Crypto_Clustering.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import required libraries and dependencies\n",
    "import pandas as pd\n",
    "import hvplot.pandas\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>price_change_percentage_24h</th>\n",
       "      <th>price_change_percentage_7d</th>\n",
       "      <th>price_change_percentage_14d</th>\n",
       "      <th>price_change_percentage_30d</th>\n",
       "      <th>price_change_percentage_60d</th>\n",
       "      <th>price_change_percentage_200d</th>\n",
       "      <th>price_change_percentage_1y</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>coin_id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bitcoin</th>\n",
       "      <td>1.08388</td>\n",
       "      <td>7.60278</td>\n",
       "      <td>6.57509</td>\n",
       "      <td>7.67258</td>\n",
       "      <td>-3.25185</td>\n",
       "      <td>83.51840</td>\n",
       "      <td>37.51761</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ethereum</th>\n",
       "      <td>0.22392</td>\n",
       "      <td>10.38134</td>\n",
       "      <td>4.80849</td>\n",
       "      <td>0.13169</td>\n",
       "      <td>-12.88890</td>\n",
       "      <td>186.77418</td>\n",
       "      <td>101.96023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tether</th>\n",
       "      <td>-0.21173</td>\n",
       "      <td>0.04935</td>\n",
       "      <td>0.00640</td>\n",
       "      <td>-0.04237</td>\n",
       "      <td>0.28037</td>\n",
       "      <td>-0.00542</td>\n",
       "      <td>0.01954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ripple</th>\n",
       "      <td>-0.37819</td>\n",
       "      <td>-0.60926</td>\n",
       "      <td>2.24984</td>\n",
       "      <td>0.23455</td>\n",
       "      <td>-17.55245</td>\n",
       "      <td>39.53888</td>\n",
       "      <td>-16.60193</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bitcoin-cash</th>\n",
       "      <td>2.90585</td>\n",
       "      <td>17.09717</td>\n",
       "      <td>14.75334</td>\n",
       "      <td>15.74903</td>\n",
       "      <td>-13.71793</td>\n",
       "      <td>21.66042</td>\n",
       "      <td>14.49384</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>binancecoin</th>\n",
       "      <td>2.10423</td>\n",
       "      <td>12.85511</td>\n",
       "      <td>6.80688</td>\n",
       "      <td>0.05865</td>\n",
       "      <td>36.33486</td>\n",
       "      <td>155.61937</td>\n",
       "      <td>69.69195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>chainlink</th>\n",
       "      <td>-0.23935</td>\n",
       "      <td>20.69459</td>\n",
       "      <td>9.30098</td>\n",
       "      <td>-11.21747</td>\n",
       "      <td>-43.69522</td>\n",
       "      <td>403.22917</td>\n",
       "      <td>325.13186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cardano</th>\n",
       "      <td>0.00322</td>\n",
       "      <td>13.99302</td>\n",
       "      <td>5.55476</td>\n",
       "      <td>10.10553</td>\n",
       "      <td>-22.84776</td>\n",
       "      <td>264.51418</td>\n",
       "      <td>156.09756</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>litecoin</th>\n",
       "      <td>-0.06341</td>\n",
       "      <td>6.60221</td>\n",
       "      <td>7.28931</td>\n",
       "      <td>1.21662</td>\n",
       "      <td>-17.23960</td>\n",
       "      <td>27.49919</td>\n",
       "      <td>-12.66408</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bitcoin-cash-sv</th>\n",
       "      <td>0.92530</td>\n",
       "      <td>3.29641</td>\n",
       "      <td>-1.86656</td>\n",
       "      <td>2.88926</td>\n",
       "      <td>-24.87434</td>\n",
       "      <td>7.42562</td>\n",
       "      <td>93.73082</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 price_change_percentage_24h  price_change_percentage_7d  \\\n",
       "coin_id                                                                    \n",
       "bitcoin                              1.08388                     7.60278   \n",
       "ethereum                             0.22392                    10.38134   \n",
       "tether                              -0.21173                     0.04935   \n",
       "ripple                              -0.37819                    -0.60926   \n",
       "bitcoin-cash                         2.90585                    17.09717   \n",
       "binancecoin                          2.10423                    12.85511   \n",
       "chainlink                           -0.23935                    20.69459   \n",
       "cardano                              0.00322                    13.99302   \n",
       "litecoin                            -0.06341                     6.60221   \n",
       "bitcoin-cash-sv                      0.92530                     3.29641   \n",
       "\n",
       "                 price_change_percentage_14d  price_change_percentage_30d  \\\n",
       "coin_id                                                                     \n",
       "bitcoin                              6.57509                      7.67258   \n",
       "ethereum                             4.80849                      0.13169   \n",
       "tether                               0.00640                     -0.04237   \n",
       "ripple                               2.24984                      0.23455   \n",
       "bitcoin-cash                        14.75334                     15.74903   \n",
       "binancecoin                          6.80688                      0.05865   \n",
       "chainlink                            9.30098                    -11.21747   \n",
       "cardano                              5.55476                     10.10553   \n",
       "litecoin                             7.28931                      1.21662   \n",
       "bitcoin-cash-sv                     -1.86656                      2.88926   \n",
       "\n",
       "                 price_change_percentage_60d  price_change_percentage_200d  \\\n",
       "coin_id                                                                      \n",
       "bitcoin                             -3.25185                      83.51840   \n",
       "ethereum                           -12.88890                     186.77418   \n",
       "tether                               0.28037                      -0.00542   \n",
       "ripple                             -17.55245                      39.53888   \n",
       "bitcoin-cash                       -13.71793                      21.66042   \n",
       "binancecoin                         36.33486                     155.61937   \n",
       "chainlink                          -43.69522                     403.22917   \n",
       "cardano                            -22.84776                     264.51418   \n",
       "litecoin                           -17.23960                      27.49919   \n",
       "bitcoin-cash-sv                    -24.87434                       7.42562   \n",
       "\n",
       "                 price_change_percentage_1y  \n",
       "coin_id                                      \n",
       "bitcoin                            37.51761  \n",
       "ethereum                          101.96023  \n",
       "tether                              0.01954  \n",
       "ripple                            -16.60193  \n",
       "bitcoin-cash                       14.49384  \n",
       "binancecoin                        69.69195  \n",
       "chainlink                         325.13186  \n",
       "cardano                           156.09756  \n",
       "litecoin                          -12.66408  \n",
       "bitcoin-cash-sv                    93.73082  "
      ]
     },
     "execution_count": 187,
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     "output_type": "execute_result"
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   ],
   "source": [
    "# Load the data into a Pandas DataFrame\n",
    "df_market_data = pd.read_csv(\n",
    "    \"Resources/crypto_market_data.csv\",\n",
    "    index_col=\"coin_id\")\n",
    "\n",
    "# Display sample data\n",
    "df_market_data.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>price_change_percentage_24h</th>\n",
       "      <th>price_change_percentage_7d</th>\n",
       "      <th>price_change_percentage_14d</th>\n",
       "      <th>price_change_percentage_30d</th>\n",
       "      <th>price_change_percentage_60d</th>\n",
       "      <th>price_change_percentage_200d</th>\n",
       "      <th>price_change_percentage_1y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>41.000000</td>\n",
       "      <td>41.000000</td>\n",
       "      <td>41.000000</td>\n",
       "      <td>41.000000</td>\n",
       "      <td>41.000000</td>\n",
       "      <td>41.000000</td>\n",
       "      <td>41.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-0.269686</td>\n",
       "      <td>4.497147</td>\n",
       "      <td>0.185787</td>\n",
       "      <td>1.545693</td>\n",
       "      <td>-0.094119</td>\n",
       "      <td>236.537432</td>\n",
       "      <td>347.667956</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.694793</td>\n",
       "      <td>6.375218</td>\n",
       "      <td>8.376939</td>\n",
       "      <td>26.344218</td>\n",
       "      <td>47.365803</td>\n",
       "      <td>435.225304</td>\n",
       "      <td>1247.842884</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-13.527860</td>\n",
       "      <td>-6.094560</td>\n",
       "      <td>-18.158900</td>\n",
       "      <td>-34.705480</td>\n",
       "      <td>-44.822480</td>\n",
       "      <td>-0.392100</td>\n",
       "      <td>-17.567530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-0.608970</td>\n",
       "      <td>0.047260</td>\n",
       "      <td>-5.026620</td>\n",
       "      <td>-10.438470</td>\n",
       "      <td>-25.907990</td>\n",
       "      <td>21.660420</td>\n",
       "      <td>0.406170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>-0.063410</td>\n",
       "      <td>3.296410</td>\n",
       "      <td>0.109740</td>\n",
       "      <td>-0.042370</td>\n",
       "      <td>-7.544550</td>\n",
       "      <td>83.905200</td>\n",
       "      <td>69.691950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.612090</td>\n",
       "      <td>7.602780</td>\n",
       "      <td>5.510740</td>\n",
       "      <td>4.578130</td>\n",
       "      <td>0.657260</td>\n",
       "      <td>216.177610</td>\n",
       "      <td>168.372510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>4.840330</td>\n",
       "      <td>20.694590</td>\n",
       "      <td>24.239190</td>\n",
       "      <td>140.795700</td>\n",
       "      <td>223.064370</td>\n",
       "      <td>2227.927820</td>\n",
       "      <td>7852.089700</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       price_change_percentage_24h  price_change_percentage_7d  \\\n",
       "count                    41.000000                   41.000000   \n",
       "mean                     -0.269686                    4.497147   \n",
       "std                       2.694793                    6.375218   \n",
       "min                     -13.527860                   -6.094560   \n",
       "25%                      -0.608970                    0.047260   \n",
       "50%                      -0.063410                    3.296410   \n",
       "75%                       0.612090                    7.602780   \n",
       "max                       4.840330                   20.694590   \n",
       "\n",
       "       price_change_percentage_14d  price_change_percentage_30d  \\\n",
       "count                    41.000000                    41.000000   \n",
       "mean                      0.185787                     1.545693   \n",
       "std                       8.376939                    26.344218   \n",
       "min                     -18.158900                   -34.705480   \n",
       "25%                      -5.026620                   -10.438470   \n",
       "50%                       0.109740                    -0.042370   \n",
       "75%                       5.510740                     4.578130   \n",
       "max                      24.239190                   140.795700   \n",
       "\n",
       "       price_change_percentage_60d  price_change_percentage_200d  \\\n",
       "count                    41.000000                     41.000000   \n",
       "mean                     -0.094119                    236.537432   \n",
       "std                      47.365803                    435.225304   \n",
       "min                     -44.822480                     -0.392100   \n",
       "25%                     -25.907990                     21.660420   \n",
       "50%                      -7.544550                     83.905200   \n",
       "75%                       0.657260                    216.177610   \n",
       "max                     223.064370                   2227.927820   \n",
       "\n",
       "       price_change_percentage_1y  \n",
       "count                   41.000000  \n",
       "mean                   347.667956  \n",
       "std                   1247.842884  \n",
       "min                    -17.567530  \n",
       "25%                      0.406170  \n",
       "50%                     69.691950  \n",
       "75%                    168.372510  \n",
       "max                   7852.089700  "
      ]
     },
     "execution_count": 188,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "# Generate summary statistics\n",
    "df_market_data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
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fa-exclamation-triangle\"],[\"tagName\",\"i\"],[\"color\",\"white\"]]}]]},{\"type\":\"map\",\"entries\":[[\"type\",\"info\"],[\"background\",\"#007bff\"],[\"icon\",{\"type\":\"map\",\"entries\":[[\"className\",\"fas fa-info-circle\"],[\"tagName\",\"i\"],[\"color\",\"white\"]]}]]}]}]},{\"type\":\"model\",\"name\":\"Notification\",\"properties\":[{\"name\":\"background\",\"kind\":\"Any\",\"default\":null},{\"name\":\"duration\",\"kind\":\"Any\",\"default\":3000},{\"name\":\"icon\",\"kind\":\"Any\",\"default\":null},{\"name\":\"message\",\"kind\":\"Any\",\"default\":\"\"},{\"name\":\"notification_type\",\"kind\":\"Any\",\"default\":null},{\"name\":\"_destroyed\",\"kind\":\"Any\",\"default\":false}]},{\"type\":\"model\",\"name\":\"TemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"BootstrapTemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"MaterialTemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]}]}};\n",
       "  var render_items = [{\"docid\":\"203d6bff-0523-43c9-9eba-3d96f1ee063f\",\"roots\":{\"p6391\":\"d712647a-f0ed-4219-9df5-0f81b879180c\"},\"root_ids\":[\"p6391\"]}];\n",
       "  var docs = Object.values(docs_json)\n",
       "  if (!docs) {\n",
       "    return\n",
       "  }\n",
       "  const py_version = docs[0].version.replace('rc', '-rc.').replace('.dev', '-dev.')\n",
       "  const is_dev = py_version.indexOf(\"+\") !== -1 || py_version.indexOf(\"-\") !== -1\n",
       "  function embed_document(root) {\n",
       "    var Bokeh = get_bokeh(root)\n",
       "    Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "    for (const render_item of render_items) {\n",
       "      for (const root_id of render_item.root_ids) {\n",
       "\tconst id_el = document.getElementById(root_id)\n",
       "\tif (id_el.children.length && (id_el.children[0].className === 'bk-root')) {\n",
       "\t  const root_el = id_el.children[0]\n",
       "\t  root_el.id = root_el.id + '-rendered'\n",
       "\t}\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "  function get_bokeh(root) {\n",
       "    if (root.Bokeh === undefined) {\n",
       "      return null\n",
       "    } else if (root.Bokeh.version !== py_version && !is_dev) {\n",
       "      if (root.Bokeh.versions === undefined || !root.Bokeh.versions.has(py_version)) {\n",
       "\treturn null\n",
       "      }\n",
       "      return root.Bokeh.versions.get(py_version);\n",
       "    } else if (root.Bokeh.version === py_version) {\n",
       "      return root.Bokeh\n",
       "    }\n",
       "    return null\n",
       "  }\n",
       "  function is_loaded(root) {\n",
       "    var Bokeh = get_bokeh(root)\n",
       "    return (Bokeh != null && Bokeh.Panel !== undefined)\n",
       "  }\n",
       "  if (is_loaded(root)) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (is_loaded(root)) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else if (document.readyState == \"complete\") {\n",
       "        attempts++;\n",
       "        if (attempts > 200) {\n",
       "          clearInterval(timer);\n",
       "\t  var Bokeh = get_bokeh(root)\n",
       "\t  if (Bokeh == null || Bokeh.Panel == null) {\n",
       "            console.warn(\"Panel: ERROR: Unable to run Panel code because Bokeh or Panel library is missing\");\n",
       "\t  } else {\n",
       "\t    console.warn(\"Panel: WARNING: Attempting to render but not all required libraries could be resolved.\")\n",
       "\t    embed_document(root)\n",
       "\t  }\n",
       "        }\n",
       "      }\n",
       "    }, 25, root)\n",
       "  }\n",
       "})(window);</script>"
      ],
      "text/plain": [
       ":NdOverlay   [Variable]\n",
       "   :Curve   [coin_id]   (value)"
      ]
     },
     "execution_count": 189,
     "metadata": {
      "application/vnd.holoviews_exec.v0+json": {
       "id": "p6391"
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plot your data to see what's in your DataFrame\n",
    "df_market_data.hvplot.line(\n",
    "    width=800,\n",
    "    height=400,\n",
    "    rot=90\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prepare the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 5.08529366e-01  4.93193071e-01  7.72200433e-01  2.35459633e-01\n",
      "  -6.74950963e-02 -3.55953481e-01 -2.51636882e-01]\n",
      " [ 1.85445894e-01  9.34445040e-01  5.58692121e-01 -5.43409317e-02\n",
      "  -2.73482725e-01 -1.15759474e-01 -1.99352110e-01]\n",
      " [ 2.17739616e-02 -7.06336853e-01 -2.16804207e-02 -6.10301536e-02\n",
      "   8.00452481e-03 -5.50246924e-01 -2.82060506e-01]\n",
      " [-4.07643829e-02 -8.10928066e-01  2.49457974e-01 -5.03879651e-02\n",
      "  -3.73164019e-01 -4.58258816e-01 -2.95546142e-01]\n",
      " [ 1.19303608e+00  2.00095907e+00  1.76061001e+00  5.45842065e-01\n",
      "  -2.91202870e-01 -4.99847761e-01 -2.70316950e-01]\n",
      " [ 8.91870708e-01  1.32729453e+00  8.00214184e-01 -5.71478992e-02\n",
      "   7.78653106e-01 -1.88231917e-01 -2.25532605e-01]\n",
      " [ 1.13972400e-02  2.57225091e+00  1.10164693e+00 -4.90495415e-01\n",
      "  -9.31954023e-01  3.87758986e-01 -1.82843995e-02]\n",
      " [ 1.02529802e-01  1.50800146e+00  6.48885061e-01  3.28959245e-01\n",
      "  -4.86348899e-01  6.50796233e-02 -1.55428416e-01]\n",
      " [ 7.74971820e-02  3.34296562e-01  8.58519864e-01 -1.26464730e-02\n",
      "  -3.66476990e-01 -4.86265591e-01 -2.92351214e-01]\n",
      " [ 4.48951505e-01 -1.90684278e-01 -2.48043224e-01  5.16340055e-02\n",
      "  -5.29666139e-01 -5.32960809e-01 -2.06028947e-01]\n",
      " [ 3.31279783e-01 -1.61484369e+00 -1.05452114e+00 -7.29931204e-01\n",
      "  -3.50155382e-01 -2.28656819e-02 -3.45702165e-02]\n",
      " [ 3.43522614e-02 -7.33025788e-01 -2.31403893e-02 -6.57751738e-02\n",
      "   2.92464871e-03 -5.50599321e-01 -2.82232177e-01]\n",
      " [ 1.55709561e-01 -9.22490861e-01  1.15023636e-01 -2.37488260e-01\n",
      "  -6.42836699e-01 -5.08220490e-01 -2.96329571e-01]\n",
      " [ 2.62722790e-01  1.79260243e+00  2.20266503e+00  1.43784246e+00\n",
      "   8.93864936e-01 -1.55892797e-01 -1.67644252e-01]\n",
      " [ 1.30049529e-01 -4.10175729e-02  1.47155030e-01 -5.43776301e-01\n",
      "   1.20115762e-01 -2.41118188e-01 -2.34014125e-01]\n",
      " [-1.51583411e-01  7.08195735e-01  2.58012326e-01 -6.02296039e-01\n",
      "  -9.56048701e-01 -4.49210952e-01 -1.68478608e-01]\n",
      " [-9.23202741e-01 -1.43735894e+00 -6.29962775e-01 -4.60558015e-01\n",
      "  -5.85038908e-02 -4.57282624e-01 -1.66900457e-01]\n",
      " [-2.77542986e-01 -3.85208910e-01 -1.53243165e-01 -3.71816490e-01\n",
      "  -6.56403341e-01 -3.53387283e-01 -2.70874088e-01]\n",
      " [-2.55978040e-01  1.84027440e+00  6.43564878e-01  1.16538212e-01\n",
      "  -1.51912822e-01 -1.17565353e-01 -2.15190977e-01]\n",
      " [ 1.80851132e-01 -7.04931420e-01 -1.81614685e-03 -1.43236947e-01\n",
      "   1.60603798e-02 -5.51146420e-01 -2.82309887e-01]\n",
      " [ 2.86545668e-01 -3.26301416e-01 -1.21267030e+00 -9.03133859e-01\n",
      "   2.90969825e-01 -1.81187334e-01 -1.75550428e-01]\n",
      " [ 5.15453442e-01  4.61843180e-01  7.69975432e-01  2.24045375e-01\n",
      "  -7.46741671e-02 -3.55053705e-01 -2.51623389e-01]\n",
      " [ 5.17582538e-02 -9.28380975e-01 -8.71917511e-01  5.87817038e-02\n",
      "  -1.59249637e-01 -5.12070892e-01 -2.65036119e-01]\n",
      " [-5.20315039e-02 -4.57229014e-01  3.25221197e-02 -1.84488686e-01\n",
      "  -7.08090069e-02 -4.51982345e-01 -2.62140444e-01]\n",
      " [-2.17983910e-01 -8.49381348e-01  2.97632101e-01 -1.99820170e-01\n",
      "   1.77312724e+00 -4.73610984e-02 -1.19226165e-01]\n",
      " [ 6.13385000e-02 -7.06668758e-01 -1.53208558e-02 -5.86935760e-02\n",
      "   4.01731582e-03 -5.50002649e-01 -2.81963356e-01]\n",
      " [ 2.59097324e-01  2.49508456e-01 -4.78952718e-01 -2.18996632e-01\n",
      "  -7.35815146e-01 -3.29179315e-01 -2.85309811e-01]\n",
      " [ 5.85088683e-01 -9.94231467e-01 -2.21710811e+00 -6.03897825e-01\n",
      "  -9.30422964e-01  7.71490396e-02 -1.17481544e-01]\n",
      " [-1.27467490e-01  9.29118687e-01  6.77532109e-01  2.23834007e-01\n",
      "  -4.37067731e-01 -2.65163438e-01 -2.14828585e-01]\n",
      " [-1.61218775e+00 -1.68202656e+00 -8.16920931e-01  1.14860683e+00\n",
      "   1.71264110e+00  1.50299207e+00  2.86976907e-01]\n",
      " [-2.96940167e-01  9.47631360e-02  4.00395074e-02 -3.58829654e-01\n",
      "  -5.58527342e-01 -5.35731946e-01 -2.84071416e-01]\n",
      " [-7.13122190e-02 -2.29483757e-01 -1.75543942e-01  5.18822668e-02\n",
      "  -5.51759945e-01 -5.26060334e-01 -2.73061627e-01]\n",
      " [-4.98104189e+00 -4.51782898e-02 -1.20695612e+00 -1.21212587e+00\n",
      "   4.77355426e-02  4.63238025e+00  6.08862545e+00]\n",
      " [-1.25168231e-01  5.80730108e-01 -2.02356361e-01  5.82911022e-01\n",
      "  -3.95923001e-01 -3.58240047e-01 -2.73433342e-01]\n",
      " [-1.42857388e+00 -2.55101681e-02 -1.62885923e+00 -8.60353737e-01\n",
      "  -8.40713540e-01  8.98815486e-01  2.68647377e-01]\n",
      " [ 1.91981234e+00  3.70447157e-01 -1.61976101e+00 -4.09716316e-01\n",
      "   1.69648044e+00  8.11206969e-01 -2.18878129e-02]\n",
      " [ 1.04553034e+00 -6.18328162e-01  2.90705393e+00  5.35145461e+00\n",
      "   4.76991278e+00  3.14887546e+00  1.34848839e+00]\n",
      " [-4.09044076e-01 -9.06962812e-01 -1.29898610e+00 -1.39315260e+00\n",
      "  -6.96936973e-01 -4.22834707e-01 -2.92343790e-01]\n",
      " [ 4.14710578e-01  4.14044166e-01 -4.73857773e-02 -4.65379896e-01\n",
      "   1.28184655e-01 -4.16502012e-01 -1.45469278e-01]\n",
      " [ 7.80381841e-02 -6.87745436e-01 -9.19092169e-03 -5.82143470e-02\n",
      "   7.38829646e-03 -5.50440743e-01 -2.81746818e-01]\n",
      " [ 1.21745256e+00 -6.07713570e-01 -9.07065528e-01  4.49939006e-01\n",
      "  -6.62529501e-01  5.72366557e-01 -1.32481673e-01]]\n"
     ]
    }
   ],
   "source": [
    "# Use the `StandardScaler()` module from scikit-learn to normalize the data from the CSV file\n",
    "market_data_scaled = StandardScaler().fit_transform(df_market_data)\n",
    "print(market_data_scaled)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "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",
       "        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>price_change_percentage_24h</th>\n",
       "      <th>price_change_percentage_7d</th>\n",
       "      <th>price_change_percentage_14d</th>\n",
       "      <th>price_change_percentage_30d</th>\n",
       "      <th>price_change_percentage_60d</th>\n",
       "      <th>price_change_percentage_200d</th>\n",
       "      <th>price_change_percentage_1y</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>coin_id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bitcoin</th>\n",
       "      <td>0.508529</td>\n",
       "      <td>0.493193</td>\n",
       "      <td>0.772200</td>\n",
       "      <td>0.235460</td>\n",
       "      <td>-0.067495</td>\n",
       "      <td>-0.355953</td>\n",
       "      <td>-0.251637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ethereum</th>\n",
       "      <td>0.185446</td>\n",
       "      <td>0.934445</td>\n",
       "      <td>0.558692</td>\n",
       "      <td>-0.054341</td>\n",
       "      <td>-0.273483</td>\n",
       "      <td>-0.115759</td>\n",
       "      <td>-0.199352</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tether</th>\n",
       "      <td>0.021774</td>\n",
       "      <td>-0.706337</td>\n",
       "      <td>-0.021680</td>\n",
       "      <td>-0.061030</td>\n",
       "      <td>0.008005</td>\n",
       "      <td>-0.550247</td>\n",
       "      <td>-0.282061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ripple</th>\n",
       "      <td>-0.040764</td>\n",
       "      <td>-0.810928</td>\n",
       "      <td>0.249458</td>\n",
       "      <td>-0.050388</td>\n",
       "      <td>-0.373164</td>\n",
       "      <td>-0.458259</td>\n",
       "      <td>-0.295546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bitcoin-cash</th>\n",
       "      <td>1.193036</td>\n",
       "      <td>2.000959</td>\n",
       "      <td>1.760610</td>\n",
       "      <td>0.545842</td>\n",
       "      <td>-0.291203</td>\n",
       "      <td>-0.499848</td>\n",
       "      <td>-0.270317</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              price_change_percentage_24h  price_change_percentage_7d  \\\n",
       "coin_id                                                                 \n",
       "bitcoin                          0.508529                    0.493193   \n",
       "ethereum                         0.185446                    0.934445   \n",
       "tether                           0.021774                   -0.706337   \n",
       "ripple                          -0.040764                   -0.810928   \n",
       "bitcoin-cash                     1.193036                    2.000959   \n",
       "\n",
       "              price_change_percentage_14d  price_change_percentage_30d  \\\n",
       "coin_id                                                                  \n",
       "bitcoin                          0.772200                     0.235460   \n",
       "ethereum                         0.558692                    -0.054341   \n",
       "tether                          -0.021680                    -0.061030   \n",
       "ripple                           0.249458                    -0.050388   \n",
       "bitcoin-cash                     1.760610                     0.545842   \n",
       "\n",
       "              price_change_percentage_60d  price_change_percentage_200d  \\\n",
       "coin_id                                                                   \n",
       "bitcoin                         -0.067495                     -0.355953   \n",
       "ethereum                        -0.273483                     -0.115759   \n",
       "tether                           0.008005                     -0.550247   \n",
       "ripple                          -0.373164                     -0.458259   \n",
       "bitcoin-cash                    -0.291203                     -0.499848   \n",
       "\n",
       "              price_change_percentage_1y  \n",
       "coin_id                                   \n",
       "bitcoin                        -0.251637  \n",
       "ethereum                       -0.199352  \n",
       "tether                         -0.282061  \n",
       "ripple                         -0.295546  \n",
       "bitcoin-cash                   -0.270317  "
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a DataFrame with the scaled data\n",
    "df_scaled_data = pd.DataFrame(market_data_scaled, columns=df_market_data.columns)\n",
    "#df_scaled_data\n",
    "\n",
    "# Copy the crypto names from the original data\n",
    "df_scaled_data['coin_id'] = df_market_data.index\n",
    "\n",
    "# Set the coinid column as index\n",
    "df_scaled_data = df_scaled_data.set_index('coin_id')\n",
    "\n",
    "# Display sample data\n",
    "df_scaled_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Find the Best Value for k Using the Original Data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a list with the number of k-values from 1 to 11\n",
    "k = list(range(1, 11))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create an empty list to store the inertia values\n",
    "inertia = []\n",
    "\n",
    "# Create a for loop to compute the inertia with each possible value of k\n",
    "# Inside the loop:\n",
    "# 1. Create a KMeans model using the loop counter for the n_clusters\n",
    "# 2. Fit the model to the data using `df_market_data_scaled`\n",
    "# 3. Append the model.inertia_ to the inertia list\n",
    "for i in k:\n",
    "    model = KMeans(n_clusters=i, n_init=10)\n",
    "    model.fit(df_scaled_data)\n",
    "    inertia.append(model.inertia_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "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>k</th>\n",
       "      <th>inertia</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>287.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>195.820218</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>123.190482</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>79.022435</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>65.122199</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>56.168712</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7</td>\n",
       "      <td>43.375876</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8</td>\n",
       "      <td>37.259125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9</td>\n",
       "      <td>32.825450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10</td>\n",
       "      <td>28.491724</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    k     inertia\n",
       "0   1  287.000000\n",
       "1   2  195.820218\n",
       "2   3  123.190482\n",
       "3   4   79.022435\n",
       "4   5   65.122199\n",
       "5   6   56.168712\n",
       "6   7   43.375876\n",
       "7   8   37.259125\n",
       "8   9   32.825450\n",
       "9  10   28.491724"
      ]
     },
     "execution_count": 194,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a dictionary with the data to plot the Elbow curve\n",
    "elbow_data = {'k': k, 'inertia':inertia}\n",
    "\n",
    "# Create a DataFrame with the data to plot the Elbow curve\n",
    "df_elbow_data = pd.DataFrame(elbow_data)\n",
    "df_elbow_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
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      ],
      "text/plain": [
       ":Curve   [k]   (inertia)"
      ]
     },
     "execution_count": 195,
     "metadata": {
      "application/vnd.holoviews_exec.v0+json": {
       "id": "p6559"
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plot a line chart with all the inertia values computed with \n",
    "# the different values of k to visually identify the optimal value for k.\n",
    "elbow_k = df_elbow_data.hvplot.line(\n",
    "    x='k',\n",
    "    y='inertia',\n",
    "    title='Elbow Curve',\n",
    "    xticks=k\n",
    ")\n",
    "elbow_k"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Answer the following question: \n",
    "\n",
    "**Question:** What is the best value for `k`?\n",
    "\n",
    "**Answer:** The choice is subjective, possibly 3 or 4. \n",
    "Best practice would be to try both and see which one provides the more concise clusters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cluster Cryptocurrencies with K-means Using the Original Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize the K-Means model using the best value for k\n",
    "model = KMeans(n_clusters=4, random_state=1, n_init='auto')\n",
    "#model = KMeans(n_clusters=3, random_state=1, n_init='auto')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
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      ],
      "text/plain": [
       "KMeans(n_clusters=4, n_init='auto', random_state=1)"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit the K-Means model using the scaled data\n",
    "model.fit(df_scaled_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 2 0 0 2 2 2 2 2 0 0 0 0 2 0 2 0 0 2 0 0 2 0 0 0 0 0 0 2 0 0 0 3 2 0 0 1\n",
      " 0 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "# Predict the clusters to group the cryptocurrencies using the scaled data\n",
    "cluster_labels = model.predict(df_scaled_data)\n",
    "\n",
    "# Print the resulting array of cluster values.\n",
    "print(cluster_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a copy of the DataFrame\n",
    "df_scaled_data_predict = df_scaled_data.copy() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "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>price_change_percentage_24h</th>\n",
       "      <th>price_change_percentage_7d</th>\n",
       "      <th>price_change_percentage_14d</th>\n",
       "      <th>price_change_percentage_30d</th>\n",
       "      <th>price_change_percentage_60d</th>\n",
       "      <th>price_change_percentage_200d</th>\n",
       "      <th>price_change_percentage_1y</th>\n",
       "      <th>cluster</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>coin_id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bitcoin</th>\n",
       "      <td>0.508529</td>\n",
       "      <td>0.493193</td>\n",
       "      <td>0.772200</td>\n",
       "      <td>0.235460</td>\n",
       "      <td>-0.067495</td>\n",
       "      <td>-0.355953</td>\n",
       "      <td>-0.251637</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ethereum</th>\n",
       "      <td>0.185446</td>\n",
       "      <td>0.934445</td>\n",
       "      <td>0.558692</td>\n",
       "      <td>-0.054341</td>\n",
       "      <td>-0.273483</td>\n",
       "      <td>-0.115759</td>\n",
       "      <td>-0.199352</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tether</th>\n",
       "      <td>0.021774</td>\n",
       "      <td>-0.706337</td>\n",
       "      <td>-0.021680</td>\n",
       "      <td>-0.061030</td>\n",
       "      <td>0.008005</td>\n",
       "      <td>-0.550247</td>\n",
       "      <td>-0.282061</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ripple</th>\n",
       "      <td>-0.040764</td>\n",
       "      <td>-0.810928</td>\n",
       "      <td>0.249458</td>\n",
       "      <td>-0.050388</td>\n",
       "      <td>-0.373164</td>\n",
       "      <td>-0.458259</td>\n",
       "      <td>-0.295546</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bitcoin-cash</th>\n",
       "      <td>1.193036</td>\n",
       "      <td>2.000959</td>\n",
       "      <td>1.760610</td>\n",
       "      <td>0.545842</td>\n",
       "      <td>-0.291203</td>\n",
       "      <td>-0.499848</td>\n",
       "      <td>-0.270317</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              price_change_percentage_24h  price_change_percentage_7d  \\\n",
       "coin_id                                                                 \n",
       "bitcoin                          0.508529                    0.493193   \n",
       "ethereum                         0.185446                    0.934445   \n",
       "tether                           0.021774                   -0.706337   \n",
       "ripple                          -0.040764                   -0.810928   \n",
       "bitcoin-cash                     1.193036                    2.000959   \n",
       "\n",
       "              price_change_percentage_14d  price_change_percentage_30d  \\\n",
       "coin_id                                                                  \n",
       "bitcoin                          0.772200                     0.235460   \n",
       "ethereum                         0.558692                    -0.054341   \n",
       "tether                          -0.021680                    -0.061030   \n",
       "ripple                           0.249458                    -0.050388   \n",
       "bitcoin-cash                     1.760610                     0.545842   \n",
       "\n",
       "              price_change_percentage_60d  price_change_percentage_200d  \\\n",
       "coin_id                                                                   \n",
       "bitcoin                         -0.067495                     -0.355953   \n",
       "ethereum                        -0.273483                     -0.115759   \n",
       "tether                           0.008005                     -0.550247   \n",
       "ripple                          -0.373164                     -0.458259   \n",
       "bitcoin-cash                    -0.291203                     -0.499848   \n",
       "\n",
       "              price_change_percentage_1y  cluster  \n",
       "coin_id                                            \n",
       "bitcoin                        -0.251637        2  \n",
       "ethereum                       -0.199352        2  \n",
       "tether                         -0.282061        0  \n",
       "ripple                         -0.295546        0  \n",
       "bitcoin-cash                   -0.270317        2  "
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Add a new column to the DataFrame with the predicted clusters\n",
    "df_scaled_data_predict['cluster'] = model.labels_\n",
    "\n",
    "# Display sample data\n",
    "df_scaled_data_predict.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
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      ],
      "text/plain": [
       ":NdOverlay   [cluster]\n",
       "   :Scatter   [price_change_percentage_24h]   (price_change_percentage_7d,coin_id)"
      ]
     },
     "execution_count": 201,
     "metadata": {
      "application/vnd.holoviews_exec.v0+json": {
       "id": "p6619"
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a scatter plot using hvPlot by setting \n",
    "# `x=\"price_change_percentage_24h\"` and `y=\"price_change_percentage_7d\"`. \n",
    "# Color the graph points with the labels found using K-Means and \n",
    "# add the crypto name in the `hover_cols` parameter to identify \n",
    "# the cryptocurrency represented by each data point.\n",
    "clusters_k = df_scaled_data_predict.hvplot.scatter(\n",
    "    x=\"price_change_percentage_24h\",\n",
    "    y=\"price_change_percentage_7d\",\n",
    "    by='cluster',\n",
    "    hover_cols='coin_id'\n",
    ")\n",
    "clusters_k"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimize Clusters with Principal Component Analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a PCA model instance and set `n_components=3`.\n",
    "pca = PCA(n_components=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PC1</th>\n",
       "      <th>PC2</th>\n",
       "      <th>PC3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.600667</td>\n",
       "      <td>0.842760</td>\n",
       "      <td>0.461595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.458261</td>\n",
       "      <td>0.458466</td>\n",
       "      <td>0.952877</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.433070</td>\n",
       "      <td>-0.168126</td>\n",
       "      <td>-0.641752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.471835</td>\n",
       "      <td>-0.222660</td>\n",
       "      <td>-0.479053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1.157800</td>\n",
       "      <td>2.041209</td>\n",
       "      <td>1.859715</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        PC1       PC2       PC3\n",
       "0 -0.600667  0.842760  0.461595\n",
       "1 -0.458261  0.458466  0.952877\n",
       "2 -0.433070 -0.168126 -0.641752\n",
       "3 -0.471835 -0.222660 -0.479053\n",
       "4 -1.157800  2.041209  1.859715"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use the PCA model with `fit_transform` to reduce to \n",
    "# three principal components.\n",
    "pca_data = pca.fit_transform(df_scaled_data)\n",
    "df_pca = pd.DataFrame(pca_data, columns=['PC1', 'PC2', 'PC3'])\n",
    "\n",
    "# View the first five rows of the DataFrame. \n",
    "df_pca.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.3719856 , 0.34700813, 0.17603793])"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Retrieve the explained variance to determine how much information \n",
    "# can be attributed to each principal component.\n",
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Answer the following question: \n",
    "\n",
    "**Question:** What is the total explained variance of the three principal components?\n",
    "\n",
    "**Answer:** Total explained variance is 89.5% which means that these 3 principal components \n",
    "represent a significant portion of the variability in the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PC1</th>\n",
       "      <th>PC2</th>\n",
       "      <th>PC3</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>coin_id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bitcoin</th>\n",
       "      <td>-0.600667</td>\n",
       "      <td>0.842760</td>\n",
       "      <td>0.461595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ethereum</th>\n",
       "      <td>-0.458261</td>\n",
       "      <td>0.458466</td>\n",
       "      <td>0.952877</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tether</th>\n",
       "      <td>-0.433070</td>\n",
       "      <td>-0.168126</td>\n",
       "      <td>-0.641752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ripple</th>\n",
       "      <td>-0.471835</td>\n",
       "      <td>-0.222660</td>\n",
       "      <td>-0.479053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bitcoin-cash</th>\n",
       "      <td>-1.157800</td>\n",
       "      <td>2.041209</td>\n",
       "      <td>1.859715</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   PC1       PC2       PC3\n",
       "coin_id                                   \n",
       "bitcoin      -0.600667  0.842760  0.461595\n",
       "ethereum     -0.458261  0.458466  0.952877\n",
       "tether       -0.433070 -0.168126 -0.641752\n",
       "ripple       -0.471835 -0.222660 -0.479053\n",
       "bitcoin-cash -1.157800  2.041209  1.859715"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a new DataFrame with the PCA data.\n",
    "\n",
    "# Creating a DataFrame with the PCA data\n",
    "pca_data_df = pd.DataFrame(\n",
    "    pca_data,\n",
    "    columns=['PC1', 'PC2', 'PC3']\n",
    ")\n",
    "\n",
    "#pca_data_df\n",
    "\n",
    "# Copy the crypto names from the original data\n",
    "pca_data_df['coin_id'] = df_market_data.index\n",
    "\n",
    "# Set the coinid column as index\n",
    "pca_data_df.set_index('coin_id', inplace=True)\n",
    "\n",
    "# Display sample data\n",
    "pca_data_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Find the Best Value for k Using the PCA Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a list with the number of k-values from 1 to 11\n",
    "k = list(range(1, 11))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create an empty list to store the inertia values\n",
    "inertia = []\n",
    "\n",
    "# Create a for loop to compute the inertia with each possible value of k\n",
    "# Inside the loop:\n",
    "# 1. Create a KMeans model using the loop counter for the n_clusters\n",
    "# 2. Fit the model to the data using `df_market_data_pca`\n",
    "# 3. Append the model.inertia_ to the inertia list\n",
    "for i in k:\n",
    "    k_model = KMeans(n_clusters=i, random_state=1, n_init=10)\n",
    "    k_model.fit(pca_data_df)\n",
    "    inertia.append(k_model.inertia_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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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>k</th>\n",
       "      <th>interia</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>256.874086</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>165.901994</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>93.774626</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>49.665497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>38.072792</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   k     interia\n",
       "0  1  256.874086\n",
       "1  2  165.901994\n",
       "2  3   93.774626\n",
       "3  4   49.665497\n",
       "4  5   38.072792"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a dictionary with the data to plot the Elbow curve\n",
    "elbow_data_new = {'k': k, 'interia': inertia}\n",
    "\n",
    "# Create a DataFrame with the data to plot the Elbow curve\n",
    "df_elbow_new = pd.DataFrame(elbow_data_new)\n",
    "df_elbow_new.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {},
   "outputs": [
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       "</div>\n",
       "<script type=\"application/javascript\">(function(root) {\n",
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       "  const py_version = docs[0].version.replace('rc', '-rc.').replace('.dev', '-dev.')\n",
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      ],
      "text/plain": [
       ":Curve   [k]   (interia)"
      ]
     },
     "execution_count": 209,
     "metadata": {
      "application/vnd.holoviews_exec.v0+json": {
       "id": "p6737"
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plot a line chart with all the inertia values computed with \n",
    "# the different values of k to visually identify the optimal value for k.\n",
    "elbow_pca = df_elbow_new.hvplot.line(\n",
    "    x='k',\n",
    "    y='interia',\n",
    "    title='Elbow Curve',\n",
    "    xticks=k\n",
    ")\n",
    "elbow_pca"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Answer the following questions: \n",
    "\n",
    "* **Question:** What is the best value for `k` when using the PCA data?\n",
    "\n",
    "  * **Answer:** Again the best value for k is 3 or possibly 4.\n",
    "\n",
    "\n",
    "* **Question:** Does it differ from the best k value found using the original data?\n",
    "\n",
    "  * **Answer:** There is a more distinct change in the elbow curve using the PCA data vs the original."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cluster Cryptocurrencies with K-means Using the PCA Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize the K-Means model using the best value for k\n",
    "model = KMeans(n_clusters=4, random_state=1, n_init=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [
    {
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      ],
      "text/plain": [
       "KMeans(n_clusters=4, n_init=10, random_state=1)"
      ]
     },
     "execution_count": 211,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit the K-Means model using the PCA data\n",
    "model.fit(pca_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 2 0 0 2 2 2 2 2 0 0 0 0 2 0 2 0 0 2 0 0 2 0 0 0 0 0 0 2 0 0 0 3 2 0 0 1\n",
      " 0 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "# Predict the clusters to group the cryptocurrencies using the PCA data\n",
    "clusters = model.predict(pca_data)\n",
    "# Print the resulting array of cluster values.\n",
    "print(clusters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .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>PC1</th>\n",
       "      <th>PC2</th>\n",
       "      <th>PC3</th>\n",
       "      <th>cluster</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>coin_id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bitcoin</th>\n",
       "      <td>-0.600667</td>\n",
       "      <td>0.842760</td>\n",
       "      <td>0.461595</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ethereum</th>\n",
       "      <td>-0.458261</td>\n",
       "      <td>0.458466</td>\n",
       "      <td>0.952877</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tether</th>\n",
       "      <td>-0.433070</td>\n",
       "      <td>-0.168126</td>\n",
       "      <td>-0.641752</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ripple</th>\n",
       "      <td>-0.471835</td>\n",
       "      <td>-0.222660</td>\n",
       "      <td>-0.479053</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bitcoin-cash</th>\n",
       "      <td>-1.157800</td>\n",
       "      <td>2.041209</td>\n",
       "      <td>1.859715</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   PC1       PC2       PC3  cluster\n",
       "coin_id                                            \n",
       "bitcoin      -0.600667  0.842760  0.461595        2\n",
       "ethereum     -0.458261  0.458466  0.952877        2\n",
       "tether       -0.433070 -0.168126 -0.641752        0\n",
       "ripple       -0.471835 -0.222660 -0.479053        0\n",
       "bitcoin-cash -1.157800  2.041209  1.859715        2"
      ]
     },
     "execution_count": 213,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a copy of the DataFrame with the PCA data\n",
    "df_pca_copy = pca_data_df.copy()\n",
    "\n",
    "# Add a new column to the DataFrame with the predicted clusters\n",
    "df_pca_copy['cluster'] = clusters\n",
    "\n",
    "# Display sample data\n",
    "df_pca_copy.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
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      "text/plain": [
       ":NdOverlay   [cluster]\n",
       "   :Scatter   [PC1]   (PC2,coin_id)"
      ]
     },
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   "source": [
    "# Create a scatter plot using hvPlot by setting \n",
    "# `x=\"PC1\"` and `y=\"PC2\"`. \n",
    "# Color the graph points with the labels found using K-Means and \n",
    "# add the crypto name in the `hover_cols` parameter to identify \n",
    "# the cryptocurrency represented by each data point.\n",
    "clusters_pca = df_pca_copy.hvplot.scatter(\n",
    "    x='PC1',\n",
    "    y='PC2',\n",
    "    by='cluster',\n",
    "    hover_cols='coin_id'\n",
    ")\n",
    "clusters_pca"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "### Visualize and Compare the Results\n",
    "\n",
    "In this section, you will visually analyze the cluster analysis results by contrasting the outcome with and without using the optimization techniques."
   ]
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  {
   "cell_type": "code",
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.pn-loading.pn-arc:before {\\n  background-image: url(\\\"data:image/svg+xml;base64,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\\\");\\n  background-size: auto calc(min(50%, 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fa-exclamation-triangle\"],[\"tagName\",\"i\"],[\"color\",\"white\"]]}]]},{\"type\":\"map\",\"entries\":[[\"type\",\"info\"],[\"background\",\"#007bff\"],[\"icon\",{\"type\":\"map\",\"entries\":[[\"className\",\"fas fa-info-circle\"],[\"tagName\",\"i\"],[\"color\",\"white\"]]}]]}]}]},{\"type\":\"model\",\"name\":\"Notification\",\"properties\":[{\"name\":\"background\",\"kind\":\"Any\",\"default\":null},{\"name\":\"duration\",\"kind\":\"Any\",\"default\":3000},{\"name\":\"icon\",\"kind\":\"Any\",\"default\":null},{\"name\":\"message\",\"kind\":\"Any\",\"default\":\"\"},{\"name\":\"notification_type\",\"kind\":\"Any\",\"default\":null},{\"name\":\"_destroyed\",\"kind\":\"Any\",\"default\":false}]},{\"type\":\"model\",\"name\":\"TemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"BootstrapTemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"MaterialTemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]}]}};\n",
       "  var render_items = [{\"docid\":\"c9278e22-b1fb-4dcc-b163-baf8cafcae6e\",\"roots\":{\"p7680\":\"eaf105f2-843a-4eda-95d7-f630a44a80d0\"},\"root_ids\":[\"p7680\"]}];\n",
       "  var docs = Object.values(docs_json)\n",
       "  if (!docs) {\n",
       "    return\n",
       "  }\n",
       "  const py_version = docs[0].version.replace('rc', '-rc.').replace('.dev', '-dev.')\n",
       "  const is_dev = py_version.indexOf(\"+\") !== -1 || py_version.indexOf(\"-\") !== -1\n",
       "  function embed_document(root) {\n",
       "    var Bokeh = get_bokeh(root)\n",
       "    Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "    for (const render_item of render_items) {\n",
       "      for (const root_id of render_item.root_ids) {\n",
       "\tconst id_el = document.getElementById(root_id)\n",
       "\tif (id_el.children.length && (id_el.children[0].className === 'bk-root')) {\n",
       "\t  const root_el = id_el.children[0]\n",
       "\t  root_el.id = root_el.id + '-rendered'\n",
       "\t}\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "  function get_bokeh(root) {\n",
       "    if (root.Bokeh === undefined) {\n",
       "      return null\n",
       "    } else if (root.Bokeh.version !== py_version && !is_dev) {\n",
       "      if (root.Bokeh.versions === undefined || !root.Bokeh.versions.has(py_version)) {\n",
       "\treturn null\n",
       "      }\n",
       "      return root.Bokeh.versions.get(py_version);\n",
       "    } else if (root.Bokeh.version === py_version) {\n",
       "      return root.Bokeh\n",
       "    }\n",
       "    return null\n",
       "  }\n",
       "  function is_loaded(root) {\n",
       "    var Bokeh = get_bokeh(root)\n",
       "    return (Bokeh != null && Bokeh.Panel !== undefined)\n",
       "  }\n",
       "  if (is_loaded(root)) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (is_loaded(root)) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else if (document.readyState == \"complete\") {\n",
       "        attempts++;\n",
       "        if (attempts > 200) {\n",
       "          clearInterval(timer);\n",
       "\t  var Bokeh = get_bokeh(root)\n",
       "\t  if (Bokeh == null || Bokeh.Panel == null) {\n",
       "            console.warn(\"Panel: ERROR: Unable to run Panel code because Bokeh or Panel library is missing\");\n",
       "\t  } else {\n",
       "\t    console.warn(\"Panel: WARNING: Attempting to render but not all required libraries could be resolved.\")\n",
       "\t    embed_document(root)\n",
       "\t  }\n",
       "        }\n",
       "      }\n",
       "    }, 25, root)\n",
       "  }\n",
       "})(window);</script>"
      ],
      "text/plain": [
       ":Layout\n",
       "   .Curve.I  :Curve   [k]   (inertia)\n",
       "   .Curve.II :Curve   [k]   (interia)"
      ]
     },
     "execution_count": 220,
     "metadata": {
      "application/vnd.holoviews_exec.v0+json": {
       "id": "p7680"
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Composite plot to contrast the Elbow curves\n",
    "elbow_k + elbow_pca"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.holoviews_exec.v0+json": "",
      "text/html": [
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       "  <div id=\"e6a454ee-107e-4db7-bae8-cf7ec31281c2\" data-root-id=\"p7034\" style=\"display: contents;\"></div>\n",
       "</div>\n",
       "<script type=\"application/javascript\">(function(root) {\n",
       "  var docs_json = {\"3a6c8217-1870-4527-b15f-5ce8e85f211f\":{\"version\":\"3.2.2\",\"title\":\"Bokeh Application\",\"roots\":[{\"type\":\"object\",\"name\":\"Row\",\"id\":\"p7034\",\"attributes\":{\"name\":\"Row12637\",\"tags\":[\"embedded\"],\"stylesheets\":[\"\\n:host(.pn-loading.pn-arc):before, .pn-loading.pn-arc:before {\\n  background-image: 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       "  var render_items = [{\"docid\":\"3a6c8217-1870-4527-b15f-5ce8e85f211f\",\"roots\":{\"p7034\":\"e6a454ee-107e-4db7-bae8-cf7ec31281c2\"},\"root_ids\":[\"p7034\"]}];\n",
       "  var docs = Object.values(docs_json)\n",
       "  if (!docs) {\n",
       "    return\n",
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       "  const py_version = docs[0].version.replace('rc', '-rc.').replace('.dev', '-dev.')\n",
       "  const is_dev = py_version.indexOf(\"+\") !== -1 || py_version.indexOf(\"-\") !== -1\n",
       "  function embed_document(root) {\n",
       "    var Bokeh = get_bokeh(root)\n",
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      ],
      "text/plain": [
       ":Layout\n",
       "   .NdOverlay.I  :NdOverlay   [cluster]\n",
       "      :Scatter   [price_change_percentage_24h]   (price_change_percentage_7d,coin_id)\n",
       "   .NdOverlay.II :NdOverlay   [cluster]\n",
       "      :Scatter   [PC1]   (PC2,coin_id)"
      ]
     },
     "execution_count": 216,
     "metadata": {
      "application/vnd.holoviews_exec.v0+json": {
       "id": "p7034"
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Composite plot to contrast the clusters\n",
    "clusters_k + clusters_pca"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Answer the following question: \n",
    "\n",
    "  * **Question:** After visually analyzing the cluster analysis results, what is the impact of using fewer features to cluster the data using K-Means?\n",
    "\n",
    "  * **Answer:** The PCA reduced the dimensionality of the data, making more disctint and compact clusters. Both scatter plots have the weird cluster 3 outlier, which bears more analysis. Using 3 clusters as shown below does not provide an accurate clustering of the data, putting most of the PCA data into cluster 0 and does not provide clear clustering using the original data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.holoviews_exec.v0+json": "",
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fa-exclamation-triangle\"],[\"tagName\",\"i\"],[\"color\",\"white\"]]}]]},{\"type\":\"map\",\"entries\":[[\"type\",\"info\"],[\"background\",\"#007bff\"],[\"icon\",{\"type\":\"map\",\"entries\":[[\"className\",\"fas fa-info-circle\"],[\"tagName\",\"i\"],[\"color\",\"white\"]]}]]}]}]},{\"type\":\"model\",\"name\":\"Notification\",\"properties\":[{\"name\":\"background\",\"kind\":\"Any\",\"default\":null},{\"name\":\"duration\",\"kind\":\"Any\",\"default\":3000},{\"name\":\"icon\",\"kind\":\"Any\",\"default\":null},{\"name\":\"message\",\"kind\":\"Any\",\"default\":\"\"},{\"name\":\"notification_type\",\"kind\":\"Any\",\"default\":null},{\"name\":\"_destroyed\",\"kind\":\"Any\",\"default\":false}]},{\"type\":\"model\",\"name\":\"TemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"BootstrapTemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"MaterialTemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]}]}};\n",
       "  var render_items = [{\"docid\":\"510485cb-553a-43ec-a43d-3700c0d09c6e\",\"roots\":{\"p7799\":\"bd892975-2b73-45b9-9eb0-c887d696c6e3\"},\"root_ids\":[\"p7799\"]}];\n",
       "  var docs = Object.values(docs_json)\n",
       "  if (!docs) {\n",
       "    return\n",
       "  }\n",
       "  const py_version = docs[0].version.replace('rc', '-rc.').replace('.dev', '-dev.')\n",
       "  const is_dev = py_version.indexOf(\"+\") !== -1 || py_version.indexOf(\"-\") !== -1\n",
       "  function embed_document(root) {\n",
       "    var Bokeh = get_bokeh(root)\n",
       "    Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "    for (const render_item of render_items) {\n",
       "      for (const root_id of render_item.root_ids) {\n",
       "\tconst id_el = document.getElementById(root_id)\n",
       "\tif (id_el.children.length && (id_el.children[0].className === 'bk-root')) {\n",
       "\t  const root_el = id_el.children[0]\n",
       "\t  root_el.id = root_el.id + '-rendered'\n",
       "\t}\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "  function get_bokeh(root) {\n",
       "    if (root.Bokeh === undefined) {\n",
       "      return null\n",
       "    } else if (root.Bokeh.version !== py_version && !is_dev) {\n",
       "      if (root.Bokeh.versions === undefined || !root.Bokeh.versions.has(py_version)) {\n",
       "\treturn null\n",
       "      }\n",
       "      return root.Bokeh.versions.get(py_version);\n",
       "    } else if (root.Bokeh.version === py_version) {\n",
       "      return root.Bokeh\n",
       "    }\n",
       "    return null\n",
       "  }\n",
       "  function is_loaded(root) {\n",
       "    var Bokeh = get_bokeh(root)\n",
       "    return (Bokeh != null && Bokeh.Panel !== undefined)\n",
       "  }\n",
       "  if (is_loaded(root)) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (is_loaded(root)) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else if (document.readyState == \"complete\") {\n",
       "        attempts++;\n",
       "        if (attempts > 200) {\n",
       "          clearInterval(timer);\n",
       "\t  var Bokeh = get_bokeh(root)\n",
       "\t  if (Bokeh == null || Bokeh.Panel == null) {\n",
       "            console.warn(\"Panel: ERROR: Unable to run Panel code because Bokeh or Panel library is missing\");\n",
       "\t  } else {\n",
       "\t    console.warn(\"Panel: WARNING: Attempting to render but not all required libraries could be resolved.\")\n",
       "\t    embed_document(root)\n",
       "\t  }\n",
       "        }\n",
       "      }\n",
       "    }, 25, root)\n",
       "  }\n",
       "})(window);</script>"
      ],
      "text/plain": [
       ":NdOverlay   [cluster]\n",
       "   :Scatter   [price_change_percentage_24h]   (price_change_percentage_7d,coin_id)"
      ]
     },
     "execution_count": 221,
     "metadata": {
      "application/vnd.holoviews_exec.v0+json": {
       "id": "p7799"
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# model = KMeans(n_clusters=3, random_state=1, n_init='auto')\n",
    "# model.fit(df_scaled_data)\n",
    "# cluster_labels = model.predict(df_scaled_data)\n",
    "# df_scaled_data_predict = df_scaled_data.copy() \n",
    "# df_scaled_data_predict['cluster'] = model.labels_\n",
    "# clusters_k3 = df_scaled_data_predict.hvplot.scatter(\n",
    "#     x=\"price_change_percentage_24h\",\n",
    "#     y=\"price_change_percentage_7d\",\n",
    "#     by='cluster',\n",
    "#     hover_cols='coin_id'\n",
    "# )\n",
    "\n",
    "# clusters_k3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.holoviews_exec.v0+json": "",
      "text/html": [
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       "</div>\n",
       "<script type=\"application/javascript\">(function(root) {\n",
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fa-exclamation-triangle\"],[\"tagName\",\"i\"],[\"color\",\"white\"]]}]]},{\"type\":\"map\",\"entries\":[[\"type\",\"info\"],[\"background\",\"#007bff\"],[\"icon\",{\"type\":\"map\",\"entries\":[[\"className\",\"fas fa-info-circle\"],[\"tagName\",\"i\"],[\"color\",\"white\"]]}]]}]}]},{\"type\":\"model\",\"name\":\"Notification\",\"properties\":[{\"name\":\"background\",\"kind\":\"Any\",\"default\":null},{\"name\":\"duration\",\"kind\":\"Any\",\"default\":3000},{\"name\":\"icon\",\"kind\":\"Any\",\"default\":null},{\"name\":\"message\",\"kind\":\"Any\",\"default\":\"\"},{\"name\":\"notification_type\",\"kind\":\"Any\",\"default\":null},{\"name\":\"_destroyed\",\"kind\":\"Any\",\"default\":false}]},{\"type\":\"model\",\"name\":\"TemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"BootstrapTemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"MaterialTemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]}]}};\n",
       "  var render_items = [{\"docid\":\"aa3e0062-a5d3-482e-ade0-7f77633cb39a\",\"roots\":{\"p7898\":\"fd09ecd5-d9c3-451a-b7ca-a2cd176a2fc2\"},\"root_ids\":[\"p7898\"]}];\n",
       "  var docs = Object.values(docs_json)\n",
       "  if (!docs) {\n",
       "    return\n",
       "  }\n",
       "  const py_version = docs[0].version.replace('rc', '-rc.').replace('.dev', '-dev.')\n",
       "  const is_dev = py_version.indexOf(\"+\") !== -1 || py_version.indexOf(\"-\") !== -1\n",
       "  function embed_document(root) {\n",
       "    var Bokeh = get_bokeh(root)\n",
       "    Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "    for (const render_item of render_items) {\n",
       "      for (const root_id of render_item.root_ids) {\n",
       "\tconst id_el = document.getElementById(root_id)\n",
       "\tif (id_el.children.length && (id_el.children[0].className === 'bk-root')) {\n",
       "\t  const root_el = id_el.children[0]\n",
       "\t  root_el.id = root_el.id + '-rendered'\n",
       "\t}\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "  function get_bokeh(root) {\n",
       "    if (root.Bokeh === undefined) {\n",
       "      return null\n",
       "    } else if (root.Bokeh.version !== py_version && !is_dev) {\n",
       "      if (root.Bokeh.versions === undefined || !root.Bokeh.versions.has(py_version)) {\n",
       "\treturn null\n",
       "      }\n",
       "      return root.Bokeh.versions.get(py_version);\n",
       "    } else if (root.Bokeh.version === py_version) {\n",
       "      return root.Bokeh\n",
       "    }\n",
       "    return null\n",
       "  }\n",
       "  function is_loaded(root) {\n",
       "    var Bokeh = get_bokeh(root)\n",
       "    return (Bokeh != null && Bokeh.Panel !== undefined)\n",
       "  }\n",
       "  if (is_loaded(root)) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (is_loaded(root)) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else if (document.readyState == \"complete\") {\n",
       "        attempts++;\n",
       "        if (attempts > 200) {\n",
       "          clearInterval(timer);\n",
       "\t  var Bokeh = get_bokeh(root)\n",
       "\t  if (Bokeh == null || Bokeh.Panel == null) {\n",
       "            console.warn(\"Panel: ERROR: Unable to run Panel code because Bokeh or Panel library is missing\");\n",
       "\t  } else {\n",
       "\t    console.warn(\"Panel: WARNING: Attempting to render but not all required libraries could be resolved.\")\n",
       "\t    embed_document(root)\n",
       "\t  }\n",
       "        }\n",
       "      }\n",
       "    }, 25, root)\n",
       "  }\n",
       "})(window);</script>"
      ],
      "text/plain": [
       ":NdOverlay   [cluster]\n",
       "   :Scatter   [PC1]   (PC2,coin_id)"
      ]
     },
     "execution_count": 222,
     "metadata": {
      "application/vnd.holoviews_exec.v0+json": {
       "id": "p7898"
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# model = KMeans(n_clusters=3, random_state=1, n_init=10)\n",
    "# model.fit(pca_data)\n",
    "# clusters = model.predict(pca_data)\n",
    "# df_pca_copy = pca_data_df.copy()\n",
    "# df_pca_copy['cluster'] = clusters\n",
    "# clusters_pca3 = df_pca_copy.hvplot.scatter(\n",
    "#     x='PC1',\n",
    "#     y='PC2',\n",
    "#     by='cluster',\n",
    "#     hover_cols='coin_id'\n",
    "# )\n",
    "# clusters_pca3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.holoviews_exec.v0+json": "",
      "text/html": [
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       "  <div id=\"b93d8ad8-f7b2-4096-a492-7bfa70ee7815\" data-root-id=\"p7997\" style=\"display: contents;\"></div>\n",
       "</div>\n",
       "<script type=\"application/javascript\">(function(root) {\n",
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       "  var render_items = [{\"docid\":\"4e3c463d-d7e4-4424-a540-282fe1fef349\",\"roots\":{\"p7997\":\"b93d8ad8-f7b2-4096-a492-7bfa70ee7815\"},\"root_ids\":[\"p7997\"]}];\n",
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       "    return\n",
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       "  function embed_document(root) {\n",
       "    var Bokeh = get_bokeh(root)\n",
       "    Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "    for (const render_item of render_items) {\n",
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       "      return null\n",
       "    } else if (root.Bokeh.version !== py_version && !is_dev) {\n",
       "      if (root.Bokeh.versions === undefined || !root.Bokeh.versions.has(py_version)) {\n",
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       "    } else if (root.Bokeh.version === py_version) {\n",
       "      return root.Bokeh\n",
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       "    var Bokeh = get_bokeh(root)\n",
       "    return (Bokeh != null && Bokeh.Panel !== undefined)\n",
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       "\t  var Bokeh = get_bokeh(root)\n",
       "\t  if (Bokeh == null || Bokeh.Panel == null) {\n",
       "            console.warn(\"Panel: ERROR: Unable to run Panel code because Bokeh or Panel library is missing\");\n",
       "\t  } else {\n",
       "\t    console.warn(\"Panel: WARNING: Attempting to render but not all required libraries could be resolved.\")\n",
       "\t    embed_document(root)\n",
       "\t  }\n",
       "        }\n",
       "      }\n",
       "    }, 25, root)\n",
       "  }\n",
       "})(window);</script>"
      ],
      "text/plain": [
       ":Layout\n",
       "   .NdOverlay.I  :NdOverlay   [cluster]\n",
       "      :Scatter   [price_change_percentage_24h]   (price_change_percentage_7d,coin_id)\n",
       "   .NdOverlay.II :NdOverlay   [cluster]\n",
       "      :Scatter   [PC1]   (PC2,coin_id)"
      ]
     },
     "execution_count": 223,
     "metadata": {
      "application/vnd.holoviews_exec.v0+json": {
       "id": "p7997"
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#clusters_k3 + clusters_pca3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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