SVM.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "SVM.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyOcyOJ1uaGw/DUdP86s6q5k"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "BngHr0bPnMTB"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M4S6p-Q4TJB3"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "x = np.linspace(-5.0, 5.0, 100)\n",
        "y = np.sqrt(15**2 - x**2)\n",
        "y=np.hstack([y,-y])\n",
        "x=np.hstack([x,-x])"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ihqQYRnBTTmY"
      },
      "source": [
        "x1 = np.linspace(-5.0, 5.0, 100)\n",
        "y1 = np.sqrt(5**2 - x1**2)\n",
        "y1=np.hstack([y1,-y1])\n",
        "x1=np.hstack([x1,-x1])"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "CP_rBtRMTc6K",
        "outputId": "45683008-ee2a-4abf-9c8a-2aadcc3c48e9"
      },
      "source": [
        "plt.scatter(y,x)\n",
        "plt.scatter(y1,x1)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f36c49310d0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "HvLZMIMQTiW4",
        "outputId": "fd70edcd-3c83-4af3-d6e7-eedb948792a4"
      },
      "source": [
        "import pandas as pd\n",
        "df1 =pd.DataFrame(np.vstack([y,x]).T,columns=['X1','X2'])\n",
        "df1['Y']=0\n",
        "df2 =pd.DataFrame(np.vstack([y1,x1]).T,columns=['X1','X2'])\n",
        "df2['Y']=1\n",
        "df = df1.append(df2)\n",
        "df.head(5)"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>X1</th>\n",
              "      <th>X2</th>\n",
              "      <th>Y</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>14.142136</td>\n",
              "      <td>-5.00000</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>14.177443</td>\n",
              "      <td>-4.89899</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>14.211945</td>\n",
              "      <td>-4.79798</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>14.245648</td>\n",
              "      <td>-4.69697</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>14.278556</td>\n",
              "      <td>-4.59596</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "          X1       X2  Y\n",
              "0  14.142136 -5.00000  0\n",
              "1  14.177443 -4.89899  0\n",
              "2  14.211945 -4.79798  0\n",
              "3  14.245648 -4.69697  0\n",
              "4  14.278556 -4.59596  0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gAJP7RguTsPa",
        "outputId": "66e5b59f-9b84-487b-fcc2-3c40d85eaac3"
      },
      "source": [
        "### Independent and Dependent features\n",
        "X = df.iloc[:, :2]  \n",
        "y = df.Y\n",
        "y"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0      0\n",
              "1      0\n",
              "2      0\n",
              "3      0\n",
              "4      0\n",
              "      ..\n",
              "195    1\n",
              "196    1\n",
              "197    1\n",
              "198    1\n",
              "199    1\n",
              "Name: Y, Length: 400, dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LVe7d_ioTwJx",
        "outputId": "ecc5397a-6989-48c2-f7ca-dd705694fa12"
      },
      "source": [
        "## Split the dataset into train and test\n",
        "from sklearn.model_selection import train_test_split\n",
        "X_train,X_test,y_train,y_test=train_test_split(X,y,test_size=0.20,random_state=0)\n",
        "y_train"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "136    1\n",
              "64     0\n",
              "55     0\n",
              "106    0\n",
              "100    1\n",
              "      ..\n",
              "123    1\n",
              "192    0\n",
              "117    0\n",
              "47     0\n",
              "172    0\n",
              "Name: Y, Length: 320, dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eeDUzBfOURPH",
        "outputId": "e0554174-35ca-47dd-fd8f-feadb57eea69"
      },
      "source": [
        "from sklearn.svm import SVC\n",
        "classifier=SVC(kernel=\"linear\")\n",
        "classifier.fit(X_train,y_train)\n",
        "from sklearn.metrics import accuracy_score\n",
        "y_pred = classifier.predict(X_test)\n",
        "accuracy_score(y_test, y_pred)"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.4125"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CkY5bYaqUZkO"
      },
      "source": [
        "Using Linear kernel on such a data gives us a low accuracy score, let us increase the features now and apply an rbf/polynomial kernel. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "98SsWcuzUnfa",
        "outputId": "7423bc57-1f2a-428b-d807-f79ff1241c57"
      },
      "source": [
        "from sklearn.svm import SVC\n",
        "classifier=SVC(kernel=\"rbf\")\n",
        "classifier.fit(X_train,y_train)\n",
        "from sklearn.metrics import accuracy_score\n",
        "y_pred = classifier.predict(X_test)\n",
        "accuracy_score(y_test, y_pred)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bWp4ehyDUq9j"
      },
      "source": [
        "The rbf kernel on such a data gives a very good accuracy score. \n",
        "\n",
        "  Let's try using a Polynomial Kernel now."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "M-eoKbJqU6Vw",
        "outputId": "151f65ba-41d4-4803-be7f-8d871e42a1e3"
      },
      "source": [
        "# Finding all the second degree components for a polynomial kernel \n",
        "df['X1_Square']= df['X1']**2\n",
        "df['X2_Square']= df['X2']**2\n",
        "df['X1*X2'] = (df['X1'] *df['X2'])\n",
        "df.head()"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>X1</th>\n",
              "      <th>X2</th>\n",
              "      <th>Y</th>\n",
              "      <th>X1_Square</th>\n",
              "      <th>X2_Square</th>\n",
              "      <th>X1*X2</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>14.142136</td>\n",
              "      <td>-5.00000</td>\n",
              "      <td>0</td>\n",
              "      <td>200.000000</td>\n",
              "      <td>25.000000</td>\n",
              "      <td>-70.710678</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>14.177443</td>\n",
              "      <td>-4.89899</td>\n",
              "      <td>0</td>\n",
              "      <td>200.999898</td>\n",
              "      <td>24.000102</td>\n",
              "      <td>-69.455151</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>14.211945</td>\n",
              "      <td>-4.79798</td>\n",
              "      <td>0</td>\n",
              "      <td>201.979390</td>\n",
              "      <td>23.020610</td>\n",
              "      <td>-68.188627</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>14.245648</td>\n",
              "      <td>-4.69697</td>\n",
              "      <td>0</td>\n",
              "      <td>202.938476</td>\n",
              "      <td>22.061524</td>\n",
              "      <td>-66.911375</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>14.278556</td>\n",
              "      <td>-4.59596</td>\n",
              "      <td>0</td>\n",
              "      <td>203.877155</td>\n",
              "      <td>21.122845</td>\n",
              "      <td>-65.623665</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "          X1       X2  Y   X1_Square  X2_Square      X1*X2\n",
              "0  14.142136 -5.00000  0  200.000000  25.000000 -70.710678\n",
              "1  14.177443 -4.89899  0  200.999898  24.000102 -69.455151\n",
              "2  14.211945 -4.79798  0  201.979390  23.020610 -68.188627\n",
              "3  14.245648 -4.69697  0  202.938476  22.061524 -66.911375\n",
              "4  14.278556 -4.59596  0  203.877155  21.122845 -65.623665"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fWe7fIsJVKLr",
        "outputId": "9929d5dd-f230-4f9e-9abe-c2e742071fb9"
      },
      "source": [
        "X = df[['X1','X2','X1_Square','X2_Square','X1*X2']]\n",
        "y = df['Y']\n",
        "y"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0      0\n",
              "1      0\n",
              "2      0\n",
              "3      0\n",
              "4      0\n",
              "      ..\n",
              "195    1\n",
              "196    1\n",
              "197    1\n",
              "198    1\n",
              "199    1\n",
              "Name: Y, Length: 400, dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        },
        "id": "MMoGggq9VORR",
        "outputId": "6b2ef0c5-d636-4ab2-e647-f6e06f438845"
      },
      "source": [
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.20, random_state = 0)\n",
        "X_train"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "\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>X1</th>\n",
              "      <th>X2</th>\n",
              "      <th>X1_Square</th>\n",
              "      <th>X2_Square</th>\n",
              "      <th>X1*X2</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>136</th>\n",
              "      <td>-4.810457</td>\n",
              "      <td>1.363636</td>\n",
              "      <td>23.140496</td>\n",
              "      <td>1.859504</td>\n",
              "      <td>-6.559714</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>64</th>\n",
              "      <td>14.928322</td>\n",
              "      <td>1.464646</td>\n",
              "      <td>222.854811</td>\n",
              "      <td>2.145189</td>\n",
              "      <td>21.864715</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>55</th>\n",
              "      <td>14.989708</td>\n",
              "      <td>0.555556</td>\n",
              "      <td>224.691358</td>\n",
              "      <td>0.308642</td>\n",
              "      <td>8.327616</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>106</th>\n",
              "      <td>-14.342012</td>\n",
              "      <td>4.393939</td>\n",
              "      <td>205.693297</td>\n",
              "      <td>19.306703</td>\n",
              "      <td>-63.017930</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>100</th>\n",
              "      <td>-0.000000</td>\n",
              "      <td>5.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>25.000000</td>\n",
              "      <td>-0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>123</th>\n",
              "      <td>-4.223140</td>\n",
              "      <td>2.676768</td>\n",
              "      <td>17.834915</td>\n",
              "      <td>7.165085</td>\n",
              "      <td>-11.304366</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>192</th>\n",
              "      <td>-14.372570</td>\n",
              "      <td>-4.292929</td>\n",
              "      <td>206.570758</td>\n",
              "      <td>18.429242</td>\n",
              "      <td>61.700425</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>117</th>\n",
              "      <td>-14.636360</td>\n",
              "      <td>3.282828</td>\n",
              "      <td>214.223038</td>\n",
              "      <td>10.776962</td>\n",
              "      <td>-48.048657</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>47</th>\n",
              "      <td>14.997874</td>\n",
              "      <td>-0.252525</td>\n",
              "      <td>224.936231</td>\n",
              "      <td>0.063769</td>\n",
              "      <td>-3.787342</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>172</th>\n",
              "      <td>-14.826824</td>\n",
              "      <td>-2.272727</td>\n",
              "      <td>219.834711</td>\n",
              "      <td>5.165289</td>\n",
              "      <td>33.697327</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>320 rows × 5 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "            X1        X2   X1_Square  X2_Square      X1*X2\n",
              "136  -4.810457  1.363636   23.140496   1.859504  -6.559714\n",
              "64   14.928322  1.464646  222.854811   2.145189  21.864715\n",
              "55   14.989708  0.555556  224.691358   0.308642   8.327616\n",
              "106 -14.342012  4.393939  205.693297  19.306703 -63.017930\n",
              "100  -0.000000  5.000000    0.000000  25.000000  -0.000000\n",
              "..         ...       ...         ...        ...        ...\n",
              "123  -4.223140  2.676768   17.834915   7.165085 -11.304366\n",
              "192 -14.372570 -4.292929  206.570758  18.429242  61.700425\n",
              "117 -14.636360  3.282828  214.223038  10.776962 -48.048657\n",
              "47   14.997874 -0.252525  224.936231   0.063769  -3.787342\n",
              "172 -14.826824 -2.272727  219.834711   5.165289  33.697327\n",
              "\n",
              "[320 rows x 5 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "id": "0jaF1CdSowwE",
        "outputId": "2eb397cb-aec1-4da2-9bae-765f3854d406"
      },
      "source": [
        "import plotly.express as px\n",
        "\n",
        "fig = px.scatter_3d(df, x='X1', y='X2', z='X1*X2',\n",
        "              color='Y')\n",
        "fig.show()"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
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              "                    window.PLOTLYENV=window.PLOTLYENV || {};\n",
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W2ibx8D8o71D"
      },
      "source": [
        "This isn't really a desired sort of kernel we'd like to use, so let's plot ${x_1^2}$ and ${x_2^2}$ on the x, and y axes. "
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    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "id": "Ad7E-QggVvDl",
        "outputId": "3f2a1ec0-901f-43f7-df0a-2567ac99eb96"
      },
      "source": [
        "#Adding higher order terms as new features to increase it's complexity\n",
        "fig = px.scatter_3d(df, x='X1_Square', y='X1_Square', z='X1*X2',\n",
        "              color='Y')\n",
        "fig.show()\n",
        "\n"
      ],
      "execution_count": 13,
      "outputs": [
        {
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          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "71uhB6sSWTMC",
        "outputId": "6c02816e-6b80-48bc-af0a-f824f4eaf3a6"
      },
      "source": [
        "classifier = SVC(kernel=\"linear\")\n",
        "classifier.fit(X_train, y_train)\n",
        "y_pred = classifier.predict(X_test)\n",
        "accuracy_score(y_test, y_pred)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 55
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jsm59x87WX9u"
      },
      "source": [
        "So, even a polynomial kernel works well and does a good job in classifying this scatter plot. "
      ]
    }
  ]
}