    "# splitting data into Training and Test sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(iris.data, iris.target, test_size=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9333333333333333"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = KNeighborsClassifier(\n",
    "    n_neighbors = 3,\n",
    "    weights = \"distance\"\n",
    "    )\n",
    "model.fit(X_train, y_train)\n",
    "model.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       1.00      1.00      1.00        12\n",
      "           1       1.00      0.71      0.83         7\n",
      "           2       0.85      1.00      0.92        11\n",
      "\n",
      "    accuracy                           0.93        30\n",
      "   macro avg       0.95      0.90      0.92        30\n",
      "weighted avg       0.94      0.93      0.93        30\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(42.0, 0.5, 'Truth')"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 504x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred = model.predict(X_test)\n",
    "print(classification_report(y_test, y_pred))\n",
    "plt.figure(figsize = (7, 5))\n",
    "sns.heatmap(confusion_matrix(y_test, y_pred), annot = True)\n",
    "plt.xlabel(\"Prediction\")\n",
    "plt.ylabel(\"Truth\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Principal Component Analysis (PCA)\n",
    "---\n",
    "---\n",
    "- Identifying dimensions/features that are most influencial with regards to the target variable, used for speeding up computation\n",
    "- find features with **high variance** within given dataset, omit less influencial ones, the newly calculated features after this reduction of dimensions are referred to as **principal components**\n",
    "-> [additional information](https://jakevdp.github.io/PythonDataScienceHandbook/05.09-principal-component-analysis.html) (accessed: 10.02.22)\n",
    "- ⚠️ Features need to be scaled before PCA is applied\n",
    "- ⚠️ PCA can become a trade-off between computational complexity and accuracy, due to the interaction of features is not taken into consideration here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>pixel_0_0</th>\n",
       "      <th>pixel_0_1</th>\n",
       "      <th>pixel_0_2</th>\n",
       "      <th>pixel_0_3</th>\n",
       "      <th>pixel_0_4</th>\n",
       "      <th>pixel_0_5</th>\n",
       "      <th>pixel_0_6</th>\n",
       "      <th>pixel_0_7</th>\n",
       "      <th>pixel_1_0</th>\n",
       "      <th>pixel_1_1</th>\n",
       "      <th>...</th>\n",
       "      <th>pixel_6_6</th>\n",
       "      <th>pixel_6_7</th>\n",
       "      <th>pixel_7_0</th>\n",
       "      <th>pixel_7_1</th>\n",
       "      <th>pixel_7_2</th>\n",
       "      <th>pixel_7_3</th>\n",
       "      <th>pixel_7_4</th>\n",
       "      <th>pixel_7_5</th>\n",
       "      <th>pixel_7_6</th>\n",
       "      <th>pixel_7_7</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1797.0</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.303840</td>\n",
       "      <td>5.204786</td>\n",
       "      <td>11.835838</td>\n",
       "      <td>11.848080</td>\n",
       "      <td>5.781859</td>\n",
       "      <td>1.362270</td>\n",
       "      <td>0.129661</td>\n",
       "      <td>0.005565</td>\n",
       "      <td>1.993879</td>\n",
       "      <td>...</td>\n",
       "      <td>3.725097</td>\n",
       "      <td>0.206455</td>\n",
       "      <td>0.000556</td>\n",
       "      <td>0.279354</td>\n",
       "      <td>5.557596</td>\n",
       "      <td>12.089037</td>\n",
       "      <td>11.809126</td>\n",
       "      <td>6.764051</td>\n",
       "      <td>2.067891</td>\n",
       "      <td>0.364496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.907192</td>\n",
       "      <td>4.754826</td>\n",
       "      <td>4.248842</td>\n",
       "      <td>4.287388</td>\n",
       "      <td>5.666418</td>\n",
       "      <td>3.325775</td>\n",
       "      <td>1.037383</td>\n",
       "      <td>0.094222</td>\n",
       "      <td>3.196160</td>\n",
       "      <td>...</td>\n",
       "      <td>4.919406</td>\n",
       "      <td>0.984401</td>\n",
       "      <td>0.023590</td>\n",
       "      <td>0.934302</td>\n",
       "      <td>5.103019</td>\n",
       "      <td>4.374694</td>\n",
       "      <td>4.933947</td>\n",
       "      <td>5.900623</td>\n",
       "      <td>4.090548</td>\n",
       "      <td>1.860122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>11.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>14.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>15.000000</td>\n",
       "      <td>15.000000</td>\n",
       "      <td>11.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>12.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>0.0</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>15.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 64 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       pixel_0_0    pixel_0_1    pixel_0_2    pixel_0_3    pixel_0_4  \\\n",
       "count     1797.0  1797.000000  1797.000000  1797.000000  1797.000000   \n",
       "mean         0.0     0.303840     5.204786    11.835838    11.848080   \n",
       "std          0.0     0.907192     4.754826     4.248842     4.287388   \n",
       "min          0.0     0.000000     0.000000     0.000000     0.000000   \n",
       "25%          0.0     0.000000     1.000000    10.000000    10.000000   \n",
       "50%          0.0     0.000000     4.000000    13.000000    13.000000   \n",
       "75%          0.0     0.000000     9.000000    15.000000    15.000000   \n",
       "max          0.0     8.000000    16.000000    16.000000    16.000000   \n",
       "\n",
       "         pixel_0_5    pixel_0_6    pixel_0_7    pixel_1_0    pixel_1_1  ...  \\\n",
       "count  1797.000000  1797.000000  1797.000000  1797.000000  1797.000000  ...   \n",
       "mean      5.781859     1.362270     0.129661     0.005565     1.993879  ...   \n",
       "std       5.666418     3.325775     1.037383     0.094222     3.196160  ...   \n",
       "min       0.000000     0.000000     0.000000     0.000000     0.000000  ...   \n",
       "25%       0.000000     0.000000     0.000000     0.000000     0.000000  ...   \n",
       "50%       4.000000     0.000000     0.000000     0.000000     0.000000  ...   \n",
       "75%      11.000000     0.000000     0.000000     0.000000     3.000000  ...   \n",
       "max      16.000000    16.000000    15.000000     2.000000    16.000000  ...   \n",
       "\n",
       "         pixel_6_6    pixel_6_7    pixel_7_0    pixel_7_1    pixel_7_2  \\\n",
       "count  1797.000000  1797.000000  1797.000000  1797.000000  1797.000000   \n",
       "mean      3.725097     0.206455     0.000556     0.279354     5.557596   \n",
       "std       4.919406     0.984401     0.023590     0.934302     5.103019   \n",
       "min       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "25%       0.000000     0.000000     0.000000     0.000000     1.000000   \n",
       "50%       1.000000     0.000000     0.000000     0.000000     4.000000   \n",
       "75%       7.000000     0.000000     0.000000     0.000000    10.000000   \n",
       "max      16.000000    13.000000     1.000000     9.000000    16.000000   \n",
       "\n",
       "         pixel_7_3    pixel_7_4    pixel_7_5    pixel_7_6    pixel_7_7  \n",
       "count  1797.000000  1797.000000  1797.000000  1797.000000  1797.000000  \n",
       "mean     12.089037    11.809126     6.764051     2.067891     0.364496  \n",
       "std       4.374694     4.933947     5.900623     4.090548     1.860122  \n",
       "min       0.000000     0.000000     0.000000     0.000000     0.000000  \n",
       "25%      11.000000    10.000000     0.000000     0.000000     0.000000  \n",
       "50%      13.000000    14.000000     6.000000     0.000000     0.000000  \n",
       "75%      16.000000    16.000000    12.000000     2.000000     0.000000  \n",
       "max      16.000000    16.000000    16.000000    16.000000    16.000000  \n",
       "\n",
       "[8 rows x 64 columns]"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# again using the handwritten dataset, where each array of shape (8, 8) represented as handwritten number and the entries can be interpreted as brightness values\n",
    "raw_data = load_digits()\n",
    "df = pd.DataFrame(raw_data.data, columns = raw_data.feature_names)\n",
    "# explore dataset numerically\n",
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Performance without PCA: 0.9583333333333334\n"
     ]
    }
   ],
   "source": [
    "# Scaling features \n",
    "scalar = StandardScaler()\n",
    "scaled_data = scalar.fit_transform(df)\n",
    "# splitting data into Training and Test sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(scaled_data, raw_data.target, test_size=0.2)\n",
    "\n",
    "# Training and Testing a modell on unreduced data\n",
    "model = LogisticRegression().fit(X_train, y_train)\n",
    "print(\"Performance without PCA:\", model.score(X_test, y_test))\n",
    "\n",
    "# NOTE: n_compoments can be used to determine how many features to keep, but PCA accepts float vallues as well, indicating a percentage of all available features\n",
    "pca = PCA(0.95)\n",
    "scaled_data_pca = pca.fit_transform(scaled_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.12033916, 0.09561054, 0.08444415, 0.06498408, 0.04860155,\n",
       "       0.0421412 , 0.03942083, 0.03389381, 0.02998221, 0.02932003,\n",
       "       0.02781805, 0.02577055, 0.02275303, 0.0222718 , 0.02165229,\n",
       "       0.01914167, 0.01775547, 0.01638069, 0.0159646 , 0.01489191,\n",
       "       0.0134797 , 0.01271931, 0.01165837, 0.01057647, 0.00975316,\n",
       "       0.00944559, 0.00863014, 0.00836643, 0.00797693, 0.00746471,\n",
       "       0.00725582, 0.00691911, 0.00653909, 0.00640793, 0.00591384,\n",
       "       0.00571162, 0.00523637, 0.00481808, 0.00453719, 0.00423163])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# show how much variance of the dataset is associated with newly computatetd principal components\n",
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Performance with PCA: 0.9666666666666667\n"
     ]
    }
   ],
   "source": [
    "# splitting data into Training and Test sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(scaled_data_pca, raw_data.target, test_size=0.2)\n",
    "# Training and Testing a modell on unreduced data\n",
    "model = LogisticRegression().fit(X_train, y_train)\n",
    "print(\"Performance with PCA:\", model.score(X_test, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ensemble Learning\n",
    "---\n",
    "---\n",
    "- combining the results of multiple, different (*weak learned*) models in form of an average (regression) or a majority vote (classification)\n",
    "    - *weak learners* are models trained only on a subset of the available data (*bootstrap*), retrieved using *resampling with replacements* (allows for a sample to be used multiple times within the set); by doing so, the change of these models to overfit is reduced\n",
    "    - sometimes refered to as *bootstrap aggregation*, or *bagging* for short\n",
    "- recommended usage in case of unstable classifiers or data with high variance    \n",
    "- ⚠️ distinction: \n",
    "    - **Bagging**: different models can be used (SVM, KNN, Logistic Regression, ...)\n",
    "    - **Bagged Treed**: (Random Forest) each model is a tree, also features are randomly selected"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fall back onto some previously used data \n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    # features\n",
    "    breast_cancer_dataset.data, \n",
    "    # targets\n",
    "    breast_cancer_dataset.target, \n",
    "    # train : test split ratio\n",
    "    train_size = .8, \n",
    "    # due to the distribution of targets is somewhat unbalanced (0 = 212, 1 = 357), stratify will assure that the ratio remains more balanced during split\n",
    "    stratify = breast_cancer_dataset.target, \n",
    "    # arbitrary choosen random seed, alows for reproducability\n",
    "    random_state = 10\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.9122807  0.92105263 0.92105263 0.94736842 0.91150442] avg: 0.9226517621487347\n"
     ]
    }
   ],
   "source": [
    "# evaluate the performance of a Decision Tree Model, using the entire dataset, five times cross-validated\n",
    "scores = cross_val_score(tree.DecisionTreeClassifier(), breast_cancer_dataset.data, breast_cancer_dataset.target, cv = 5)\n",
    "print(scores, \"avg:\", scores.mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9560439560439561"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = BaggingClassifier(\n",
    "    # type of models to be used\n",
    "    base_estimator = tree.DecisionTreeClassifier(),\n",
    "    # number of models \n",
    "    n_estimators = 100,\n",
    "    # percentage of how much of the available data should be used, size of subsets\n",
    "    max_samples = .8,\n",
    "    # out of bag refers to samples not contained in any subset, can be used to testing purpose\n",
    "    oob_score = True,\n",
    "    # see above\n",
    "    random_state = 0\n",
    ")\n",
    "\n",
    "model.fit(X_train, y_train)\n",
    "model.oob_score_"
   ]
  }
 ],
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