{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This notebook is part of my [Python data science curriculum](http://www.terran.us/articles/python_curriculum.html)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"RendererRegistry.enable('notebook')"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import altair as alt\n",
"alt.renderers.enable('notebook')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Data"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.datasets import load_boston\n",
"skBoston = load_boston()"
]
},
{
"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>CRIM</th>\n",
" <th>ZN</th>\n",
" <th>INDUS</th>\n",
" <th>CHAS</th>\n",
" <th>NOX</th>\n",
" <th>RM</th>\n",
" <th>AGE</th>\n",
" <th>DIS</th>\n",
" <th>RAD</th>\n",
" <th>TAX</th>\n",
" <th>PTRATIO</th>\n",
" <th>B</th>\n",
" <th>LSTAT</th>\n",
" <th>MEDV</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0.00632</td>\n",
" <td>18.0</td>\n",
" <td>2.31</td>\n",
" <td>0.0</td>\n",
" <td>0.538</td>\n",
" <td>6.575</td>\n",
" <td>65.2</td>\n",
" <td>4.0900</td>\n",
" <td>1.0</td>\n",
" <td>296.0</td>\n",
" <td>15.3</td>\n",
" <td>396.90</td>\n",
" <td>4.98</td>\n",
" <td>24.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.02731</td>\n",
" <td>0.0</td>\n",
" <td>7.07</td>\n",
" <td>0.0</td>\n",
" <td>0.469</td>\n",
" <td>6.421</td>\n",
" <td>78.9</td>\n",
" <td>4.9671</td>\n",
" <td>2.0</td>\n",
" <td>242.0</td>\n",
" <td>17.8</td>\n",
" <td>396.90</td>\n",
" <td>9.14</td>\n",
" <td>21.6</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.02729</td>\n",
" <td>0.0</td>\n",
" <td>7.07</td>\n",
" <td>0.0</td>\n",
" <td>0.469</td>\n",
" <td>7.185</td>\n",
" <td>61.1</td>\n",
" <td>4.9671</td>\n",
" <td>2.0</td>\n",
" <td>242.0</td>\n",
" <td>17.8</td>\n",
" <td>392.83</td>\n",
" <td>4.03</td>\n",
" <td>34.7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0.03237</td>\n",
" <td>0.0</td>\n",
" <td>2.18</td>\n",
" <td>0.0</td>\n",
" <td>0.458</td>\n",
" <td>6.998</td>\n",
" <td>45.8</td>\n",
" <td>6.0622</td>\n",
" <td>3.0</td>\n",
" <td>222.0</td>\n",
" <td>18.7</td>\n",
" <td>394.63</td>\n",
" <td>2.94</td>\n",
" <td>33.4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0.06905</td>\n",
" <td>0.0</td>\n",
" <td>2.18</td>\n",
" <td>0.0</td>\n",
" <td>0.458</td>\n",
" <td>7.147</td>\n",
" <td>54.2</td>\n",
" <td>6.0622</td>\n",
" <td>3.0</td>\n",
" <td>222.0</td>\n",
" <td>18.7</td>\n",
" <td>396.90</td>\n",
" <td>5.33</td>\n",
" <td>36.2</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX \\\n",
"0 0.00632 18.0 2.31 0.0 0.538 6.575 65.2 4.0900 1.0 296.0 \n",
"1 0.02731 0.0 7.07 0.0 0.469 6.421 78.9 4.9671 2.0 242.0 \n",
"2 0.02729 0.0 7.07 0.0 0.469 7.185 61.1 4.9671 2.0 242.0 \n",
"3 0.03237 0.0 2.18 0.0 0.458 6.998 45.8 6.0622 3.0 222.0 \n",
"4 0.06905 0.0 2.18 0.0 0.458 7.147 54.2 6.0622 3.0 222.0 \n",
"\n",
" PTRATIO B LSTAT MEDV \n",
"0 15.3 396.90 4.98 24.0 \n",
"1 17.8 396.90 9.14 21.6 \n",
"2 17.8 392.83 4.03 34.7 \n",
"3 18.7 394.63 2.94 33.4 \n",
"4 18.7 396.90 5.33 36.2 "
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# sklearn data is in a format with precomputed X and y, which is not what we want.\n",
"Boston = pd.DataFrame(data= skBoston['data'],\n",
" columns= skBoston['feature_names'])\n",
"Boston['MEDV']=skBoston.target\n",
"Boston.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Statsmodels"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model Fitting"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"from statsmodels.multivariate.pca import PCA"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"smpca = PCA(Boston,standardize=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Scree Plot"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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" } else if (typeof(MozWebSocket) !== 'undefined') {\n",
" return MozWebSocket;\n",
" } else {\n",
" alert('Your browser does not have WebSocket support.' +\n",
" 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
" 'Firefox 4 and 5 are also supported but you ' +\n",
" 'have to enable WebSockets in about:config.');\n",
" };\n",
"}\n",
"\n",
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" if (warnings) {\n",
" warnings.style.display = 'block';\n",
" warnings.textContent = (\n",
" \"This browser does not support binary websocket messages. \" +\n",
" \"Performance may be slow.\");\n",
" }\n",
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"\n",
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" 'ui-helper-clearfix\"/>');\n",
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" }\n",
"\n",
" canvas_div.keydown('key_press', canvas_keyboard_event);\n",
" canvas_div.keyup('key_release', canvas_keyboard_event);\n",
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"\n",
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" canvas.addClass('mpl-canvas');\n",
" canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
"\n",
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"\tthis.context.webkitBackingStorePixelRatio ||\n",
"\tthis.context.mozBackingStorePixelRatio ||\n",
"\tthis.context.msBackingStorePixelRatio ||\n",
"\tthis.context.oBackingStorePixelRatio ||\n",
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"\n",
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"\n",
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" var name = mpl.toolbar_items[toolbar_ind][0];\n",
" var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
" var image = mpl.toolbar_items[toolbar_ind][2];\n",
" var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
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" 'ui-button-icon-only');\n",
" button.attr('role', 'button');\n",
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"\n",
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"\n",
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"\n",
"\n",
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" fig._resize_canvas(size[0], size[1]);\n",
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" };\n",
"}\n",
"\n",
"mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
" var x0 = msg['x0'] / mpl.ratio;\n",
" var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
" var x1 = msg['x1'] / mpl.ratio;\n",
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" x0 = Math.floor(x0) + 0.5;\n",
" y0 = Math.floor(y0) + 0.5;\n",
" x1 = Math.floor(x1) + 0.5;\n",
" y1 = Math.floor(y1) + 0.5;\n",
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" var width = Math.abs(x1 - x0);\n",
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"\n",
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"\n",
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"}\n",
"\n",
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"\n",
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"}\n",
"\n",
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"}\n",
"\n",
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"}\n",
"\n",
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" /* FIXME: We get \"Resource interpreted as Image but\n",
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"\n",
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" }\n",
"\n",
" fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
" evt.data);\n",
" fig.updated_canvas_event();\n",
" fig.waiting = false;\n",
" return;\n",
" }\n",
" else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
" fig.imageObj.src = evt.data;\n",
" fig.updated_canvas_event();\n",
" fig.waiting = false;\n",
" return;\n",
" }\n",
"\n",
" var msg = JSON.parse(evt.data);\n",
" var msg_type = msg['type'];\n",
"\n",
" // Call the \"handle_{type}\" callback, which takes\n",
" // the figure and JSON message as its only arguments.\n",
" try {\n",
" var callback = fig[\"handle_\" + msg_type];\n",
" } catch (e) {\n",
" console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
" return;\n",
" }\n",
"\n",
" if (callback) {\n",
" try {\n",
" // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
" callback(fig, msg);\n",
" } catch (e) {\n",
" console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
" }\n",
" }\n",
" };\n",
"}\n",
"\n",
"// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
"mpl.findpos = function(e) {\n",
" //this section is from http://www.quirksmode.org/js/events_properties.html\n",
" var targ;\n",
" if (!e)\n",
" e = window.event;\n",
" if (e.target)\n",
" targ = e.target;\n",
" else if (e.srcElement)\n",
" targ = e.srcElement;\n",
" if (targ.nodeType == 3) // defeat Safari bug\n",
" targ = targ.parentNode;\n",
"\n",
" // jQuery normalizes the pageX and pageY\n",
" // pageX,Y are the mouse positions relative to the document\n",
" // offset() returns the position of the element relative to the document\n",
" var x = e.pageX - $(targ).offset().left;\n",
" var y = e.pageY - $(targ).offset().top;\n",
"\n",
" return {\"x\": x, \"y\": y};\n",
"};\n",
"\n",
"/*\n",
" * return a copy of an object with only non-object keys\n",
" * we need this to avoid circular references\n",
" * http://stackoverflow.com/a/24161582/3208463\n",
" */\n",
"function simpleKeys (original) {\n",
" return Object.keys(original).reduce(function (obj, key) {\n",
" if (typeof original[key] !== 'object')\n",
" obj[key] = original[key]\n",
" return obj;\n",
" }, {});\n",
"}\n",
"\n",
"mpl.figure.prototype.mouse_event = function(event, name) {\n",
" var canvas_pos = mpl.findpos(event)\n",
"\n",
" if (name === 'button_press')\n",
" {\n",
" this.canvas.focus();\n",
" this.canvas_div.focus();\n",
" }\n",
"\n",
" var x = canvas_pos.x * mpl.ratio;\n",
" var y = canvas_pos.y * mpl.ratio;\n",
"\n",
" this.send_message(name, {x: x, y: y, button: event.button,\n",
" step: event.step,\n",
" guiEvent: simpleKeys(event)});\n",
"\n",
" /* This prevents the web browser from automatically changing to\n",
" * the text insertion cursor when the button is pressed. We want\n",
" * to control all of the cursor setting manually through the\n",
" * 'cursor' event from matplotlib */\n",
" event.preventDefault();\n",
" return false;\n",
"}\n",
"\n",
"mpl.figure.prototype._key_event_extra = function(event, name) {\n",
" // Handle any extra behaviour associated with a key event\n",
"}\n",
"\n",
"mpl.figure.prototype.key_event = function(event, name) {\n",
"\n",
" // Prevent repeat events\n",
" if (name == 'key_press')\n",
" {\n",
" if (event.which === this._key)\n",
" return;\n",
" else\n",
" this._key = event.which;\n",
" }\n",
" if (name == 'key_release')\n",
" this._key = null;\n",
"\n",
" var value = '';\n",
" if (event.ctrlKey && event.which != 17)\n",
" value += \"ctrl+\";\n",
" if (event.altKey && event.which != 18)\n",
" value += \"alt+\";\n",
" if (event.shiftKey && event.which != 16)\n",
" value += \"shift+\";\n",
"\n",
" value += 'k';\n",
" value += event.which.toString();\n",
"\n",
" this._key_event_extra(event, name);\n",
"\n",
" this.send_message(name, {key: value,\n",
" guiEvent: simpleKeys(event)});\n",
" return false;\n",
"}\n",
"\n",
"mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
" if (name == 'download') {\n",
" this.handle_save(this, null);\n",
" } else {\n",
" this.send_message(\"toolbar_button\", {name: name});\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
" this.message.textContent = tooltip;\n",
"};\n",
"mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
"\n",
"mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
"\n",
"mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
" // Create a \"websocket\"-like object which calls the given IPython comm\n",
" // object with the appropriate methods. Currently this is a non binary\n",
" // socket, so there is still some room for performance tuning.\n",
" var ws = {};\n",
"\n",
" ws.close = function() {\n",
" comm.close()\n",
" };\n",
" ws.send = function(m) {\n",
" //console.log('sending', m);\n",
" comm.send(m);\n",
" };\n",
" // Register the callback with on_msg.\n",
" comm.on_msg(function(msg) {\n",
" //console.log('receiving', msg['content']['data'], msg);\n",
" // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
" ws.onmessage(msg['content']['data'])\n",
" });\n",
" return ws;\n",
"}\n",
"\n",
"mpl.mpl_figure_comm = function(comm, msg) {\n",
" // This is the function which gets called when the mpl process\n",
" // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
"\n",
" var id = msg.content.data.id;\n",
" // Get hold of the div created by the display call when the Comm\n",
" // socket was opened in Python.\n",
" var element = $(\"#\" + id);\n",
" var ws_proxy = comm_websocket_adapter(comm)\n",
"\n",
" function ondownload(figure, format) {\n",
" window.open(figure.imageObj.src);\n",
" }\n",
"\n",
" var fig = new mpl.figure(id, ws_proxy,\n",
" ondownload,\n",
" element.get(0));\n",
"\n",
" // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
" // web socket which is closed, not our websocket->open comm proxy.\n",
" ws_proxy.onopen();\n",
"\n",
" fig.parent_element = element.get(0);\n",
" fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
" if (!fig.cell_info) {\n",
" console.error(\"Failed to find cell for figure\", id, fig);\n",
" return;\n",
" }\n",
"\n",
" var output_index = fig.cell_info[2]\n",
" var cell = fig.cell_info[0];\n",
"\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_close = function(fig, msg) {\n",
" var width = fig.canvas.width/mpl.ratio\n",
" fig.root.unbind('remove')\n",
"\n",
" // Update the output cell to use the data from the current canvas.\n",
" fig.push_to_output();\n",
" var dataURL = fig.canvas.toDataURL();\n",
" // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
" // the notebook keyboard shortcuts fail.\n",
" IPython.keyboard_manager.enable()\n",
" $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
" fig.close_ws(fig, msg);\n",
"}\n",
"\n",
"mpl.figure.prototype.close_ws = function(fig, msg){\n",
" fig.send_message('closing', msg);\n",
" // fig.ws.close()\n",
"}\n",
"\n",
"mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
" // Turn the data on the canvas into data in the output cell.\n",
" var width = this.canvas.width/mpl.ratio\n",
" var dataURL = this.canvas.toDataURL();\n",
" this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
"}\n",
"\n",
"mpl.figure.prototype.updated_canvas_event = function() {\n",
" // Tell IPython that the notebook contents must change.\n",
" IPython.notebook.set_dirty(true);\n",
" this.send_message(\"ack\", {});\n",
" var fig = this;\n",
" // Wait a second, then push the new image to the DOM so\n",
" // that it is saved nicely (might be nice to debounce this).\n",
" setTimeout(function () { fig.push_to_output() }, 1000);\n",
"}\n",
"\n",
"mpl.figure.prototype._init_toolbar = function() {\n",
" var fig = this;\n",
"\n",
" var nav_element = $('<div/>')\n",
" nav_element.attr('style', 'width: 100%');\n",
" this.root.append(nav_element);\n",
"\n",
" // Define a callback function for later on.\n",
" function toolbar_event(event) {\n",
" return fig.toolbar_button_onclick(event['data']);\n",
" }\n",
" function toolbar_mouse_event(event) {\n",
" return fig.toolbar_button_onmouseover(event['data']);\n",
" }\n",
"\n",
" for(var toolbar_ind in mpl.toolbar_items){\n",
" var name = mpl.toolbar_items[toolbar_ind][0];\n",
" var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
" var image = mpl.toolbar_items[toolbar_ind][2];\n",
" var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
"\n",
" if (!name) { continue; };\n",
"\n",
" var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
" button.click(method_name, toolbar_event);\n",
" button.mouseover(tooltip, toolbar_mouse_event);\n",
" nav_element.append(button);\n",
" }\n",
"\n",
" // Add the status bar.\n",
" var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
" nav_element.append(status_bar);\n",
" this.message = status_bar[0];\n",
"\n",
" // Add the close button to the window.\n",
" var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
" var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
" button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
" button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
" buttongrp.append(button);\n",
" var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
" titlebar.prepend(buttongrp);\n",
"}\n",
"\n",
"mpl.figure.prototype._root_extra_style = function(el){\n",
" var fig = this\n",
" el.on(\"remove\", function(){\n",
"\tfig.close_ws(fig, {});\n",
" });\n",
"}\n",
"\n",
"mpl.figure.prototype._canvas_extra_style = function(el){\n",
" // this is important to make the div 'focusable\n",
" el.attr('tabindex', 0)\n",
" // reach out to IPython and tell the keyboard manager to turn it's self\n",
" // off when our div gets focus\n",
"\n",
" // location in version 3\n",
" if (IPython.notebook.keyboard_manager) {\n",
" IPython.notebook.keyboard_manager.register_events(el);\n",
" }\n",
" else {\n",
" // location in version 2\n",
" IPython.keyboard_manager.register_events(el);\n",
" }\n",
"\n",
"}\n",
"\n",
"mpl.figure.prototype._key_event_extra = function(event, name) {\n",
" var manager = IPython.notebook.keyboard_manager;\n",
" if (!manager)\n",
" manager = IPython.keyboard_manager;\n",
"\n",
" // Check for shift+enter\n",
" if (event.shiftKey && event.which == 13) {\n",
" this.canvas_div.blur();\n",
" event.shiftKey = false;\n",
" // Send a \"J\" for go to next cell\n",
" event.which = 74;\n",
" event.keyCode = 74;\n",
" manager.command_mode();\n",
" manager.handle_keydown(event);\n",
" }\n",
"}\n",
"\n",
"mpl.figure.prototype.handle_save = function(fig, msg) {\n",
" fig.ondownload(fig, null);\n",
"}\n",
"\n",
"\n",
"mpl.find_output_cell = function(html_output) {\n",
" // Return the cell and output element which can be found *uniquely* in the notebook.\n",
" // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
" // IPython event is triggered only after the cells have been serialised, which for\n",
" // our purposes (turning an active figure into a static one), is too late.\n",
" var cells = IPython.notebook.get_cells();\n",
" var ncells = cells.length;\n",
" for (var i=0; i<ncells; i++) {\n",
" var cell = cells[i];\n",
" if (cell.cell_type === 'code'){\n",
" for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
" var data = cell.output_area.outputs[j];\n",
" if (data.data) {\n",
" // IPython >= 3 moved mimebundle to data attribute of output\n",
" data = data.data;\n",
" }\n",
" if (data['text/html'] == html_output) {\n",
" return [cell, data, j];\n",
" }\n",
" }\n",
" }\n",
" }\n",
"}\n",
"\n",
"// Register the function which deals with the matplotlib target/channel.\n",
"// The kernel may be null if the page has been refreshed.\n",
"if (IPython.notebook.kernel != null) {\n",
" IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
"}\n"
],
"text/plain": [
"<IPython.core.display.Javascript object>"
]
},
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"output_type": "display_data"
},
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\" width=\"640\">"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib notebook\n",
"smpca.plot_scree();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This suggets that 1 component would be the right number. Note that the vertical axis is the eigenvalue on a log scale, _not_ the more common proportion of variance explained."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Biplot\n",
"\n",
"No biplot for you!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Loadings/Rotations"
]
},
{
"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>comp_00</th>\n",
" <th>comp_01</th>\n",
" <th>comp_02</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>CRIM</th>\n",
" <td>0.240962</td>\n",
" <td>-0.065950</td>\n",
" <td>0.393820</td>\n",
" </tr>\n",
" <tr>\n",
" <th>ZN</th>\n",
" <td>-0.245618</td>\n",
" <td>-0.147745</td>\n",
" <td>0.394760</td>\n",
" </tr>\n",
" <tr>\n",
" <th>INDUS</th>\n",
" <td>0.332027</td>\n",
" <td>0.126979</td>\n",
" <td>-0.065289</td>\n",
" </tr>\n",
" <tr>\n",
" <th>CHAS</th>\n",
" <td>-0.004989</td>\n",
" <td>0.410562</td>\n",
" <td>-0.125809</td>\n",
" </tr>\n",
" <tr>\n",
" <th>NOX</th>\n",
" <td>0.325298</td>\n",
" <td>0.254262</td>\n",
" <td>-0.046524</td>\n",
" </tr>\n",
" <tr>\n",
" <th>RM</th>\n",
" <td>-0.203014</td>\n",
" <td>0.434305</td>\n",
" <td>0.352838</td>\n",
" </tr>\n",
" <tr>\n",
" <th>AGE</th>\n",
" <td>0.297132</td>\n",
" <td>0.260158</td>\n",
" <td>-0.200950</td>\n",
" </tr>\n",
" <tr>\n",
" <th>DIS</th>\n",
" <td>-0.298328</td>\n",
" <td>-0.359005</td>\n",
" <td>0.156994</td>\n",
" </tr>\n",
" <tr>\n",
" <th>RAD</th>\n",
" <td>0.303431</td>\n",
" <td>0.031323</td>\n",
" <td>0.420101</td>\n",
" </tr>\n",
" <tr>\n",
" <th>TAX</th>\n",
" <td>0.324095</td>\n",
" <td>0.008978</td>\n",
" <td>0.344904</td>\n",
" </tr>\n",
" <tr>\n",
" <th>PTRATIO</th>\n",
" <td>0.207762</td>\n",
" <td>-0.314675</td>\n",
" <td>0.001774</td>\n",
" </tr>\n",
" <tr>\n",
" <th>B</th>\n",
" <td>-0.196425</td>\n",
" <td>0.025932</td>\n",
" <td>-0.359408</td>\n",
" </tr>\n",
" <tr>\n",
" <th>LSTAT</th>\n",
" <td>0.311485</td>\n",
" <td>-0.201303</td>\n",
" <td>-0.161419</td>\n",
" </tr>\n",
" <tr>\n",
" <th>MEDV</th>\n",
" <td>-0.266727</td>\n",
" <td>0.444997</td>\n",
" <td>0.163144</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" comp_00 comp_01 comp_02\n",
"CRIM 0.240962 -0.065950 0.393820\n",
"ZN -0.245618 -0.147745 0.394760\n",
"INDUS 0.332027 0.126979 -0.065289\n",
"CHAS -0.004989 0.410562 -0.125809\n",
"NOX 0.325298 0.254262 -0.046524\n",
"RM -0.203014 0.434305 0.352838\n",
"AGE 0.297132 0.260158 -0.200950\n",
"DIS -0.298328 -0.359005 0.156994\n",
"RAD 0.303431 0.031323 0.420101\n",
"TAX 0.324095 0.008978 0.344904\n",
"PTRATIO 0.207762 -0.314675 0.001774\n",
"B -0.196425 0.025932 -0.359408\n",
"LSTAT 0.311485 -0.201303 -0.161419\n",
"MEDV -0.266727 0.444997 0.163144"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"smpca.loadings.iloc[:,0:3]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# H2O\n",
"\n",
"Overall I'm not very pleased with the PCA implementation in H2O; it doesn't offer much functionality and the UI is awkward."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Init"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Checking whether there is an H2O instance running at http://localhost:54321..... not found.\n",
"Attempting to start a local H2O server...\n",
" Java Version: java version \"1.7.0_71\"; Java(TM) SE Runtime Environment (build 1.7.0_71-b14); Java HotSpot(TM) 64-Bit Server VM (build 24.71-b01, mixed mode)\n",
" Starting server from /Users/terran/.pyenv/versions/anaconda3-5.2.0/lib/python3.6/site-packages/h2o/backend/bin/h2o.jar\n",
" Ice root: /var/folders/55/2417s3bs6s977dvsrs15x3n00000gp/T/tmpunlw44_o\n",
" JVM stdout: /var/folders/55/2417s3bs6s977dvsrs15x3n00000gp/T/tmpunlw44_o/h2o_terran_started_from_python.out\n",
" JVM stderr: /var/folders/55/2417s3bs6s977dvsrs15x3n00000gp/T/tmpunlw44_o/h2o_terran_started_from_python.err\n",
" Server is running at http://127.0.0.1:54321\n",
"Connecting to H2O server at http://127.0.0.1:54321... successful.\n"
]
},
{
"data": {
"text/html": [
"<div style=\"overflow:auto\"><table style=\"width:50%\"><tr><td>H2O cluster uptime:</td>\n",
"<td>03 secs</td></tr>\n",
"<tr><td>H2O cluster timezone:</td>\n",
"<td>America/New_York</td></tr>\n",
"<tr><td>H2O data parsing timezone:</td>\n",
"<td>UTC</td></tr>\n",
"<tr><td>H2O cluster version:</td>\n",
"<td>3.22.0.2</td></tr>\n",
"<tr><td>H2O cluster version age:</td>\n",
"<td>1 month and 23 days </td></tr>\n",
"<tr><td>H2O cluster name:</td>\n",
"<td>H2O_from_python_terran_96nm83</td></tr>\n",
"<tr><td>H2O cluster total nodes:</td>\n",
"<td>1</td></tr>\n",
"<tr><td>H2O cluster free memory:</td>\n",
"<td>1.778 Gb</td></tr>\n",
"<tr><td>H2O cluster total cores:</td>\n",
"<td>4</td></tr>\n",
"<tr><td>H2O cluster allowed cores:</td>\n",
"<td>4</td></tr>\n",
"<tr><td>H2O cluster status:</td>\n",
"<td>accepting new members, healthy</td></tr>\n",
"<tr><td>H2O connection url:</td>\n",
"<td>http://127.0.0.1:54321</td></tr>\n",
"<tr><td>H2O connection proxy:</td>\n",
"<td>None</td></tr>\n",
"<tr><td>H2O internal security:</td>\n",
"<td>False</td></tr>\n",
"<tr><td>H2O API Extensions:</td>\n",
"<td>AutoML, XGBoost, Algos, Core V3, Core V4</td></tr>\n",
"<tr><td>Python version:</td>\n",
"<td>3.6.5 final</td></tr></table></div>"
],
"text/plain": [
"-------------------------- ----------------------------------------\n",
"H2O cluster uptime: 03 secs\n",
"H2O cluster timezone: America/New_York\n",
"H2O data parsing timezone: UTC\n",
"H2O cluster version: 3.22.0.2\n",
"H2O cluster version age: 1 month and 23 days\n",
"H2O cluster name: H2O_from_python_terran_96nm83\n",
"H2O cluster total nodes: 1\n",
"H2O cluster free memory: 1.778 Gb\n",
"H2O cluster total cores: 4\n",
"H2O cluster allowed cores: 4\n",
"H2O cluster status: accepting new members, healthy\n",
"H2O connection url: http://127.0.0.1:54321\n",
"H2O connection proxy:\n",
"H2O internal security: False\n",
"H2O API Extensions: AutoML, XGBoost, Algos, Core V3, Core V4\n",
"Python version: 3.6.5 final\n",
"-------------------------- ----------------------------------------"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import h2o\n",
"h2o.init()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Data Loading"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Parse progress: |█████████████████████████████████████████████████████████| 100%\n"
]
}
],
"source": [
"hbos = h2o.H2OFrame(Boston, destination_frame=\"Boston\")"
]
},
{
"cell_type": "code",
"execution_count": 10,
"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>key</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>Boston</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" key\n",
"0 Boston"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"h2o.ls()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<table>\n",
"<thead>\n",
"<tr><th style=\"text-align: right;\"> CRIM</th><th style=\"text-align: right;\"> ZN</th><th style=\"text-align: right;\"> INDUS</th><th style=\"text-align: right;\"> CHAS</th><th style=\"text-align: right;\"> NOX</th><th style=\"text-align: right;\"> RM</th><th style=\"text-align: right;\"> AGE</th><th style=\"text-align: right;\"> DIS</th><th style=\"text-align: right;\"> RAD</th><th style=\"text-align: right;\"> TAX</th><th style=\"text-align: right;\"> PTRATIO</th><th style=\"text-align: right;\"> B</th><th style=\"text-align: right;\"> LSTAT</th><th style=\"text-align: right;\"> MEDV</th></tr>\n",
"</thead>\n",
"<tbody>\n",
"<tr><td style=\"text-align: right;\">0.00632</td><td style=\"text-align: right;\">18 </td><td style=\"text-align: right;\"> 2.31</td><td style=\"text-align: right;\"> 0</td><td style=\"text-align: right;\">0.538</td><td style=\"text-align: right;\">6.575</td><td style=\"text-align: right;\"> 65.2</td><td style=\"text-align: right;\">4.09 </td><td style=\"text-align: right;\"> 1</td><td style=\"text-align: right;\"> 296</td><td style=\"text-align: right;\"> 15.3</td><td style=\"text-align: right;\">396.9 </td><td style=\"text-align: right;\"> 4.98</td><td style=\"text-align: right;\"> 24 </td></tr>\n",
"<tr><td style=\"text-align: right;\">0.02731</td><td style=\"text-align: right;\"> 0 </td><td style=\"text-align: right;\"> 7.07</td><td style=\"text-align: right;\"> 0</td><td style=\"text-align: right;\">0.469</td><td style=\"text-align: right;\">6.421</td><td style=\"text-align: right;\"> 78.9</td><td style=\"text-align: right;\">4.9671</td><td style=\"text-align: right;\"> 2</td><td style=\"text-align: right;\"> 242</td><td style=\"text-align: right;\"> 17.8</td><td style=\"text-align: right;\">396.9 </td><td style=\"text-align: right;\"> 9.14</td><td style=\"text-align: right;\"> 21.6</td></tr>\n",
"<tr><td style=\"text-align: right;\">0.02729</td><td style=\"text-align: right;\"> 0 </td><td style=\"text-align: right;\"> 7.07</td><td style=\"text-align: right;\"> 0</td><td style=\"text-align: right;\">0.469</td><td style=\"text-align: right;\">7.185</td><td style=\"text-align: right;\"> 61.1</td><td style=\"text-align: right;\">4.9671</td><td style=\"text-align: right;\"> 2</td><td style=\"text-align: right;\"> 242</td><td style=\"text-align: right;\"> 17.8</td><td style=\"text-align: right;\">392.83</td><td style=\"text-align: right;\"> 4.03</td><td style=\"text-align: right;\"> 34.7</td></tr>\n",
"<tr><td style=\"text-align: right;\">0.03237</td><td style=\"text-align: right;\"> 0 </td><td style=\"text-align: right;\"> 2.18</td><td style=\"text-align: right;\"> 0</td><td style=\"text-align: right;\">0.458</td><td style=\"text-align: right;\">6.998</td><td style=\"text-align: right;\"> 45.8</td><td style=\"text-align: right;\">6.0622</td><td style=\"text-align: right;\"> 3</td><td style=\"text-align: right;\"> 222</td><td style=\"text-align: right;\"> 18.7</td><td style=\"text-align: right;\">394.63</td><td style=\"text-align: right;\"> 2.94</td><td style=\"text-align: right;\"> 33.4</td></tr>\n",
"<tr><td style=\"text-align: right;\">0.06905</td><td style=\"text-align: right;\"> 0 </td><td style=\"text-align: right;\"> 2.18</td><td style=\"text-align: right;\"> 0</td><td style=\"text-align: right;\">0.458</td><td style=\"text-align: right;\">7.147</td><td style=\"text-align: right;\"> 54.2</td><td style=\"text-align: right;\">6.0622</td><td style=\"text-align: right;\"> 3</td><td style=\"text-align: right;\"> 222</td><td style=\"text-align: right;\"> 18.7</td><td style=\"text-align: right;\">396.9 </td><td style=\"text-align: right;\"> 5.33</td><td style=\"text-align: right;\"> 36.2</td></tr>\n",
"<tr><td style=\"text-align: right;\">0.02985</td><td style=\"text-align: right;\"> 0 </td><td style=\"text-align: right;\"> 2.18</td><td style=\"text-align: right;\"> 0</td><td style=\"text-align: right;\">0.458</td><td style=\"text-align: right;\">6.43 </td><td style=\"text-align: right;\"> 58.7</td><td style=\"text-align: right;\">6.0622</td><td style=\"text-align: right;\"> 3</td><td style=\"text-align: right;\"> 222</td><td style=\"text-align: right;\"> 18.7</td><td style=\"text-align: right;\">394.12</td><td style=\"text-align: right;\"> 5.21</td><td style=\"text-align: right;\"> 28.7</td></tr>\n",
"<tr><td style=\"text-align: right;\">0.08829</td><td style=\"text-align: right;\">12.5</td><td style=\"text-align: right;\"> 7.87</td><td style=\"text-align: right;\"> 0</td><td style=\"text-align: right;\">0.524</td><td style=\"text-align: right;\">6.012</td><td style=\"text-align: right;\"> 66.6</td><td style=\"text-align: right;\">5.5605</td><td style=\"text-align: right;\"> 5</td><td style=\"text-align: right;\"> 311</td><td style=\"text-align: right;\"> 15.2</td><td style=\"text-align: right;\">395.6 </td><td style=\"text-align: right;\"> 12.43</td><td style=\"text-align: right;\"> 22.9</td></tr>\n",
"<tr><td style=\"text-align: right;\">0.14455</td><td style=\"text-align: right;\">12.5</td><td style=\"text-align: right;\"> 7.87</td><td style=\"text-align: right;\"> 0</td><td style=\"text-align: right;\">0.524</td><td style=\"text-align: right;\">6.172</td><td style=\"text-align: right;\"> 96.1</td><td style=\"text-align: right;\">5.9505</td><td style=\"text-align: right;\"> 5</td><td style=\"text-align: right;\"> 311</td><td style=\"text-align: right;\"> 15.2</td><td style=\"text-align: right;\">396.9 </td><td style=\"text-align: right;\"> 19.15</td><td style=\"text-align: right;\"> 27.1</td></tr>\n",
"<tr><td style=\"text-align: right;\">0.21124</td><td style=\"text-align: right;\">12.5</td><td style=\"text-align: right;\"> 7.87</td><td style=\"text-align: right;\"> 0</td><td style=\"text-align: right;\">0.524</td><td style=\"text-align: right;\">5.631</td><td style=\"text-align: right;\">100 </td><td style=\"text-align: right;\">6.0821</td><td style=\"text-align: right;\"> 5</td><td style=\"text-align: right;\"> 311</td><td style=\"text-align: right;\"> 15.2</td><td style=\"text-align: right;\">386.63</td><td style=\"text-align: right;\"> 29.93</td><td style=\"text-align: right;\"> 16.5</td></tr>\n",
"<tr><td style=\"text-align: right;\">0.17004</td><td style=\"text-align: right;\">12.5</td><td style=\"text-align: right;\"> 7.87</td><td style=\"text-align: right;\"> 0</td><td style=\"text-align: right;\">0.524</td><td style=\"text-align: right;\">6.004</td><td style=\"text-align: right;\"> 85.9</td><td style=\"text-align: right;\">6.5921</td><td style=\"text-align: right;\"> 5</td><td style=\"text-align: right;\"> 311</td><td style=\"text-align: right;\"> 15.2</td><td style=\"text-align: right;\">386.71</td><td style=\"text-align: right;\"> 17.1 </td><td style=\"text-align: right;\"> 18.9</td></tr>\n",
"</tbody>\n",
"</table>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": []
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"hbos"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model Fitting"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"# In h2o, it is mandatory to state the number of components to keep - it does not just assume\n",
"# full rank if unspecified.\n",
"modpca = h2o.estimators.pca.H2OPrincipalComponentAnalysisEstimator(\n",
" transform='standardize',k=9)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"pca Model Build progress: |███████████████████████████████████████████████| 100%\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/terran/.pyenv/versions/anaconda3-5.2.0/lib/python3.6/site-packages/h2o/job.py:69: UserWarning: _train: Dataset used may contain fewer number of rows due to removal of rows with NA/missing values. If this is not desirable, set impute_missing argument in pca call to TRUE/True/true/... depending on the client language.\n",
" warnings.warn(w)\n"
]
}
],
"source": [
"# It is mandatory to state which columns are to be used for x\n",
"modpca.train(x=list(range(hbos.ncol)),training_frame=hbos)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"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></th>\n",
" <th>pc1</th>\n",
" <th>pc2</th>\n",
" <th>pc3</th>\n",
" <th>pc4</th>\n",
" <th>pc5</th>\n",
" <th>pc6</th>\n",
" <th>pc7</th>\n",
" <th>pc8</th>\n",
" <th>pc9</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>Standard deviation</td>\n",
" <td>2.55769</td>\n",
" <td>1.284347</td>\n",
" <td>1.160291</td>\n",
" <td>0.941489</td>\n",
" <td>0.922435</td>\n",
" <td>0.813827</td>\n",
" <td>0.734218</td>\n",
" <td>0.635248</td>\n",
" <td>0.527020</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>Proportion of Variance</td>\n",
" <td>0.46727</td>\n",
" <td>0.117825</td>\n",
" <td>0.096162</td>\n",
" <td>0.063314</td>\n",
" <td>0.060778</td>\n",
" <td>0.047308</td>\n",
" <td>0.038505</td>\n",
" <td>0.028824</td>\n",
" <td>0.019839</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>Cumulative Proportion</td>\n",
" <td>0.46727</td>\n",
" <td>0.585095</td>\n",
" <td>0.681257</td>\n",
" <td>0.744571</td>\n",
" <td>0.805349</td>\n",
" <td>0.852657</td>\n",
" <td>0.891163</td>\n",
" <td>0.919987</td>\n",
" <td>0.939826</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" pc1 pc2 pc3 pc4 pc5 \\\n",
"0 Standard deviation 2.55769 1.284347 1.160291 0.941489 0.922435 \n",
"1 Proportion of Variance 0.46727 0.117825 0.096162 0.063314 0.060778 \n",
"2 Cumulative Proportion 0.46727 0.585095 0.681257 0.744571 0.805349 \n",
"\n",
" pc6 pc7 pc8 pc9 \n",
"0 0.813827 0.734218 0.635248 0.527020 \n",
"1 0.047308 0.038505 0.028824 0.019839 \n",
"2 0.852657 0.891163 0.919987 0.939826 "
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"modpca.varimp(use_pandas=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Scree Plot"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"KeyError('server',)\n"
]
}
],
"source": [
"# Haha, no\n",
"try:\n",
" modpca.screeplot()\n",
"except Exception as e:\n",
" print(repr(e))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So I guess we're going to do it the manual way."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
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" 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>index</th>\n",
" <th>Standard deviation</th>\n",
" <th>Proportion of Variance</th>\n",
" <th>Cumulative Proportion</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>pc1</td>\n",
" <td>2.55769</td>\n",
" <td>0.46727</td>\n",
" <td>0.46727</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>pc2</td>\n",
" <td>1.28435</td>\n",
" <td>0.117825</td>\n",
" <td>0.585095</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>pc3</td>\n",
" <td>1.16029</td>\n",
" <td>0.0961625</td>\n",
" <td>0.681257</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>pc4</td>\n",
" <td>0.941489</td>\n",
" <td>0.0633144</td>\n",
" <td>0.744571</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>pc5</td>\n",
" <td>0.922435</td>\n",
" <td>0.0607776</td>\n",
" <td>0.805349</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" index Standard deviation Proportion of Variance Cumulative Proportion\n",
"0 pc1 2.55769 0.46727 0.46727\n",
"1 pc2 1.28435 0.117825 0.585095\n",
"2 pc3 1.16029 0.0961625 0.681257\n",
"3 pc4 0.941489 0.0633144 0.744571\n",
"4 pc5 0.922435 0.0607776 0.805349"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"vi = modpca.varimp(use_pandas=True).transpose()\n",
"# The column headers are now in the first row, so put that row back on the columns.\n",
"vi.columns=vi.iloc[0,:]\n",
"vi.drop('',inplace=True)\n",
"# and, as always, remove the index before using with Altair\n",
"vi.reset_index(inplace=True)\n",
"vi.head()"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"application/javascript": [
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"var opt = {};\n",
"var type = \"vega-lite\";\n",
"var id = \"b964e0ad-c3a2-42b9-940f-461ed43b940a\";\n",
"\n",
"var output_area = this;\n",
"\n",
"require([\"nbextensions/jupyter-vega/index\"], function(vega) {\n",
" var target = document.createElement(\"div\");\n",
" target.id = id;\n",
" target.className = \"vega-embed\";\n",
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" var style = document.createElement(\"style\");\n",
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" \" color: firebrick;\",\n",
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" element[0].appendChild(style);\n",
"\n",
" vega.render(\"#\" + id, spec, type, opt, output_area);\n",
"}, function (err) {\n",
" if (err.requireType !== \"scripterror\") {\n",
" throw(err);\n",
" }\n",
"});\n"
],
"text/plain": [
"<vega.vegalite.VegaLite at 0x11672d978>"
]
},
"metadata": {
"jupyter-vega": "#b964e0ad-c3a2-42b9-940f-461ed43b940a"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": []
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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"
},
"metadata": {
"jupyter-vega": "#b964e0ad-c3a2-42b9-940f-461ed43b940a"
},
"output_type": "display_data"
}
],
"source": [
"alt.Chart(vi).mark_bar().encode(\n",
" x='index',y='Proportion of Variance').interactive()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This suggests that reasonable choices would be 1 or 3 components to retain."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Loadings/Rotations"
]
},
{
"cell_type": "code",
"execution_count": 18,
"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></th>\n",
" <th>pc1</th>\n",
" <th>pc2</th>\n",
" <th>pc3</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>CRIM</td>\n",
" <td>-0.240962</td>\n",
" <td>-0.065950</td>\n",
" <td>-0.393820</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>ZN</td>\n",
" <td>0.245618</td>\n",
" <td>-0.147745</td>\n",
" <td>-0.394760</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>INDUS</td>\n",
" <td>-0.332027</td>\n",
" <td>0.126979</td>\n",
" <td>0.065289</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>CHAS</td>\n",
" <td>0.004989</td>\n",
" <td>0.410562</td>\n",
" <td>0.125809</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>NOX</td>\n",
" <td>-0.325298</td>\n",
" <td>0.254262</td>\n",
" <td>0.046524</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>RM</td>\n",
" <td>0.203014</td>\n",
" <td>0.434305</td>\n",
" <td>-0.352838</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>AGE</td>\n",
" <td>-0.297132</td>\n",
" <td>0.260158</td>\n",
" <td>0.200950</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>DIS</td>\n",
" <td>0.298328</td>\n",
" <td>-0.359005</td>\n",
" <td>-0.156994</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>RAD</td>\n",
" <td>-0.303431</td>\n",
" <td>0.031323</td>\n",
" <td>-0.420101</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>TAX</td>\n",
" <td>-0.324095</td>\n",
" <td>0.008978</td>\n",
" <td>-0.344904</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>PTRATIO</td>\n",
" <td>-0.207762</td>\n",
" <td>-0.314675</td>\n",
" <td>-0.001774</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>B</td>\n",
" <td>0.196425</td>\n",
" <td>0.025932</td>\n",
" <td>0.359408</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>LSTAT</td>\n",
" <td>-0.311485</td>\n",
" <td>-0.201303</td>\n",
" <td>0.161419</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>MEDV</td>\n",
" <td>0.266727</td>\n",
" <td>0.444997</td>\n",
" <td>-0.163144</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" pc1 pc2 pc3\n",
"0 CRIM -0.240962 -0.065950 -0.393820\n",
"1 ZN 0.245618 -0.147745 -0.394760\n",
"2 INDUS -0.332027 0.126979 0.065289\n",
"3 CHAS 0.004989 0.410562 0.125809\n",
"4 NOX -0.325298 0.254262 0.046524\n",
"5 RM 0.203014 0.434305 -0.352838\n",
"6 AGE -0.297132 0.260158 0.200950\n",
"7 DIS 0.298328 -0.359005 -0.156994\n",
"8 RAD -0.303431 0.031323 -0.420101\n",
"9 TAX -0.324095 0.008978 -0.344904\n",
"10 PTRATIO -0.207762 -0.314675 -0.001774\n",
"11 B 0.196425 0.025932 0.359408\n",
"12 LSTAT -0.311485 -0.201303 0.161419\n",
"13 MEDV 0.266727 0.444997 -0.163144"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
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],
"source": [
"modpca.rotation().as_data_frame().iloc[:,0:4]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Comparison to R results"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"(ignore sign changes; those are arbitrary)\n",
"```\n",
"> prcomp(MASS::Boston,scale=T)$rotation[,1:3]\n",
" PC1 PC2 PC3\n",
"crim 0.242284451 -0.065873108 0.395077419\n",
"zn -0.245435005 -0.148002653 0.394545713\n",
"indus 0.331859746 0.127075668 -0.066081913\n",
"chas -0.005027133 0.410668763 -0.125305293\n",
"nox 0.325193880 0.254276363 -0.046475549\n",
"rm -0.202816554 0.434005810 0.353406095\n",
"age 0.296976574 0.260303205 -0.200823078\n",
"dis -0.298169809 -0.359149977 0.157068710\n",
"rad 0.303412754 0.031149596 0.418510334\n",
"tax 0.324033052 0.008851406 0.343232194\n",
"ptratio 0.207679535 -0.314623061 0.000399092\n",
"black -0.196638358 0.026481032 -0.361375914\n",
"lstat 0.311397955 -0.201245177 -0.161060336\n",
"medv -0.266636396 0.444924411 0.163188735\n",
"```"
]
},
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