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 = '3.2.1'.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/1.2.3/dist/bundled/gridstack/gridstack@7.2.3/dist/gridstack-all.js'];\n",
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       "      var urls = ['https://cdn.holoviz.org/panel/1.2.3/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.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",
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       "  var js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-3.2.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-3.2.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-3.2.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-3.2.1.min.js\", \"https://cdn.holoviz.org/panel/1.2.3/dist/panel.min.js\"];\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/1.2.3/dist/bundled/floatpanel/jspanel4@4.12.0/dist/jspanel.js', 'https://cdn.holoviz.org/panel/1.2.3/dist/bundled/floatpanel/jspanel4@4.12.0/dist/extensions/modal/jspanel.modal.js', 'https://cdn.holoviz.org/panel/1.2.3/dist/bundled/floatpanel/jspanel4@4.12.0/dist/extensions/tooltip/jspanel.tooltip.js', 'https://cdn.holoviz.org/panel/1.2.3/dist/bundled/floatpanel/jspanel4@4.12.0/dist/extensions/hint/jspanel.hint.js', 'https://cdn.holoviz.org/panel/1.2.3/dist/bundled/floatpanel/jspanel4@4.12.0/dist/extensions/layout/jspanel.layout.js', 'https://cdn.holoviz.org/panel/1.2.3/dist/bundled/floatpanel/jspanel4@4.12.0/dist/extensions/contextmenu/jspanel.contextmenu.js', 'https://cdn.holoviz.org/panel/1.2.3/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/1.2.3/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/1.2.3/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-3.2.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-3.2.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-3.2.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-3.2.1.min.js\", \"https://cdn.holoviz.org/panel/1.2.3/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 nchildren = toinsert.length;\n",
       "    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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       "    var bk_div = document.createElement(\"div\");\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"
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    {
     "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 warnings\n",
    "warnings.filterwarnings('ignore')\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": [
    {
     "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": 2,
     "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": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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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",
       "  </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": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Generate summary statistics\n",
    "df_market_data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.holoviews_exec.v0+json": "",
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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",
       "\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": 4,
     "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",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prepare the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5.08529366e-01,  4.93193071e-01,  7.72200433e-01,\n",
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       "         2.24045375e-01, -7.46741671e-02, -3.55053705e-01,\n",
       "        -2.51623389e-01],\n",
       "       [ 5.17582538e-02, -9.28380975e-01, -8.71917511e-01,\n",
       "         5.87817038e-02, -1.59249637e-01, -5.12070892e-01,\n",
       "        -2.65036119e-01],\n",
       "       [-5.20315039e-02, -4.57229014e-01,  3.25221197e-02,\n",
       "        -1.84488686e-01, -7.08090069e-02, -4.51982345e-01,\n",
       "        -2.62140444e-01],\n",
       "       [-2.17983910e-01, -8.49381348e-01,  2.97632101e-01,\n",
       "        -1.99820170e-01,  1.77312724e+00, -4.73610984e-02,\n",
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       "       [-1.42857388e+00, -2.55101681e-02, -1.62885923e+00,\n",
       "        -8.60353737e-01, -8.40713540e-01,  8.98815486e-01,\n",
       "         2.68647377e-01],\n",
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       "        -4.09716316e-01,  1.69648044e+00,  8.11206969e-01,\n",
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       "         5.35145461e+00,  4.76991278e+00,  3.14887546e+00,\n",
       "         1.34848839e+00],\n",
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       "        -1.39315260e+00, -6.96936973e-01, -4.22834707e-01,\n",
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       "       [ 4.14710578e-01,  4.14044166e-01, -4.73857773e-02,\n",
       "        -4.65379896e-01,  1.28184655e-01, -4.16502012e-01,\n",
       "        -1.45469278e-01],\n",
       "       [ 7.80381841e-02, -6.87745436e-01, -9.19092169e-03,\n",
       "        -5.82143470e-02,  7.38829646e-03, -5.50440743e-01,\n",
       "        -2.81746818e-01],\n",
       "       [ 1.21745256e+00, -6.07713570e-01, -9.07065528e-01,\n",
       "         4.49939006e-01, -6.62529501e-01,  5.72366557e-01,\n",
       "        -1.32481673e-01]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use the `StandardScaler()` module from scikit-learn to normalize the data from the CSV file\n",
    "market_scaled = StandardScaler().fit_transform(df_market_data[[\"price_change_percentage_24h\",\n",
    "                                                               \"price_change_percentage_7d\",\n",
    "                                                               \"price_change_percentage_14d\",\n",
    "                                                               \"price_change_percentage_30d\",\n",
    "                                                               \"price_change_percentage_60d\",\n",
    "                                                               \"price_change_percentage_200d\",\n",
    "                                                               \"price_change_percentage_1y\"]])\n",
    "\n",
    "# Review the scaled data\n",
    "market_scaled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a DataFrame with the scaled data\n",
    "market_scaled = pd.DataFrame(market_scaled, columns = [\"price_change_percentage_24h\",\n",
    "                                                               \"price_change_percentage_7d\",\n",
    "                                                               \"price_change_percentage_14d\",\n",
    "                                                               \"price_change_percentage_30d\",\n",
    "                                                               \"price_change_percentage_60d\",\n",
    "                                                               \"price_change_percentage_200d\",\n",
    "                                                               \"price_change_percentage_1y\"])\n",
    "\n",
    "# Copy the crypto names from the original data\n",
    "market_scaled['coin_id'] = df_market_data.index\n",
    "\n",
    "# Set the coinid column as index\n",
    "market_scaled.set_index('coin_id', inplace=True)\n",
    "\n",
    "# Display sample data\n",
    "market_scaled.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": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a list with the number of k-values from 1 to 11\n",
    "k_values = range(1, 12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create an empty list to store the inertia values\n",
    "inertia_values = []\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 `market_scaled`\n",
    "# 3. Append the model.inertia_ to the inertia list\n",
    "for i in k_values:\n",
    "    k_model = KMeans(n_clusters=i, random_state=0)\n",
    "    k_model.fit(market_scaled)\n",
    "    inertia_values.append(k_model.inertia_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <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>198.571818</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>65.302379</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   k     inertia\n",
       "0  1  287.000000\n",
       "1  2  198.571818\n",
       "2  3  123.190482\n",
       "3  4   79.022435\n",
       "4  5   65.302379"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a dictionary with the data to plot the Elbow curve\n",
    "elbow_data = {\"k\": k_values, \"inertia\": inertia_values}\n",
    "df_elbow = pd.DataFrame(elbow_data)\n",
    "\n",
    "# Create a DataFrame with the data to plot the Elbow curve\n",
    "df_elbow.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
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      ],
      "text/plain": [
       ":Curve   [k]   (inertia)"
      ]
     },
     "execution_count": 11,
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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 using hvplot\n",
    "elbow_curve_original = df_elbow.hvplot.line(\n",
    "    x=\"k\", \n",
    "    y=\"inertia\", \n",
    "    title=\"Elbow Curve\", \n",
    "    xticks=list(k_values)\n",
    ")\n",
    "\n",
    "# Show the line chart\n",
    "elbow_curve_original"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Answer the following question: \n",
    "\n",
    "**Question:** What is the best value for `k`?\n",
    "\n",
    "**Answer:** 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "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, random_state = 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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      ],
      "text/plain": [
       "KMeans(n_clusters=4, random_state=4)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit the K-Means model using the scaled data\n",
    "model.fit(market_scaled)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 3, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0, 0, 3, 0, 3, 0, 0, 3, 0, 0, 3,\n",
       "       0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 3, 0, 0, 2, 0, 0, 0, 0])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Predict the clusters to group the cryptocurrencies using the scaled data\n",
    "k_4_clusters = model.predict(market_scaled)\n",
    "\n",
    "# Print the resulting array of cluster values.\n",
    "k_4_clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a copy of the DataFrame\n",
    "market_with_clusters = market_scaled.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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>clusters</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>3</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>3</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>3</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  clusters  \n",
       "coin_id                                             \n",
       "bitcoin                        -0.251637         3  \n",
       "ethereum                       -0.199352         3  \n",
       "tether                         -0.282061         0  \n",
       "ripple                         -0.295546         0  \n",
       "bitcoin-cash                   -0.270317         3  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Add a new column to the DataFrame with the predicted clusters\n",
    "market_with_clusters[\"clusters\"] = k_4_clusters\n",
    "\n",
    "# Display sample data\n",
    "market_with_clusters.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
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       "  var render_items = [{\"docid\":\"8d6d1232-8491-4a59-840d-50d400f90e81\",\"roots\":{\"p1230\":\"b29ca4d3-341a-4a7c-813b-c6d60cd923a4\"},\"root_ids\":[\"p1230\"]}];\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   [clusters]\n",
       "   :Scatter   [price_change_percentage_24h]   (price_change_percentage_7d)"
      ]
     },
     "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",
    "# `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",
    "scatter_plot_original = market_with_clusters.hvplot.scatter(\n",
    "    x=\"price_change_percentage_24h\",\n",
    "    y=\"price_change_percentage_7d\",\n",
    "    by='clusters',\n",
    "    hover_cols=['crypto_name'],\n",
    "    width=800,\n",
    "    height=500\n",
    ")\n",
    "\n",
    "# Show scatterplot\n",
    "scatter_plot_original"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "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",
    "market_pca = pca.fit_transform(market_scaled)\n",
    "\n",
    "# View the first five rows of the DataFrame. \n",
    "market_pca[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.3719856 , 0.34700813, 0.17603793])"
      ]
     },
     "execution_count": 20,
     "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": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total Explained Variance: 0.8950316570309841\n"
     ]
    }
   ],
   "source": [
    "# Retrieve the explained variance ratios\n",
    "explained_variance_ratio = pca.explained_variance_ratio_\n",
    "\n",
    "# Calculate the total explained variance\n",
    "total_explained_variance = sum(explained_variance_ratio)\n",
    "\n",
    "# Print the total explained variance\n",
    "print(\"Total Explained Variance:\", total_explained_variance)"
   ]
  },
  {
   "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:** 89.50%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PCA1</th>\n",
       "      <th>PCA2</th>\n",
       "      <th>PCA3</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": [
       "                  PCA1      PCA2      PCA3\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": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creating a DataFrame with the PCA data\n",
    "pca_columns = ['PCA1', 'PCA2', 'PCA3']\n",
    "df_pca = pd.DataFrame(market_pca, columns=pca_columns)\n",
    "\n",
    "# Copy the crypto names from the original data\n",
    "df_pca['coin_id'] = df_market_data.index\n",
    "\n",
    "# Set the coinid column as index\n",
    "df_pca.set_index('coin_id', inplace=True)\n",
    "\n",
    "\n",
    "# Display sample data\n",
    "df_pca.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": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a list with the number of k-values from 1 to 11\n",
    "k_values_pca = range(1, 12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create an empty list to store the inertia values\n",
    "inertia_values_pca = []\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_pca`\n",
    "# 3. Append the model.inertia_ to the inertia list\n",
    "for i in k_values_pca:\n",
    "    k_model = KMeans(n_clusters = i, random_state = 1)\n",
    "    k_model.fit(df_pca)\n",
    "    inertia_values_pca.append(k_model.inertia_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a dictionary with the data to plot the Elbow curve\n",
    "elbow_data_pca = {\"Number of Clusters (k)\": k_values_pca, \"Inertia\": inertia_values_pca}\n",
    "\n",
    "# Create a DataFrame with the data to plot the Elbow curve\n",
    "df_elbow_pca = pd.DataFrame(elbow_data_pca)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "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_curve_pca = df_elbow_pca.hvplot.line(\n",
    "    x=\"Number of Clusters (k)\", \n",
    "    y=\"Inertia\", \n",
    "    title=\"Elbow Curve\", \n",
    "    xticks=list(k_values_pca)\n",
    ")"
   ]
  },
  {
   "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 they are the same"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cluster Cryptocurrencies with K-means Using the PCA Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize the K-Means model using the best value for k\n",
    "model = KMeans(n_clusters = 4, random_state = 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {color: black;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>KMeans(n_clusters=4, random_state=4)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">KMeans</label><div class=\"sk-toggleable__content\"><pre>KMeans(n_clusters=4, random_state=4)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "KMeans(n_clusters=4, random_state=4)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit the K-Means model using the PCA data\n",
    "model.fit(df_pca)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 3, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0, 0, 3, 0, 3, 0, 0, 3, 0, 0, 3,\n",
       "       0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 3, 0, 0, 2, 0, 0, 0, 0])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Predict the clusters to group the cryptocurrencies using the PCA data\n",
    "pca_clusters = model.predict(df_pca)\n",
    "\n",
    "# Print the resulting array of cluster values.\n",
    "pca_clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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>PCA1</th>\n",
       "      <th>PCA2</th>\n",
       "      <th>PCA3</th>\n",
       "      <th>predicted_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>3</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>3</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>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  PCA1      PCA2      PCA3  predicted_cluster\n",
       "coin_id                                                      \n",
       "bitcoin      -0.600667  0.842760  0.461595                  3\n",
       "ethereum     -0.458261  0.458466  0.952877                  3\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                  3"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a copy of the DataFrame with the PCA data\n",
    "df_pca_with_clusters = df_pca.copy()\n",
    "\n",
    "# Add a new column to the DataFrame with the predicted clusters\n",
    "df_pca_with_clusters['predicted_cluster'] = pca_clusters\n",
    "\n",
    "# Display sample data\n",
    "df_pca_with_clusters.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
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      ],
      "text/plain": [
       ":NdOverlay   [predicted_cluster]\n",
       "   :Scatter   [PCA1]   (PCA2)"
      ]
     },
     "execution_count": 32,
     "metadata": {
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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",
    "scatter_plot_pca = df_pca_with_clusters.hvplot.scatter(\n",
    "    x=\"PCA1\",\n",
    "    y=\"PCA2\",\n",
    "    by='predicted_cluster',\n",
    "    hover_cols=['crypto_name'],\n",
    "    width=800,\n",
    "    height=500\n",
    ")\n",
    "\n",
    "# Show the scatter plot\n",
    "scatter_plot_pca"
   ]
  },
  {
   "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": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "  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   [Number of Clusters (k)]   (Inertia)"
      ]
     },
     "execution_count": 33,
     "metadata": {
      "application/vnd.holoviews_exec.v0+json": {
       "id": "p1466"
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Composite plot to contrast the Elbow curves\n",
    "# Arrange plots side by side for comparison\n",
    "elbow_curve_comparison = elbow_curve_original + elbow_curve_pca\n",
    "\n",
    "# Show the composite plot\n",
    "elbow_curve_comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.holoviews_exec.v0+json": "",
      "text/html": [
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      "text/plain": [
       ":Layout\n",
       "   .NdOverlay.I  :NdOverlay   [clusters]\n",
       "      :Scatter   [price_change_percentage_24h]   (price_change_percentage_7d)\n",
       "   .NdOverlay.II :NdOverlay   [predicted_cluster]\n",
       "      :Scatter   [PCA1]   (PCA2)"
      ]
     },
     "execution_count": 34,
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   "source": [
    "# Composite plot to contrast the clusters\n",
    "# Arrange plots side by side for comparison\n",
    "scatter_plots_comparison = scatter_plot_original + scatter_plot_pca\n",
    "\n",
    "# Show the scatter plot comparison\n",
    "scatter_plots_comparison"
   ]
  },
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   "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:** Original Data is more spread out. PCA Transformed Data is more uniform. PCA Transformed Data also identifies outlier clusters easier."
   ]
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   "source": []
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