Crypto_Clustering.ipynb

{
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    {
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       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
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       "\n",
       "  var force = true;\n",
       "  var py_version = '3.2.2'.replace('rc', '-rc.').replace('.dev', '-dev.');\n",
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       "\ton_load()\n",
       "\tcontinue;\n",
       "      }\n",
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       "      element.rel = \"stylesheet\";\n",
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       "      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
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       "      var urls = ['https://cdn.holoviz.org/panel/1.2.2/dist/bundled/gridstack/gridstack@7.2.3/dist/gridstack-all.js'];\n",
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       "      var urls = ['https://cdn.holoviz.org/panel/1.2.2/dist/bundled/notificationarea/notyf@3/notyf.min.js'];\n",
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       "\tif (!window.requirejs) {\n",
       "\t  on_load();\n",
       "\t}\n",
       "\tcontinue;\n",
       "      }\n",
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       "      element.onerror = on_error;\n",
       "      element.async = false;\n",
       "      element.src = url;\n",
       "      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.head.appendChild(element);\n",
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       "      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.head.appendChild(element);\n",
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       "    } else if (!root._bokeh_failed_load) {\n",
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       "      console.log(\"Bokeh: BokehJS was loaded multiple times but one version failed to initialize.\");\n",
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       "\tconsole.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
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i < links.length; i++) {\n      var link = links[i]\n      if (link.href != null) {\n\texisting_stylesheets.push(link.href)\n      }\n    }\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      if (existing_stylesheets.indexOf(url) !== -1) {\n\ton_load()\n\tcontinue;\n      }\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }    if (((window['jsPanel'] !== undefined) && (!(window['jsPanel'] instanceof HTMLElement))) || window.requirejs) {\n      var urls = ['https://cdn.holoviz.org/panel/1.2.2/dist/bundled/floatpanel/jspanel4@4.12.0/dist/jspanel.js', 'https://cdn.holoviz.org/panel/1.2.2/dist/bundled/floatpanel/jspanel4@4.12.0/dist/extensions/modal/jspanel.modal.js', 'https://cdn.holoviz.org/panel/1.2.2/dist/bundled/floatpanel/jspanel4@4.12.0/dist/extensions/tooltip/jspanel.tooltip.js', 'https://cdn.holoviz.org/panel/1.2.2/dist/bundled/floatpanel/jspanel4@4.12.0/dist/extensions/hint/jspanel.hint.js', 'https://cdn.holoviz.org/panel/1.2.2/dist/bundled/floatpanel/jspanel4@4.12.0/dist/extensions/layout/jspanel.layout.js', 'https://cdn.holoviz.org/panel/1.2.2/dist/bundled/floatpanel/jspanel4@4.12.0/dist/extensions/contextmenu/jspanel.contextmenu.js', 'https://cdn.holoviz.org/panel/1.2.2/dist/bundled/floatpanel/jspanel4@4.12.0/dist/extensions/dock/jspanel.dock.js'];\n      for (var i = 0; i < urls.length; i++) {\n        skip.push(urls[i])\n      }\n    }    if (((window['GridStack'] !== undefined) && (!(window['GridStack'] instanceof HTMLElement))) || window.requirejs) {\n      var urls = ['https://cdn.holoviz.org/panel/1.2.2/dist/bundled/gridstack/gridstack@7.2.3/dist/gridstack-all.js'];\n      for (var i = 0; i < urls.length; i++) {\n        skip.push(urls[i])\n      }\n    }    if (((window['Notyf'] !== undefined) && (!(window['Notyf'] instanceof HTMLElement))) || window.requirejs) {\n      var urls = ['https://cdn.holoviz.org/panel/1.2.2/dist/bundled/notificationarea/notyf@3/notyf.min.js'];\n      for (var i = 0; i < urls.length; i++) {\n        skip.push(urls[i])\n      }\n    }    var existing_scripts = []\n    var scripts = document.getElementsByTagName('script')\n    for (var i = 0; i < scripts.length; i++) {\n      var script = scripts[i]\n      if (script.src != null) {\n\texisting_scripts.push(script.src)\n      }\n    }\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      if (skip.indexOf(url) !== -1 || existing_scripts.indexOf(url) !== -1) {\n\tif (!window.requirejs) {\n\t  on_load();\n\t}\n\tcontinue;\n      }\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n    for (var i = 0; i < js_modules.length; i++) {\n      var url = js_modules[i];\n      if (skip.indexOf(url) !== -1 || existing_scripts.indexOf(url) !== -1) {\n\tif (!window.requirejs) {\n\t  on_load();\n\t}\n\tcontinue;\n      }\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      element.type = \"module\";\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n    for (const name in js_exports) {\n      var url = js_exports[name];\n      if (skip.indexOf(url) >= 0 || root[name] != null) {\n\tif (!window.requirejs) {\n\t  on_load();\n\t}\n\tcontinue;\n      }\n      var element = document.createElement('script');\n      element.onerror = on_error;\n      element.async = false;\n      element.type = \"module\";\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      element.textContent = `\n      import ${name} from \"${url}\"\n      window.${name} = ${name}\n      window._bokeh_on_load()\n      `\n      document.head.appendChild(element);\n    }\n    if (!js_urls.length && !js_modules.length) {\n      on_load()\n    }\n  };\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  var js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-3.2.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-3.2.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-3.2.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-3.2.2.min.js\", \"https://cdn.holoviz.org/panel/1.2.2/dist/panel.min.js\"];\n  var js_modules = [];\n  var js_exports = {};\n  var css_urls = [];\n  var inline_js = [    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\nfunction(Bokeh) {} // ensure no trailing comma for IE\n  ];\n\n  function run_inline_js() {\n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }\n      // Cache old bokeh versions\n      if (Bokeh != undefined && !reloading) {\n\tvar NewBokeh = root.Bokeh;\n\tif (Bokeh.versions === undefined) {\n\t  Bokeh.versions = new Map();\n\t}\n\tif (NewBokeh.version !== Bokeh.version) {\n\t  Bokeh.versions.set(NewBokeh.version, NewBokeh)\n\t}\n\troot.Bokeh = Bokeh;\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    }\n    root._bokeh_is_initializing = false\n  }\n\n  function load_or_wait() {\n    // Implement a backoff loop that tries to ensure we do not load multiple\n    // versions of Bokeh and its dependencies at the same time.\n    // In recent versions we use the root._bokeh_is_initializing flag\n    // to determine whether there is an ongoing attempt to initialize\n    // bokeh, however for backward compatibility we also try to ensure\n    // that we do not start loading a newer (Panel>=1.0 and Bokeh>3) version\n    // before older versions are fully initialized.\n    if (root._bokeh_is_initializing && Date.now() > root._bokeh_timeout) {\n      root._bokeh_is_initializing = false;\n      root._bokeh_onload_callbacks = undefined;\n      console.log(\"Bokeh: BokehJS was loaded multiple times but one version failed to initialize.\");\n      load_or_wait();\n    } else if (root._bokeh_is_initializing || (typeof root._bokeh_is_initializing === \"undefined\" && root._bokeh_onload_callbacks !== undefined)) {\n      setTimeout(load_or_wait, 100);\n    } else {\n      Bokeh = root.Bokeh;\n      bokeh_loaded = Bokeh != null && (Bokeh.version === py_version || (Bokeh.versions !== undefined && Bokeh.versions.has(py_version)));\n      root._bokeh_is_initializing = true\n      root._bokeh_onload_callbacks = []\n      if (!reloading && (!bokeh_loaded || is_dev)) {\n\troot.Bokeh = undefined;\n      }\n      load_libs(css_urls, js_urls, js_modules, js_exports, function() {\n\tconsole.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n\trun_inline_js();\n      });\n    }\n  }\n  // Give older versions of the autoload script a head-start to ensure\n  // they initialize before we start loading newer version.\n  setTimeout(load_or_wait, 100)\n}(window));"
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     "output_type": "display_data"
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     "data": {
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       "  var output = handle.output;\n",
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       "  var id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "  var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
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       "    var html_node = toinsert[nchildren-1].children[0];\n",
       "    html_node.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "    var scripts = [];\n",
       "    var nodelist = html_node.querySelectorAll(\"script\");\n",
       "    for (var i in nodelist) {\n",
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      "application/vnd.holoviews_load.v0+json": "\nif ((window.PyViz === undefined) || (window.PyViz instanceof HTMLElement)) {\n  window.PyViz = {comms: {}, comm_status:{}, kernels:{}, receivers: {}, plot_index: []}\n}\n\n\n    function JupyterCommManager() {\n    }\n\n    JupyterCommManager.prototype.register_target = function(plot_id, comm_id, msg_handler) {\n      if (window.comm_manager || ((window.Jupyter !== undefined) && (Jupyter.notebook.kernel != null))) {\n        var comm_manager = window.comm_manager || Jupyter.notebook.kernel.comm_manager;\n        comm_manager.register_target(comm_id, function(comm) {\n          comm.on_msg(msg_handler);\n        });\n      } else if ((plot_id in window.PyViz.kernels) && (window.PyViz.kernels[plot_id])) {\n        window.PyViz.kernels[plot_id].registerCommTarget(comm_id, function(comm) {\n          comm.onMsg = msg_handler;\n        });\n      } else if (typeof google != 'undefined' && google.colab.kernel != null) {\n        google.colab.kernel.comms.registerTarget(comm_id, (comm) => {\n          var messages = comm.messages[Symbol.asyncIterator]();\n          function processIteratorResult(result) {\n            var message = result.value;\n            console.log(message)\n            var content = {data: message.data, comm_id};\n            var buffers = []\n            for (var buffer of message.buffers || []) {\n              buffers.push(new DataView(buffer))\n            }\n            var metadata = message.metadata || {};\n            var msg = {content, buffers, metadata}\n            msg_handler(msg);\n            return messages.next().then(processIteratorResult);\n          }\n          return messages.next().then(processIteratorResult);\n        })\n      }\n    }\n\n    JupyterCommManager.prototype.get_client_comm = function(plot_id, comm_id, msg_handler) {\n      if (comm_id in window.PyViz.comms) {\n        return window.PyViz.comms[comm_id];\n      } else if (window.comm_manager || 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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style>*[data-root-id],\n",
       "*[data-root-id] > * {\n",
       "  box-sizing: border-box;\n",
       "  font-family: var(--jp-ui-font-family);\n",
       "  font-size: var(--jp-ui-font-size1);\n",
       "  color: var(--vscode-editor-foreground, var(--jp-ui-font-color1));\n",
       "}\n",
       "\n",
       "/* Override VSCode background color */\n",
       ".cell-output-ipywidget-background:has(\n",
       "    > .cell-output-ipywidget-background > .lm-Widget > *[data-root-id]\n",
       "  ),\n",
       ".cell-output-ipywidget-background:has(> .lm-Widget > *[data-root-id]) {\n",
       "  background-color: transparent !important;\n",
       "}\n",
       "</style>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ignore warnings from bokeh active_drag property overlap with composite charts\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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",
       "    </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": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "</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",
       "  </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": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Generate summary statistics\n",
    "df_market_data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.holoviews_exec.v0+json": "",
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       "      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",
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       "            console.warn(\"Panel: ERROR: Unable to run Panel code because Bokeh or Panel library is missing\");\n",
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       "\t    console.warn(\"Panel: WARNING: Attempting to render but not all required libraries could be resolved.\")\n",
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       "        }\n",
       "      }\n",
       "    }, 25, root)\n",
       "  }\n",
       "})(window);</script>"
      ],
      "text/plain": [
       ":NdOverlay   [Variable]\n",
       "   :Curve   [coin_id]   (value)"
      ]
     },
     "execution_count": 5,
     "metadata": {
      "application/vnd.holoviews_exec.v0+json": {
       "id": "p1002"
      }
     },
     "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",
    ")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prepare the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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>coinid</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",
       "coinid                                                                  \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",
       "coinid                                                                   \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",
       "coinid                                                                    \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",
       "coinid                                    \n",
       "bitcoin                        -0.251637  \n",
       "ethereum                       -0.199352  \n",
       "tether                         -0.282061  \n",
       "ripple                         -0.295546  \n",
       "bitcoin-cash                   -0.270317  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a DataFrame with the scaled data\n",
    "df_market_data_scaled = pd.DataFrame(market_data_scaled, columns=df_market_data.columns)\n",
    "\n",
    "# Copy the crypto names from the original data\n",
    "df_market_data_scaled['coinid'] = df_market_data.index\n",
    "\n",
    "# Set the coinid column as index\n",
    "df_market_data_scaled = df_market_data_scaled.set_index('coinid')\n",
    "\n",
    "# Display sample data\n",
    "df_market_data_scaled.head()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Find the Best Value for k Using the Original Data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": 9,
   "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",
    "for i in k:\n",
    "    # 1. Create a KMeans model using the loop counter for the n_clusters\n",
    "    k_model = KMeans(n_clusters=i, n_init=10)\n",
    "    # 2. Fit the model to the data using `df_market_data_scaled`\n",
    "    k_model.fit(df_market_data_scaled)\n",
    "    # 3. Append the model.inertia_ to the inertia list\n",
    "    inertia.append(k_model.inertia_)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "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 = pd.DataFrame(elbow_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
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      ],
      "text/plain": [
       ":Curve   [k]   (inertia)"
      ]
     },
     "execution_count": 11,
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      "application/vnd.holoviews_exec.v0+json": {
       "id": "p1170"
      }
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   ],
   "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",
    "chart_elbow = df_elbow.hvplot.line(\n",
    "    x=\"k\",\n",
    "    y=\"inertia\",\n",
    "    title=\"Elbow Curve\",\n",
    "    xticks = k\n",
    ")\n",
    "chart_elbow"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Answer the following question: \n",
    "\n",
    "**Question:** What is the best value for `k`?\n",
    "\n",
    "**Answer:** 4"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cluster Cryptocurrencies with K-means Using the Original Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize the K-Means model using the best value for k\n",
    "model = KMeans(n_clusters=4, n_init=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
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      ],
      "text/plain": [
       "KMeans(n_clusters=4, n_init=10)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit the K-Means model using the scaled data\n",
    "model.fit(df_market_data_scaled)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 1 0 0 1 1 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 2 1 0 0 3\n",
      " 0 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "# Predict the clusters to group the cryptocurrencies using the scaled data\n",
    "k_prediction = model.predict(df_market_data_scaled)\n",
    "\n",
    "# Print the resulting array of cluster values.\n",
    "print(k_prediction)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a copy of the DataFrame\n",
    "df_market_data_scaled_predictions = df_market_data_scaled.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
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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",
       "      <th>group_k</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>coinid</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>1</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>1</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>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              price_change_percentage_24h  price_change_percentage_7d  \\\n",
       "coinid                                                                  \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",
       "coinid                                                                   \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",
       "coinid                                                                    \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  group_k  \n",
       "coinid                                             \n",
       "bitcoin                        -0.251637        1  \n",
       "ethereum                       -0.199352        1  \n",
       "tether                         -0.282061        0  \n",
       "ripple                         -0.295546        0  \n",
       "bitcoin-cash                   -0.270317        1  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Add a new column to the DataFrame with the predicted clusters\n",
    "df_market_data_scaled_predictions[\"group_k\"] = k_prediction\n",
    "\n",
    "# Display sample data\n",
    "df_market_data_scaled_predictions.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
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      ],
      "text/plain": [
       ":NdOverlay   [group_k]\n",
       "   :Scatter   [price_change_percentage_24h]   (price_change_percentage_7d,coinid)"
      ]
     },
     "execution_count": 17,
     "metadata": {
      "application/vnd.holoviews_exec.v0+json": {
       "id": "p1230"
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a scatter plot using hvPlot by setting \n",
    "chart_coin = df_market_data_scaled_predictions.hvplot.scatter(\n",
    "    title=\"24 Hour Price Change % v 7 Day Price Change %\",\n",
    "    # `x=\"price_change_percentage_24h\"` and `y=\"price_change_percentage_7d\"`. \n",
    "    x=\"price_change_percentage_24h\",\n",
    "    y=\"price_change_percentage_7d\",\n",
    "    \n",
    "    # Color the graph points with the labels found using K-Means and \n",
    "    by=\"group_k\",\n",
    "    \n",
    "    # add the crypto name in the `hover_cols` parameter to identify \n",
    "    # the cryptocurrency represented by each data point.\n",
    "    hover_cols=[\"coinid\"]\n",
    ")\n",
    "chart_coin"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimize Clusters with Principal Component Analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a PCA model instance and set `n_components=3`.\n",
    "pca = PCA(n_components=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.60066733,  0.84276006,  0.46159457],\n",
       "       [-0.45826071,  0.45846566,  0.95287678],\n",
       "       [-0.43306981, -0.16812638, -0.64175193],\n",
       "       [-0.47183495, -0.22266008, -0.47905316],\n",
       "       [-1.15779997,  2.04120919,  1.85971527]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use the PCA model with `fit_transform` to reduce to \n",
    "# three principal components.\n",
    "coin_pca = pca.fit_transform(df_market_data_scaled)\n",
    "\n",
    "# View the first five rows of the DataFrame. \n",
    "coin_pca[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.3719856  0.34700813 0.17603793]\n",
      "0.8950316570309842\n"
     ]
    }
   ],
   "source": [
    "# Retrieve the explained variance to determine how much information \n",
    "# can be attributed to each principal component.\n",
    "coin_pca_variance = pca.explained_variance_ratio_\n",
    "print(coin_pca_variance)\n",
    "coin_total_variance = sum(coin_pca_variance)\n",
    "print(coin_total_variance)"
   ]
  },
  {
   "attachments": {},
   "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:** About 90% of the total variance is condensed by 3 PCA variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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>PC1</th>\n",
       "      <th>PC2</th>\n",
       "      <th>PC3</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>coinid</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",
       "coinid                                    \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": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a new DataFrame with the PCA data.\n",
    "df_coin_pca = pd.DataFrame(coin_pca, columns=[\"PC1\", \"PC2\", \"PC3\"])\n",
    "\n",
    "# Copy the crypto names from the original data\n",
    "df_coin_pca[\"coinid\"] = df_market_data_scaled.index\n",
    "\n",
    "# Set the coinid column as index\n",
    "df_coin_pca = df_coin_pca.set_index(\"coinid\")\n",
    "\n",
    "# Display sample data\n",
    "df_coin_pca.head()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Find the Best Value for k Using the PCA Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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": 23,
   "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",
    "for i in k:\n",
    "    # Inside the loop:\n",
    "    # 1. Create a KMeans model using the loop counter for the n_clusters\n",
    "    k_model = KMeans(n_clusters=i, n_init=10)\n",
    "    # 2. Fit the model to the data using `df_market_data_pca`\n",
    "    k_model.fit(df_coin_pca)\n",
    "    # 3. Append the model.inertia_ to the inertia list\n",
    "    inertia.append(k_model.inertia_)\n"
   ]
  },
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   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
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   "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_pca = pd.DataFrame(elbow_data)"
   ]
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      ],
      "text/plain": [
       ":Curve   [k]   (inertia)"
      ]
     },
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   ],
   "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",
    "chart_elbow_pca = df_elbow_pca.hvplot.line(\n",
    "    x=\"k\",\n",
    "    y=\"inertia\",\n",
    "    title=\"PCA Elbow Curve\",\n",
    "    xticks = k\n",
    ")\n",
    "\n",
    "chart_elbow_pca"
   ]
  },
  {
   "attachments": {},
   "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:** 4\n",
    "\n",
    "\n",
    "* **Question:** Does it differ from the best k value found using the original data?\n",
    "\n",
    "  * **Answer:** No"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cluster Cryptocurrencies with K-means Using the PCA Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize the K-Means model using the best value for k\n",
    "model_pca = KMeans(n_clusters=4, n_init=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
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      ],
      "text/plain": [
       "KMeans(n_clusters=4, n_init=10)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit the K-Means model using the PCA data\n",
    "model_pca.fit(df_coin_pca)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 1 1 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 3 0 1 1 2\n",
      " 1 1 1 1]\n"
     ]
    }
   ],
   "source": [
    "# Predict the clusters to group the cryptocurrencies using the PCA data\n",
    "coin_pca_prediction = model_pca.predict(df_coin_pca)\n",
    "# Print the resulting array of cluster values.\n",
    "print(coin_pca_prediction)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PC1</th>\n",
       "      <th>PC2</th>\n",
       "      <th>PC3</th>\n",
       "      <th>group_k</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>coinid</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>0</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>0</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>1</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>1</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>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   PC1       PC2       PC3  group_k\n",
       "coinid                                             \n",
       "bitcoin      -0.600667  0.842760  0.461595        0\n",
       "ethereum     -0.458261  0.458466  0.952877        0\n",
       "tether       -0.433070 -0.168126 -0.641752        1\n",
       "ripple       -0.471835 -0.222660 -0.479053        1\n",
       "bitcoin-cash -1.157800  2.041209  1.859715        0"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a copy of the DataFrame with the PCA data\n",
    "df_coin_pca_predictions = df_coin_pca.copy()\n",
    "\n",
    "# Add a new column to the DataFrame with the predicted clusters\n",
    "df_coin_pca_predictions[\"group_k\"] = coin_pca_prediction\n",
    "\n",
    "# Display sample data\n",
    "df_coin_pca_predictions.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
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      ],
      "text/plain": [
       ":NdOverlay   [group_k]\n",
       "   :Scatter   [PC1]   (PC2,coinid)"
      ]
     },
     "execution_count": 30,
     "metadata": {
      "application/vnd.holoviews_exec.v0+json": {
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     },
     "output_type": "execute_result"
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   ],
   "source": [
    "# Create a scatter plot using hvPlot by setting \n",
    "chart_coin_pca = df_coin_pca_predictions.hvplot.scatter(\n",
    "    # `x=\"PC1\"` and `y=\"PC2\"`. \n",
    "    x=\"PC1\",\n",
    "    y=\"PC2\",\n",
    "    \n",
    "    # Color the graph points with the labels found using K-Means and \n",
    "    by=\"group_k\",\n",
    "    \n",
    "    # add the crypto name in the `hover_cols` parameter to identify \n",
    "    # the cryptocurrency represented by each data point.\n",
    "    hover_cols=[\"coinid\"]\n",
    ")\n",
    "\n",
    "chart_coin_pca"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.holoviews_exec.v0+json": "",
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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%, 400px));\\n}\",{\"id\":\"p1529\"},{\"id\":\"p1527\"},{\"id\":\"p1528\"}],\"margin\":0,\"sizing_mode\":\"stretch_width\",\"align\":\"start\"}}]}}],\"defs\":[{\"type\":\"model\",\"name\":\"ReactiveHTML1\"},{\"type\":\"model\",\"name\":\"FlexBox1\",\"properties\":[{\"name\":\"align_content\",\"kind\":\"Any\",\"default\":\"flex-start\"},{\"name\":\"align_items\",\"kind\":\"Any\",\"default\":\"flex-start\"},{\"name\":\"flex_direction\",\"kind\":\"Any\",\"default\":\"row\"},{\"name\":\"flex_wrap\",\"kind\":\"Any\",\"default\":\"wrap\"},{\"name\":\"justify_content\",\"kind\":\"Any\",\"default\":\"flex-start\"}]},{\"type\":\"model\",\"name\":\"FloatPanel1\",\"properties\":[{\"name\":\"config\",\"kind\":\"Any\",\"default\":{\"type\":\"map\"}},{\"name\":\"contained\",\"kind\":\"Any\",\"default\":true},{\"name\":\"position\",\"kind\":\"Any\",\"default\":\"right-top\"},{\"name\":\"offsetx\",\"kind\":\"Any\",\"default\":null},{\"name\":\"offsety\",\"kind\":\"Any\",\"default\":null},{\"name\":\"theme\",\"kind\":\"Any\",\"default\":\"primary\"},{\"name\":\"status\",\"kind\":\"Any\",\"default\":\"normalized\"}]},{\"type\":\"model\",\"name\":\"GridStack1\",\"properties\":[{\"name\":\"mode\",\"kind\":\"Any\",\"default\":\"warn\"},{\"name\":\"ncols\",\"kind\":\"Any\",\"default\":null},{\"name\":\"nrows\",\"kind\":\"Any\",\"default\":null},{\"name\":\"allow_resize\",\"kind\":\"Any\",\"default\":true},{\"name\":\"allow_drag\",\"kind\":\"Any\",\"default\":true},{\"name\":\"state\",\"kind\":\"Any\",\"default\":[]}]},{\"type\":\"model\",\"name\":\"drag1\",\"properties\":[{\"name\":\"slider_width\",\"kind\":\"Any\",\"default\":5},{\"name\":\"slider_color\",\"kind\":\"Any\",\"default\":\"black\"},{\"name\":\"value\",\"kind\":\"Any\",\"default\":50}]},{\"type\":\"model\",\"name\":\"click1\",\"properties\":[{\"name\":\"terminal_output\",\"kind\":\"Any\",\"default\":\"\"},{\"name\":\"debug_name\",\"kind\":\"Any\",\"default\":\"\"},{\"name\":\"clears\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"FastWrapper1\",\"properties\":[{\"name\":\"object\",\"kind\":\"Any\",\"default\":null},{\"name\":\"style\",\"kind\":\"Any\",\"default\":null}]},{\"type\":\"model\",\"name\":\"NotificationAreaBase1\",\"properties\":[{\"name\":\"js_events\",\"kind\":\"Any\",\"default\":{\"type\":\"map\"}},{\"name\":\"position\",\"kind\":\"Any\",\"default\":\"bottom-right\"},{\"name\":\"_clear\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"NotificationArea1\",\"properties\":[{\"name\":\"js_events\",\"kind\":\"Any\",\"default\":{\"type\":\"map\"}},{\"name\":\"notifications\",\"kind\":\"Any\",\"default\":[]},{\"name\":\"position\",\"kind\":\"Any\",\"default\":\"bottom-right\"},{\"name\":\"_clear\",\"kind\":\"Any\",\"default\":0},{\"name\":\"types\",\"kind\":\"Any\",\"default\":[{\"type\":\"map\",\"entries\":[[\"type\",\"warning\"],[\"background\",\"#ffc107\"],[\"icon\",{\"type\":\"map\",\"entries\":[[\"className\",\"fas 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\":\"7c112fdf-a230-4293-bdd7-7656890357c9\",\"roots\":{\"p1526\":\"ca19bef0-64b7-495b-bc5d-ebb602ef7764\"},\"root_ids\":[\"p1526\"]}];\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]   (inertia)"
      ]
     },
     "execution_count": 31,
     "metadata": {
      "application/vnd.holoviews_exec.v0+json": {
       "id": "p1526"
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Composite plot to contrast the Elbow curves\n",
    "chart_elbow + chart_elbow_pca"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.holoviews_exec.v0+json": "",
      "text/html": [
       "<div id='p1650'>\n",
       "  <div id=\"dbd2e77c-547b-4273-84b5-8fd6e5657158\" data-root-id=\"p1650\" style=\"display: contents;\"></div>\n",
       "</div>\n",
       "<script type=\"application/javascript\">(function(root) {\n",
       "  var docs_json = {\"3918f1bd-4789-4ee3-8fe9-dd7562774a3e\":{\"version\":\"3.2.2\",\"title\":\"Bokeh Application\",\"roots\":[{\"type\":\"object\",\"name\":\"Row\",\"id\":\"p1650\",\"attributes\":{\"name\":\"Row02076\",\"tags\":[\"embedded\"],\"stylesheets\":[\"\\n:host(.pn-loading.pn-arc):before, .pn-loading.pn-arc:before {\\n  background-image: 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400px));\\n}\",{\"type\":\"object\",\"name\":\"ImportedStyleSheet\",\"id\":\"p1653\",\"attributes\":{\"url\":\"https://cdn.holoviz.org/panel/1.2.2/dist/css/loading.css\"}},{\"type\":\"object\",\"name\":\"ImportedStyleSheet\",\"id\":\"p1881\",\"attributes\":{\"url\":\"https://cdn.holoviz.org/panel/1.2.2/dist/css/listpanel.css\"}},{\"type\":\"object\",\"name\":\"ImportedStyleSheet\",\"id\":\"p1651\",\"attributes\":{\"url\":\"https://cdn.holoviz.org/panel/1.2.2/dist/bundled/theme/default.css\"}},{\"type\":\"object\",\"name\":\"ImportedStyleSheet\",\"id\":\"p1652\",\"attributes\":{\"url\":\"https://cdn.holoviz.org/panel/1.2.2/dist/bundled/theme/native.css\"}}],\"margin\":0,\"sizing_mode\":\"stretch_width\",\"align\":\"start\",\"children\":[{\"type\":\"object\",\"name\":\"Spacer\",\"id\":\"p1654\",\"attributes\":{\"name\":\"HSpacer02085\",\"stylesheets\":[\"\\n:host(.pn-loading.pn-arc):before, .pn-loading.pn-arc:before {\\n  background-image: 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= 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      ],
      "text/plain": [
       ":Layout\n",
       "   .NdOverlay.I  :NdOverlay   [group_k]\n",
       "      :Scatter   [price_change_percentage_24h]   (price_change_percentage_7d,coinid)\n",
       "   .NdOverlay.II :NdOverlay   [group_k]\n",
       "      :Scatter   [PC1]   (PC2,coinid)"
      ]
     },
     "execution_count": 32,
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      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Composite plot to contrast the clusters\n",
    "chart_coin + chart_coin_pca"
   ]
  },
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   "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:** When not using PCA to reduce features, two coins are marked as belonging to groups consisting of only themselves, but one (celsius-degree-token) is very had to see from a comparison of 24h to 7d price changes as it falls in the middle of the cluster. Changing the view may potentially reveal the outlying dimensions of this coin, but reducing the number of features allows easier visualization of the group. In this instance, reducing the number of features did not changes the assignment of groups at all."
   ]
  }
 ],
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