PCA.ipynb

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    "%matplotlib notebook\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import sklearn.datasets\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.rcParams['figure.figsize'] = [8, 4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "iris = sklearn.datasets.load_iris()\n",
    "\n",
    "X = pd.DataFrame(iris.data, columns=iris.feature_names)\n",
    "\n",
    "X_zscaled = (X - X.mean()) / X.std(ddof=1)\n",
    "\n",
    "Y = pd.DataFrame(iris.target, columns=['target'])\n",
    "Y['species'] = Y.apply(lambda r: iris.target_names[r])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multicollinearity Check\n",
    "\n",
    "Using $corr(X)$, check to see that we some level of multicollinearity in the data, enough to warrant using PCA of visualization in reduced-rank principal component space. As a rule of thumb, the off-diagonal correlation values (either in the upper- or lower-triangle) should have absolute values of around 0.30 or so."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation matrix:\n",
      "\n",
      "[[ 1.         -0.10936925  0.87175416  0.81795363]\n",
      " [-0.10936925  1.         -0.4205161  -0.35654409]\n",
      " [ 0.87175416 -0.4205161   1.          0.9627571 ]\n",
      " [ 0.81795363 -0.35654409  0.9627571   1.        ]]\n",
      "\n",
      "\n",
      "Multicollinearity check using off-diagonal values:\n",
      "\n",
      "count    6.000000\n",
      "mean     0.589816\n",
      "std      0.341915\n",
      "min      0.109369\n",
      "25%      0.372537\n",
      "50%      0.619235\n",
      "75%      0.858304\n",
      "max      0.962757\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "corr = X_zscaled.corr()\n",
    "\n",
    "tmp = pd.np.triu(corr) - np.eye(corr.shape[0]) \n",
    "tmp = tmp.flatten()\n",
    "tmp = tmp[np.nonzero(tmp)]\n",
    "tmp = pd.Series(np.abs(tmp))\n",
    "\n",
    "print('Correlation matrix:\\n\\n{}\\n\\n'.format(corr.values))\n",
    "\n",
    "print('Multicollinearity check using off-diagonal values:\\n\\n{}'.format(tmp.describe()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PCA via Eigen-Decomposition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Obtain eigenvalues, eigenvectors of $cov(X)$ via eigen-decomposition\n",
    "\n",
    "From the factorization of symmetric matrix $S$ into orthogonal matrix $Q$ of the eigenvectors and diagonal matrix $\\Lambda$ of the eigenvalues, we can likewise decompose $cov(X)$ (or in our case $corr(X)$ since we standardized our data).\n",
    "\n",
    "\\begin{align}\n",
    "  S &= Q \\Lambda Q^\\intercal \\\\\n",
    "  \\Rightarrow X^\\intercal X &= V \\Lambda V^\\intercal \\\\\n",
    "\\end{align}\n",
    "\n",
    "where $V$ are the orthonormal eigenvectors of $X X^\\intercal$.\n",
    "\n",
    "We can normalize the eigenvalues to see how much variance is captured per each respective principal component. We will also calculate the cumulative variance explained. This will help inform our decision of how many principal components to keep when reducing dimensions in visualizing the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "eigenvalues, eigenvectors = np.linalg.eig(X_zscaled.cov())\n",
    "\n",
    "eigenvalues_normalized = eigenvalues / eigenvalues.sum()\n",
    "\n",
    "cumvar_explained = np.cumsum(eigenvalues_normalized)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reduce dimensions and visualize\n",
    "\n",
    "To project the original data into principal component space, we obtain score matrix $T$ by taking the dot product of $X$ and the eigenvectors $V$.\n",
    "\n",
    "\\begin{align}\n",
    "  T &= X V \\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = pd.DataFrame(X_zscaled.dot(eigenvectors))\n",
    "\n",
    "# set column names\n",
    "T.columns = ['pc1', 'pc2', 'pc3', 'pc4']\n",
    "\n",
    "# also add the species label as \n",
    "T = pd.concat([T, Y.species], axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize the original, 4D iris data of $X$ by using the first $k$ eigenvectors of $X$, projecting the original data into a reduced-rank $k$-dimensional principal component space.\n",
    "\n",
    "\\begin{align}\n",
    "  T_{rank=k} &= X V_{rank=k}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
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       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\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>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"798.8889100522176\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's try using the first 2 principal components\n",
    "k = 2\n",
    "\n",
    "# divide T by label\n",
    "irises = [T[T.species=='setosa'], \n",
    "          T[T.species=='versicolor'], \n",
    "          T[T.species=='virginica']]\n",
    "\n",
    "# define a color-blind friendly set of quantative colors\n",
    "# for each species\n",
    "colors = ['#1b9e77', '#d95f02', '#7570b3']\n",
    "\n",
    "_, (ax1, ax2) = plt.subplots(1, 2, sharey=False)\n",
    "\n",
    "# plot principal component vis-a-vis total variance in data\n",
    "ax1.plot([1,2,3,4],\n",
    "         eigenvalues_normalized,\n",
    "         '-o',\n",
    "         color='#8da0cb',\n",
    "         label='eigenvalue (normalized)',\n",
    "         alpha=0.8,\n",
    "         zorder=1000)\n",
    "\n",
    "ax1.plot([1,2,3,4],\n",
    "         cumvar_explained,\n",
    "         '-o',\n",
    "         color='#fc8d62',\n",
    "         label='cum. variance explained',\n",
    "         alpha=0.8,\n",
    "         zorder=1000)\n",
    "\n",
    "ax1.set_xlim(0.8, 4.2)\n",
    "ax1.set_xticks([1,2,3,4])\n",
    "ax1.set_xlabel('Principal component')\n",
    "ax1.set_ylabel('Variance')\n",
    "ax1.legend(loc='center right', fontsize=7)\n",
    "ax1.grid(color='#fdfefe')\n",
    "ax1.set_facecolor('#f4f6f7')\n",
    "\n",
    "# plot the reduced-rank score matrix representation\n",
    "for group, color in zip(irises, colors):\n",
    "    ax2.scatter(group.pc1,\n",
    "                group.pc2,\n",
    "                marker='^',\n",
    "                color=color,\n",
    "                label=group.species,\n",
    "                alpha=0.5,\n",
    "                zorder=1000)\n",
    "ax2.set_xlabel(r'PC 1')\n",
    "ax2.set_ylabel(r'PC 2')\n",
    "ax2.grid(color='#fdfefe')\n",
    "ax2.set_facecolor('#f4f6f7')\n",
    "ax2.legend(labels=iris.target_names, fontsize=7)\n",
    "\n",
    "plt.suptitle(r'Fig. 1: PCA via eigen-decomposition, 2D visualization')\n",
    "plt.tight_layout(pad=3.0)\n",
    "plt.show()    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Relative weights of the original features in principal component space\n",
    "\n",
    "* Each row of $V$ is a vector representing the relative weights for each of the original features for each principal component.\n",
    "* Given reduced-rank $k$, the columns of $V_k$ are the weights for principal components $1, \\dots, k$.\n",
    "* Calculate the norm for each row of $V_k$, and normalize the results to obtain the relative weights for each original feature in principal component space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using 2 principal components, the original features are represented with the following weights:\n",
      "-  sepal length (cm): 0.233\n",
      "-  sepal width (cm): 0.349\n",
      "-  petal length (cm): 0.211\n",
      "-  petal width (cm): 0.207\n"
     ]
    }
   ],
   "source": [
    "feature_norms = np.linalg.norm(eigenvectors[:, 0:k], axis=1)\n",
    "feature_weights = feature_norms / feature_norms.sum()\n",
    "\n",
    "msg = ('Using {} principal components, '\n",
    "       'the original features are represented with the following weights:')\n",
    "print(msg.format(k))\n",
    "for feature, weight in zip(iris.feature_names, feature_weights):\n",
    "    print('-  {}: {:0.3f}'.format(feature, weight))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PCA via Singular Value Decomposition\n",
    "\n",
    "Singular value decomposition factors any matrix $A$ into right-singular vector matrix $U$; diagonal matrix of singular values $\\Sigma$; and right-singular vector matrix $V$.\n",
    "\n",
    "\\begin{align}\n",
    "  A &= U \\Sigma V^\\intercal \\\\\n",
    "\\end{align}\n",
    "\n",
    "If we start with \n",
    "\n",
    "\\begin{align}\n",
    "  X &= U \\Sigma V^\\intercal \\\\\n",
    "  \\\\\n",
    "  X^\\intercal X &= (U \\Sigma V^\\intercal)^\\intercal U \\Sigma V^\\intercal \\\\\n",
    "  &= V \\Sigma^\\intercal U^\\intercal U \\Sigma V^\\intercal \\\\\n",
    "  &= V \\Sigma^\\intercal \\Sigma V^\\intercal \\\\\n",
    "  \\\\\n",
    "  \\Rightarrow \\Sigma^\\intercal \\Sigma &= \\Lambda\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "U, S, Vt = np.linalg.svd(X_zscaled)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.52237162 -0.37231836 -0.72101681  0.26199559]\n",
      " [-0.26335492 -0.92555649  0.24203288 -0.12413481]\n",
      " [ 0.58125401 -0.02109478  0.14089226 -0.80115427]\n",
      " [ 0.56561105 -0.06541577  0.6338014   0.52354627]]\n"
     ]
    }
   ],
   "source": [
    "print(eigenvectors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.52237162 -0.37231836  0.72101681  0.26199559]\n",
      " [-0.26335492 -0.92555649 -0.24203288 -0.12413481]\n",
      " [ 0.58125401 -0.02109478 -0.14089226 -0.80115427]\n",
      " [ 0.56561105 -0.06541577 -0.6338014   0.52354627]]\n"
     ]
    }
   ],
   "source": [
    "print(Vt.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 4)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vt.T.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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