{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Principal Component Analysis\n",
    "\n",
    "In this exercise sheet we look into how to compute and apply a Principal Component Analysis (PCA)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Toy 4D Example\n",
    "\n",
    "We start by loading our toy example. The data is stored as a Numpy array, it is a $2585\\times 5$ matrix. The last component of each row is the label, the first four components are the coordinates in 4D. Each label is an integer from  $\\{0, 1, 2, 3, 4\\}$.\n",
    "\n",
    "The data contains a noisy 2D plane which is embded into 4D. We would like to represent the data in its _intrinsic_ 2D form."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import mllab.pca\n",
    "\n",
    "pca_toy_4d = np.load(\"data/pca_toy_4d.npy\")\n",
    "y = pca_toy_4d[:, -1]  # labels\n",
    "x = pca_toy_4d[:, :-1]  # 4D coordinates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us plot slices from this 4D data. We provide a helper function for this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Show documentation\n",
    "mllab.pca.plot_toy_slice?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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cOTMzQ39//4rBnVtdqIOtu++01szNzTE6Okpra2vdzm9bXahrVLxd1+Xq1asY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\nODg4+ghcQObg4ODoI/wfxshApVKQXV0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb3e44a3da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mllab.pca.plot_toy_slice(x, y, drop_dim=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We want to remove the noise and recover the 2D information."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 3.1\n",
    "\n",
    "Write an implementation of the function below. Use a singular value decomposition (SVD), but avoid computing it completely since we only need the first $q$ eigenvectors. You can use a NumPy/SciPy function for this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.sparse.linalg import svds\n",
    "\n",
    "def pca(x, q):\n",
    "    \"\"\"\n",
    "    Compute principal components and the coordinates.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    \n",
    "    x: (n, d) NumPy array\n",
    "    q: int\n",
    "       The number of principal components to compute.\n",
    "       Has to be less than `p`.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    \n",
    "    Vq: (d, q) NumPy array, orthonormal vectors (column-wise)\n",
    "    xq: (n, q) NumPy array, coordinates for x (row-wise)\n",
    "    \"\"\"\n",
    "    _n, p = x.shape\n",
    "    assert 0 < q < p\n",
    "    X = x - np.mean(x, axis=0)\n",
    "    _U, _sigma, VqT = svds(X, k=q)\n",
    "    xq = VqT.dot(X.T)\n",
    "    return VqT.T, xq.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can compute the 2D dimensional representation of `x` using PCA."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "V, xq = pca(x, q=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And then plot the coordinates `xq`, which are two dimensional. We provide a helper function for this task. Let us check how to use it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mllab.pca.plot_toy_2d?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IvB1oUUoNdtrm6fWec/+j2g7PCNZSfdVT+Be8B4lMw5pyNmb1XLzOXZkAqFw3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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb3e1bf4ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xq = mllab.pca.plot_toy_2d(xq, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hopefully you appreciate the result.\n",
    "\n",
    "### Task 3.2\n",
    "\n",
    "Let us see how PCA handles a non-linear transformation. To test this we map our data into 3D by keeping the y-axis as the new z-axis and bending x-coordinate onto an ellipse."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xyz = mllab.pca.map_on_ellipse(xq, a=4, b=1, gap_angle=90)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } 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",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        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",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\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) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\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",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    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",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* 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 overriden (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": {
      "text/html": [
       "<img 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width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "mllab.pca.plot_toy_3d(xyz, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(Remeber to stop the interactive plot by pressing the shutdown icon!)**\n",
    "\n",
    "Now apply PCA to our transformed data and plot the result as before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Cbg9auA2xkoAP0oLY56EL/i8M/xEGHwOnBWl5GZniW8htf5pwJI+dSZBePBPLL4kIWiKs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\nMx4bOxAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb3e0065828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "_V, xq2 = pca(xyz, q=2)\n",
    "_ = mllab.pca.plot_toy_2d(xq2, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Could be worse, but undeniably discomforting. Try different axes lengths and gap sizes of the ellipse. What do you observe?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 3.3\n",
    "\n",
    "We want to see if PCA can improve the accuracy of separating hyperlanes. First compute the singular values of the Iris dataset, then check how many percent of the variance the first two principal components capture."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "iris = load_iris()\n",
    "iris_x = iris['data']\n",
    "iris_y = iris['target']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.linalg import svdvals\n",
    "svals = svdvals(iris_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First PC:  0.9654296885622257\n",
      "First two PC:  0.9983676589194722\n"
     ]
    }
   ],
   "source": [
    "print(\"First PC: \", np.sum(svals[:1] ** 2) / np.sum(svals ** 2))\n",
    "print(\"First two PC: \", np.sum(svals[:2] ** 2) / np.sum(svals ** 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now apply PCA and compute the first two principal components. Plot the projected 2D data in a scatter plot such that the three labels are recognizable. What do you observe?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HKS6c3f12cOQgsHEZoNAt6pXy9mPSY/m7Te7iY3rZu0Bf3CFmvvsc7rKtKACAUpj+5h7r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\nCCE54/8DmkQL8V2eIkUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb3cf9c1358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "_, iris_xq = pca(iris_x, 2)\n",
    "ir_set = iris_xq[iris_y == 0,:]\n",
    "ir_ver = iris_xq[iris_y == 1,:]\n",
    "ir_vir = iris_xq[iris_y == 2,:]\n",
    "plt.scatter(ir_set[:,0], ir_set[:,1], marker='x')\n",
    "plt.scatter(ir_ver[:,0], ir_ver[:,1], marker='x')\n",
    "plt.scatter(ir_vir[:,0], ir_vir[:,1], marker='x')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAD8CAYAAACfF6SlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhJQ/QELKHyAh5Q+QkPIHSEj5AyT0FzEeJs/JfZqOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb3cf9b34a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, iris_x1 = pca(iris_x, 1)\n",
    "ir_set1 = iris_x1[iris_y == 0,0]\n",
    "ir_ver1 = iris_x1[iris_y == 1,0]\n",
    "ir_vir1 = iris_x1[iris_y == 2,0]\n",
    "\n",
    "def plot_1d_iris(a, b, c):\n",
    "    \"\"\"Show a 1D plot of three 1D datasets a, b and c.\n",
    "    \n",
    "    Top to bottom plotted in order is a, b, c.\"\"\"\n",
    "    left = min(x.min() for x in (a, b, c))\n",
    "    right = max(x.max() for x in (a, b, c))\n",
    "    for i, (x, c) in enumerate(((a, 'red'), (b, 'blue'), (c, 'green'))):\n",
    "        plt.hlines(i * .3, left, right, linestyles='dotted', colors=[(.8,.8,.8,1)])\n",
    "        plt.eventplot(x, colors=c, linewidths=.5, linelengths=.25, lineoffsets=(2 - i) * .3)\n",
    "    plt.axis('off')\n",
    "\n",
    "plot_1d_iris(ir_set1, ir_ver1, ir_vir1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, recompute the accurancy as in sheet 1 and compare the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy.linalg import lstsq\n",
    "from sklearn.metrics import confusion_matrix, accuracy_score\n",
    "\n",
    "\n",
    "def sep_plane(x1, x2):\n",
    "    \"\"\"Compute LLS hyperplane separating the two set of points\"\"\"\n",
    "    n1, n2 = x1.shape[0], x2.shape[0]\n",
    "    x = np.hstack((np.ones((n1 + n2, 1)), np.vstack((x1, x2))))\n",
    "    y = np.concatenate((np.ones(n1), np.zeros(n2)))\n",
    "    return lstsq(x, y, rcond=None)[0]\n",
    "\n",
    "\n",
    "def plane_classify(plane, x):\n",
    "    \"\"\"Classify points in x using the given plane.\"\"\"\n",
    "    return np.where(np.dot(x, plane[1:]) + plane[0] < .5, 0, 1)\n",
    "\n",
    "\n",
    "def conf_mat(plane, x1, x2):\n",
    "    \"\"\"Compute the confusion matrix.\"\"\"\n",
    "    y_real = np.concatenate((np.ones(x1.shape[0], dtype='int'), np.zeros(x2.shape[0], dtype='int')))\n",
    "    y_pred = plane_classify(plane, np.vstack((x1, x2)))\n",
    "    return confusion_matrix(y_real, y_pred)\n",
    "\n",
    "\n",
    "def accuracy(x1, x2, plane=None):\n",
    "    if plane is None:\n",
    "        plane = sep_plane(x1, x2)\n",
    "    y_real = np.concatenate((np.ones(x1.shape[0], dtype='int'), np.zeros(x2.shape[0], dtype='int')))\n",
    "    y_pred = plane_classify(plane, np.vstack((x1, x2)))\n",
    "    return accuracy_score(y_real, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4D: train 98.33% test 100.00%\n",
      "2D: train 95.83% test 96.67%\n",
      "1D: train 91.67% test 96.67%\n"
     ]
    }
   ],
   "source": [
    "# add your code here\n",
    "def build_classifier(iris_x, iris_y):\n",
    "    ir_set = iris_x[iris_y == 0,:]\n",
    "    ir_ver = iris_x[iris_y == 1,:]\n",
    "    ir_vir = iris_x[iris_y == 2,:]\n",
    "    plane_set = sep_plane(np.vstack((ir_vir, ir_ver)), ir_set)\n",
    "    plane_vir_ver = sep_plane(ir_vir, ir_ver)\n",
    "    \n",
    "    def classify(x):\n",
    "        y = plane_classify(plane_set, x)\n",
    "        y[y == 1] = plane_classify(plane_vir_ver, x[y == 1,:]) + 1\n",
    "        return y\n",
    "    \n",
    "    return classify\n",
    "\n",
    "def build_train_test(iris_x, iris_y, perc=.8):\n",
    "    test = np.array([[]]).reshape(-1, iris_x.shape[1])\n",
    "    test_y = np.array([])\n",
    "    train = np.array([[]]).reshape(-1, iris_x.shape[1])\n",
    "    train_y = np.array([])\n",
    "    for y in range(3):\n",
    "        iris_xy = iris_x[iris_y == y]\n",
    "        n = iris_xy.shape[0]\n",
    "        n_tr = int(np.round(n * perc))\n",
    "        indices = np.random.permutation(n)\n",
    "        train = np.vstack((train, iris_xy[indices[:n_tr],:]))\n",
    "        train_y = np.concatenate((train_y, np.ones(n_tr)*y))\n",
    "        test = np.vstack((test, iris_xy[indices[n_tr:]]))\n",
    "        test_y = np.concatenate((test_y, np.ones(n - n_tr)*y))\n",
    "    return train, train_y, test, test_y\n",
    "\n",
    "iris_x_tr, iris_y_tr, iris_x_te, iris_y_te = build_train_test(iris_x, iris_y)\n",
    "cf = build_classifier(iris_x_tr, iris_y_tr)\n",
    "print(\"4D: train {:2.2f}% test {:2.2f}%\".format(\n",
    "    accuracy_score(cf(iris_x_tr), iris_y_tr) * 100,\n",
    "    accuracy_score(cf(iris_x_te), iris_y_te) * 100))\n",
    "\n",
    "_, iris_x2 = pca(iris_x, 2)\n",
    "iris_x_tr, iris_y_tr, iris_x_te, iris_y_te = build_train_test(iris_x2, iris_y)\n",
    "cf = build_classifier(iris_x_tr, iris_y_tr)\n",
    "print(\"2D: train {:2.2f}% test {:2.2f}%\".format(\n",
    "    accuracy_score(cf(iris_x_tr), iris_y_tr) * 100,\n",
    "    accuracy_score(cf(iris_x_te), iris_y_te) * 100))\n",
    "\n",
    "_, iris_x1 = pca(iris_x, 1)\n",
    "iris_x_tr, iris_y_tr, iris_x_te, iris_y_te = build_train_test(iris_x1, iris_y)\n",
    "cf = build_classifier(iris_x_tr, iris_y_tr)\n",
    "print(\"1D: train {:2.2f}% test {:2.2f}%\".format(\n",
    "    accuracy_score(cf(iris_x_tr), iris_y_tr) * 100,\n",
    "    accuracy_score(cf(iris_x_te), iris_y_te) * 100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pedestrian Classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "input_file_path = \"data/pca_ped_25x50.mat\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Rread the file above into a NumPy array__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import scipy.io\n",
    "ped_data = scipy.io.loadmat(input_file_path)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Get the training data out__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Expected:\n",
    "#  1. Find the matrix names (dictionary keys)\n",
    "#  2. Notice that the first component is always 1 or -1 (ped vs. garb)\n",
    "#     remove it\n",
    "\n",
    "ped_images = ped_data['ped_train_int_25x50'][:,1:]\n",
    "garb_images = ped_data['garb_train_int_25x50'][:,1:]\n",
    "ped_test_images = ped_data['ped_test_int_25x50'][:,1:]\n",
    "garb_test_images = ped_data['garb_test_int_25x50'][:,1:]\n",
    "del ped_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Normalize the data to the range [0, 1]__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Expected:\n",
    "#  1. Figure out upper and lower bounds (-17, 273)\n",
    "#  2. Write a linear transformation\n",
    "\n",
    "def normalize_range(im):\n",
    "    \"\"\"\n",
    "    Normalize any image from the pedestrian dataset\n",
    "    to contain only values between 0 and 1.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    \n",
    "    im: array-like (any shape)\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    \n",
    "    nim: array in the shape of `im`\n",
    "    \"\"\"\n",
    "    return (im + 17) / (273 + 17)\n",
    "\n",
    "ped_images = normalize_range(ped_images)\n",
    "garb_images = normalize_range(garb_images)\n",
    "ped_test_images = normalize_range(ped_test_images)\n",
    "garb_test_images = normalize_range(garb_test_images)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Write a function to plot an image__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "\n",
    "def plot_im(im, ax=None, title=None, max_contrast=False):\n",
    "    \"\"\"\n",
    "    Plot a normalized image.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    \n",
    "    im: (1250,) array-like\n",
    "    \"\"\"\n",
    "    im = im.reshape((25, 50)).T\n",
    "    if ax is None:\n",
    "        ax = plt.gca()\n",
    "    if title:\n",
    "        ax.set_title(title)\n",
    "    if max_contrast:\n",
    "        ax.imshow(im, cmap = plt.get_cmap('gray'))\n",
    "    else:\n",
    "        ax.imshow(im, cmap = plt.get_cmap('gray'), vmin=0, vmax=1)\n",
    "    ax.axis('off')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BkiRJkiRJkqR5iohtgF93mGL/zNyvTprBiYidKYUGXRyUmXvVyDM7zcLbEylv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\nHeDyzMyRFoqI9aie/P0O4EldZPk88NcuxrVGZv5vRKwNfLx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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb3ce045c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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gCLOBk4AjKIUaDw/4/OqJiMOAf2wwtFXBWlMdPHevCbyH8j3q5/XsV8DnM/PXfTzHE4qI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\nvLU95cpxJGlomTk7Iv4NOKrQyB2B0yLiHOB/gGMy89rJDom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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb3cd7a9ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 10\n",
    "\n",
    "subset = np.random.randint(0, 1500, n)\n",
    "\n",
    "fig, axes = plt.subplots(1, n, figsize=(8*n, 16))\n",
    "fig.suptitle('Pedestrian images', fontsize=160)\n",
    "for i in range(n):\n",
    "    plot_im(ped_images[subset[i]], ax=axes[i])\n",
    "\n",
    "fig, axes = plt.subplots(1, n, figsize=(8*n, 16))\n",
    "fig.suptitle('Garbage images', fontsize=160)\n",
    "for i in range(n):\n",
    "    plot_im(garb_images[subset[i]], ax=axes[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=None, random_state=None,\n",
       "  svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "int_train_features = np.vstack((ped_images, garb_images))\n",
    "int_train_labels = np.concatenate((np.ones(ped_images.shape[0]), np.zeros(garb_images.shape[0])))\n",
    "int_train_pca = PCA()\n",
    "int_train_pca.fit(int_train_features)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "int_test_features = np.vstack((ped_test_images, garb_test_images))\n",
    "int_test_labels = np.concatenate((np.ones(ped_test_images.shape[0]), np.zeros(garb_test_images.shape[0])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb3c40e7390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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BCkTENsCJldbdxOB8tk9mnpqZNQrDyMxrM/N4YHfgU9MYXQt4R40MkiTNVBGx\nCXBM4ZrPVYjSRWk5Sqdizp74TcHs+hGxdbUkkiRJkiRJkiRJ6h1LZSRJkiRJkiRJktTVm4ENK+z5\nOnCPzDy9wq5VyszFmfl64GCmfsHY/BFGGqWXA/evsOdrDIoZ3pCZN1fYt0aZeQFwP+AtFdZ9MCJq\nfIyOy+ZATOHfXQ7cLzOfm5l/GVWYYVHNI6lTdPGsiFi/wp4Wppr7AuCAzDw5M3NUYTLzLGA/Bq/P\nUpsAb6+wp0hE3JU6hR/XAI/LzCMy89IK+9YoM2/MzH8CDh0ev8QTIuKxFWJ19Q5gywp7LgUOysy3\nZeaSCvv+RmZelZlPZlDiNNX3p+1HkUWSpBnkWcAGhTs+XiNIByWlMgsz8/pqScbv6sL50kIeSZIk\nSZIkSZIk9ZilMpIkSZIkSZIkSZq2iDgIOLrCqlOAw4flFWORmd8B7gMsGNcxxyki9gJeVbgmhzsO\nzcyx/8b2zFyamS8DjgJKCgnuBLy2Sqj++CpwYGZ+bxwHy8xlmflCyotlNgP+vkKkvjoHuG9mXjaO\ng2XmH4HDqXPR7hMiokYJVScREcCHgPUKV53LoATrc+Wppi8zvwEcAFxSuOq9EVH6WExbRNyHwTm3\n1FcYnKMurrBrjTLzZOC+wB/GcTxJkmaqiNgA+OfCNd/PzF/WyNPBnQtmJ/3ziNJSmR2rpJAkSZIk\nSZIkSVIvWSojSZIkSZIkSZKkLt4FROGOjwBHZ+at5XGmJzOvAh4IXDjuY49SRMwBTgLWKVizCHhi\nZr4hM7NOsm4y8xTgiZQVyzwvIrarFKm104C/y8w/NTj2i4CzCnfUKKLqoy8Dj8rMm8d50MxcCjwN\n+GiFde8clru08EKgtNTmEwxKsP5YIU9nmfkb4EFASaHK9sBz6iSamuFz/84Kq84GHp2ZN1bYNWWZ\neQFwCDC2gjpJkmagfwG2KtxxYo0g0xURGwLzClaUlrK0Vpp/iyopJEmSJEmSJEmS1EuWykiSJEmS\nJEmSJGlaIuJhwEGFa84BnpWZyypE6iQzrwUeyeT/VvIVPR84sGB+MfC4zDytUp5imXk6cGzBinWB\nl1eK09JngaNalDABDF+rxwLXFqy5f0RsUylSX1zE4DWzsMXBh8/LM4CvFq46ADiyPNH0RMS2wBsL\n15wMPCUzb6kQqdiw2OZQ4LcFa14WEetXijQVRwH3KtzxPeCxmbmoQp5py8xLgcOAG1ocX5KkSRYR\ndwGOK1zzR+DjFeJ0sXnh/GwvlSl9/CRJkiRJkiRJktRjlspIkiRJkiRJkiRpukovNrsMeEKrcowV\nZeZvgMcAS1pnKRUR84FXFqwnUzDcAAAgAElEQVRI4OjM/GKlSNVk5seBtxaseFZE7FArTwM/Av6+\n9WsmM/8A/GvBirWAx1WK0wd/Bh6TmTe1DJGZSxkUwvyqcFXpub2LVwHzC+ZPB47NzKyUp4rMvBo4\nAuhaNrQ18Lx6idboZYXzVzEoV2pa7JOZFwN/z+D9TJIkTd0HGJRxlnhrq3I5YLPC+ZLizD4ozV/6\n+EmSJEmSJEmSJKnHLJWRJEmSJEmSJEldvCYicgbfNmn9APdVRNwDeHDBimXA0zPzL5UiFcvM7wNv\nbJ2jgn8EtiqYf0NmnlYrzAi8Aji/4+w84FkVs4zTn4AjMrNrOUVtHwEuLZh/aKUcffDszLy8dQiA\nzPwzcBSDc2xX+0fEIXUSrVlE7Ag8s2DFpcBThqU6vZOZ5zE4b3X1/IiIWnlWJSIOB/YtWJHAkzLz\n95UiFcnMzwNvaZ1DkqRJERHHAocXrvk98P4KcbravHD+hiop2inNX/r4SZIkSZIkSZIkqccslZEk\nSZIkSZIkSdJ0vKRw/j2Z+a0qSep6A3BB6xBdRcTGwHEFK74OvKZSnJHIzFuBpwNLOq54ekRM4vdH\nX5yZV7YOsdywwOPtBSvuN46ijDH4bGZ+pnWIFWXmD4B3F655aY0sU/QaYJ2Os4uAx2XmjRXzjMK7\nge90nN0JOLRelFUqfc7f38P39dcCP2sdQpKkvouInYF3Vlj1ysy8ucKerjYrnL++Sop2SktlSh8/\nSZIkSZIkSZIk9dgk/tCkJEmSJEmSJEmSGoiI9YHHFaz4E/DqSnGqyswlwItb5yjwHGDTjrOLgGdl\n5rKKeUYiMy8C/rPj+J2Ah1aMMw5fzsyPtw6xEp8E/tpxdnNgj4pZWrgZeEHrEKvwKuCqgvlHRMSd\na4VZlYjYHnhqwYrjM3NBrTyjMjyvlry3PLNWlpWJiN2BwwtW/A7410pxqsnMRYz4sZMkadJFxFzg\n48CGhavOBz5anqhIaSlKaSlLU8Piz5JSH0tlJEmSJEmSJEmSZjBLZSRJkiRJkiRJkjRVjwbmF8y/\nKTN7+xvAM/MbwJdb55iuiAjKLp5/Y2ZeVivPGLwBWNhx9piKOUYtgeNah1iZzLwZ+FzBivvVytLI\nezLz961DrExm3gS8sWBFAEdWirM6xwJzOs5eCry1YpaRyswfAmd0HH9sRGxSM88dPLlw/vjMvLFK\nksoy81zg861zSJLUY68H7lu4YxnwnB4UlG5cOD/RpTJDJfeh9PGTJEmSJEmSJElSj1kqI0mSJEmS\nJEmSpKk6qmD2GuB9tYKM0KtbB+jgQcCuHWevBd5RMcvIDcs8Tu44/tCImFszzwh9NjMvbB1iNc4s\nmN2rWorxu4H+F5r8P+DXBfMl5/o1GhZhHVuw4rWZuaRWnjF5U8e5dYDDaga5gycVzF4OfLhWkBH5\nNwYFXZIkaQUR8QjgXyqseldmnldhT6l5hfOzvVSm9PGTJEmSJEmSJElSj1kqI0mSJEmSJEmSpDWK\niA2BhxWsOCkzF9bKMyqZ+X3gR61zTNMzC2bfkZk3VUsyPv+v49zGwH1qBhmht7UOsAZfBpZ2nN2j\nZpAxOykz/9Q6xOpk5mLgPQUr9ouI3WvlWYnDgJ06zl4KfLpelPHIzO8BF3UcL3nvXaWI2B+4a8GK\nt/W93GdYzFVSgCVJ0owTEbsCHweicNUvgFeWJ6pi7cL5Xn9OM0WLC2bXqZZCkiRJkiRJkiRJvWOp\njCRJkiRJkiRJkqbiYLpfaJTACRWzjNoHWgeYqojYAHhcx/FbgA9WjDM2mXk+8NOO4yMpaKjskmEJ\nRW9l5o3AJR3HJ7lU5j9bB5iijzB4jXf12Eo5VuZpBbPvzsxl1ZKM10c7zj20aorbPL5g9iYGF6NP\ngkn6/EOSpJEalsWeDmxSuGopcEyPimNLS1FurZKirZL7UFrKI0mSJEmSJEmSpB6zVEaSJEmSJEmS\nJElT8aCC2XMz81fVkozeKZSVMYzTocC8jrOfy8y/1AwzZl/oOHdY1RSj0bV8Yty+33HuzhFReuFn\nC9/OzItbh5iKzPwT8NmCFSXn/FWKiLXoXuy0CPhUxTjj1vWctX1E3K1qkoGHFMx+KjOvr5ZktM4G\nft06hCRJrQ0/D/sksFeFda/PzO9U2FNL6dcWS6qkaKukVGYSvzaTJEmSJEmSJEnSFFkqI0mSJEmS\nJEmSpKkoKRg4o1qKMcjMG4Gvtc4xRQ8vmD25Woo2zuo4t29EzK2apL7/bh1gihZ0nFsL2KpmkDH5\ndOsA03Rawez9R/Q6uTewWcfZz2fmdTXDjFNmXgpc3nH8gJpZImKjwp0TU+6TmcsYlMVJkjTbvQV4\nZIU93wKOr7CnprUL50sKWfrCUhlJkiRJkiRJkiStlKUykiRJkiRJkiRJWq2I2AS4e8GKiSqVGTq9\ndYAp+ruOczcDX68ZpIEfAks7zM0D9qycpabfZOYlrUNM0S8KZiexVObzrQNM05eARR1n5wMHVsyy\nXEkR1qSULa3O9zrO3aNqCngAMKfj7HXA/1TMMg6T+HmIJEnVRMRzgZdWWHUNcFRmdvk6bJRKS1Fm\nQqnMkoJZS2UkSZIkSZIkSZJmMEtlJEmSJEmSJEmStCb70f37Sldk5i9rhhmTr7QOsCYRsTewQ8fx\nb2Rm17KJXsjMhcClHcf3q5mlsm+0DjANvyqY3bpaivG4ODMvbx1iOjLzJuBrBSseWCvLCh7WcS4Z\nlORMuh91nKt9zjqkYPaLmTlpF15/D7i6dQhJklqIiEcA76mwailwdGb+rsKu2rqW5S3Xt5KcLkru\nw9xqKSRJkiRJkiRJktQ7lspIkiRJkiRJkiRpTfYumP1utRRjNCyP+EPrHGtwn4LZr1dL0daFHefu\nUTVFXT9pHWAari2Y3bJaivH4ZusAHZXk3rdaCiAi1gXu3nH8ksz8Y808jfTlnLV/wexXq6UYk8xM\nZs77niRJUxYRBwGnUl66AvCKzOxr+Wpp4d1MKFUpuQ9LqqWQJEmSJEmSJElS71gqI0mSJEmSJEmS\npDWZdaUyQ33Pvl/B7PnVUrR1Zce5naumqOuC1gGm4VogO86uVzPIGPT9fLAq3yuYLTn3r8y+dL/Y\ndbafszaNiI0r5piN7+uTmluSpE4iYk/gC8D6FdadkplvqbBnVBYXzs/2UpnSx0+SJEmSJEmSJEk9\nZqmMJEmSJEmSJEnq4nWZGTP4dl3rB7hnSi4+n+QigL5n37/jXAI/rhmkod92nNu+aoq6ft46wFRl\n5lLgxo7j82pmGYNJLaQ4D7i14+zuEVHzAtuu5yzo//l4qn5TMFvlvBURWwBbdRy/Dri0Ro4GSgqW\nJEmaKBGxI/BlYPMK674OHFNhzygtKZy3VEaSJEmSJEmSJEkzlqUykiRJkiRJkiRJWpPdCmYnpiBj\nJXqbPSLmAPt2HP/9DCpOuqbj3A5VU9SzDPh96xDTdEvHuUkqlbkpMy9rHaKLzLwZ+GXH8XnArhXj\n7Fcwu6BaioYy8yZgUcfxWue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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb3b4e01588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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KZEoumAweeMwev9jfL4yI84CfAd/KzHMKjjFtRcSmwL40F1I+AVhmAmMr80Ah0MOXsPMy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\n+XuSFhTMWiojSZIkSZIkSZI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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb3b4bc99e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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BZr4tM381nUIZgMy8MTO/nZkvAtajV1I1f5o5Xgs8cpozkiRJ0v15aeH8iTVC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\nIuJ5wIcqrXtDZp5cadcw3Fo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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb3b4984208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "evs = int_train_pca.components_.copy()\n",
    "evs -= evs.min()\n",
    "evs /= evs.max()\n",
    "#evs = pca.components_.copy()\n",
    "evs = evs.reshape(1250,25,50)\n",
    "\n",
    "fig, axes = plt.subplots(1, 10, figsize=(8*n, 16))\n",
    "fig.suptitle('Eigenped. 1-10', fontsize=160)\n",
    "for i in range(n):\n",
    "    plot_im(evs[i], ax=axes[i])\n",
    "\n",
    "fig, axes = plt.subplots(1, 10, figsize=(8*n, 16))\n",
    "fig.suptitle('Eigenped. 11-20', fontsize=160)\n",
    "for i in range(n):\n",
    "    plot_im(evs[10+i], ax=axes[i])\n",
    "    \n",
    "fig, axes = plt.subplots(1, 10, figsize=(8*n, 16))\n",
    "fig.suptitle('Eigenped. 51-60', fontsize=160)\n",
    "for i in range(n):\n",
    "    plot_im(evs[50+i], ax=axes[i])\n",
    "\n",
    "fig, axes = plt.subplots(1, 10, figsize=(8*n, 16))\n",
    "fig.suptitle('Eigenped. 111-120', fontsize=160)\n",
    "for i in range(n):\n",
    "    plot_im(evs[110+i], ax=axes[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "60\n",
      "110\n",
      "160\n",
      "210\n",
      "260\n",
      "310\n",
      "360\n",
      "410\n",
      "460\n",
      "510\n",
      "560\n",
      "610\n",
      "660\n",
      "710\n",
      "760\n",
      "810\n",
      "860\n",
      "910\n",
      "960\n",
      "1010\n",
      "1060\n",
      "1110\n",
      "1160\n",
      "1210\n"
     ]
    }
   ],
   "source": [
    "from sklearn.svm import LinearSVC\n",
    "\n",
    "int_n_used_pcs = np.arange(10,1250,50)\n",
    "int_train_scores = np.zeros(len(int_n_used_pcs))\n",
    "int_test_scores = np.zeros(len(int_n_used_pcs))\n",
    "\n",
    "int_train_pca_features = int_train_pca.transform(int_train_features)\n",
    "int_test_pca_features = int_train_pca.transform(int_test_features)\n",
    "\n",
    "for i, q in enumerate(int_n_used_pcs):\n",
    "    svc = LinearSVC()\n",
    "    print(q)\n",
    "    svc.fit(int_train_pca_features[:,:q], int_train_labels)\n",
    "    int_train_scores[i] = svc.score(int_train_pca_features[:,:q], int_train_labels)\n",
    "    int_test_scores[i] = svc.score(int_test_pca_features[:,:q], int_test_labels) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb3cd81d5c0>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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zkKU3ENZOOTWJoBlngyYmJmrcuHEaOHCgrrjiCs2bN0+7du3SmDFjJEnR0dF6/fXXlZ6e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\n7P8DGxw9KbCChycAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb3cd783208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,10))\n",
    "plt.plot(int_n_used_pcs, int_train_scores, 'o-', label='training scores')\n",
    "plt.plot(int_n_used_pcs, int_test_scores, 'o-', label='testing scores')\n",
    "plt.xlabel('number of used pc'); plt.ylabel('accuracy');plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.ndimage as ndimage\n",
    "from numpy.linalg import norm\n",
    "from scipy.ndimage.filters import convolve\n",
    "\n",
    "\n",
    "class HogFeatures:\n",
    "    def __init__(self, im_shape, n_bins=9, cell_size=8, blk_size=2, unsigned=True, clip_val=.2):\n",
    "        self.deg_range = np.pi if unsigned else 2 * np.pi\n",
    "        self.n_bins = n_bins\n",
    "        self.bins = np.linspace(0, self.deg_range, n_bins, endpoint=False)\n",
    "        self.bin_size = self.deg_range / n_bins\n",
    "        self.cell_size = cell_size\n",
    "        self.blk_size = blk_size\n",
    "        self.clip_val = clip_val\n",
    "\n",
    "        self.im_h, self.im_w = im_shape\n",
    "        x, y = np.arange(self.im_w), np.arange(self.im_h)\n",
    "        \n",
    "        # Compute logical cell indices of next lower and upper cell\n",
    "        # w.r.t. to the cell center\n",
    "        cells_x = np.arange(-cell_size, self.im_w - (cell_size + 1)/2, cell_size)\n",
    "        self.n_cells_x = len(cells_x) - (2 if cells_x[-1] >= self.im_w else 1)\n",
    "        x0 = np.digitize(x, cells_x + cell_size / 2) - 2\n",
    "        Xc = ((x0 + 1) - .5) * cell_size - .5\n",
    "        f_x = (x - Xc) / cell_size\n",
    "\n",
    "        cells_y = np.arange(-cell_size, self.im_h - (cell_size + 1)/2, cell_size)\n",
    "        self.n_cells_y = len(cells_y) - (2 if cells_y[-1] >= self.im_h else 1)\n",
    "        y0 = np.digitize(y, cells_y + cell_size / 2) - 2\n",
    "        Yc = ((y0 + 1) - .5) * cell_size - .5\n",
    "        f_y = (y - Yc) / cell_size\n",
    "        \n",
    "        self.f_x, self.f_y = np.meshgrid(f_x, f_y)\n",
    "    \n",
    "    def extract(self, im):\n",
    "        im = im.reshape(self.im_h, self.im_w)\n",
    "        dx = convolve(im, [[1,0,-1]], mode='constant')\n",
    "        dy = convolve(im, [[-1],[0],[1]], mode='constant')\n",
    "        grads_dir = np.arctan2(dy, dx) % self.deg_range\n",
    "        grads_mag = norm(np.stack((dx, dy), axis=-1), axis=2)        \n",
    "        del dx, dy\n",
    "        \n",
    "        # Compute logical bin indices of next lower (<=) and upper bin (>)\n",
    "        # w.r.t. to the bin center\n",
    "        bin0 = np.digitize(grads_dir, self.bins + .5 * self.bin_size) - 1\n",
    "        bin1 = bin0 + 1\n",
    "        dirc = (bin0 + .5) * self.bin_size\n",
    "        f_b = (grads_dir - dirc) / self.bin_size\n",
    "        del grads_dir\n",
    "        \n",
    "        bin0 %= self.n_bins\n",
    "        bin1 %= self.n_bins\n",
    "        \n",
    "        f_x, f_y = self.f_x, self.f_y\n",
    "\n",
    "        hist = np.zeros((self.n_cells_y, self.n_cells_x, self.n_bins))\n",
    "        bin_labels = np.arange(self.n_bins)\n",
    "        # Iterate over all cells\n",
    "        for ci_x in range(self.n_cells_x):\n",
    "            x_pos = (ci_x * self.cell_size - (self.cell_size + 1) // 2, ci_x * self.cell_size + (self.cell_size + 1) // 2)\n",
    "            x_pre = slice(max(0, x_pos[0] + self.cell_size), max(0, x_pos[1] + self.cell_size))\n",
    "            x_pos = slice(max(0, x_pos[0]), x_pos[1])\n",
    "            for ci_y in range(self.n_cells_y):\n",
    "                y_pos = (ci_y * self.cell_size - (self.cell_size + 1) // 2, ci_y * self.cell_size + (self.cell_size + 1) // 2)\n",
    "                y_pre = slice(max(0, y_pos[0] + self.cell_size), max(0, y_pos[1] + self.cell_size))\n",
    "                y_pos = slice(max(0, y_pos[0]), y_pos[1])\n",
    "                # Consider all four sourinding cells\n",
    "                    \n",
    "                # y-pre x-pre\n",
    "                m = (y_pre, x_pre)\n",
    "                g = grads_mag[m] * (1 - f_x[m]) * (1 - f_y[m])\n",
    "                hist[ci_y, ci_x] += ndimage.sum(g * (1 - f_b[m]), bin0[m], bin_labels) + \\\n",
    "                    ndimage.sum(g * f_b[m], bin1[m], bin_labels)\n",
    "                # y-pos x-pre\n",
    "                m = (y_pos, x_pre)\n",
    "                g = grads_mag[m] * (1 - f_x[m]) * f_y[m]\n",
    "                hist[ci_y, ci_x] += ndimage.sum(g * (1 - f_b[m]), bin0[m], bin_labels) + \\\n",
    "                    ndimage.sum(g * f_b[m], bin1[m], bin_labels)\n",
    "                # y-pre x-pos\n",
    "                m = (y_pre, x_pos)\n",
    "                g = grads_mag[m] * f_x[m] * (1 - f_y[m])\n",
    "                hist[ci_y, ci_x] += ndimage.sum(g * (1 - f_b[m]), bin0[m], bin_labels) + \\\n",
    "                    ndimage.sum(g * f_b[m], bin1[m], bin_labels)\n",
    "                # y-pos x-pos\n",
    "                m = (y_pos, x_pos)\n",
    "                g = grads_mag[m] * f_x[m] * f_y[m]\n",
    "                hist[ci_y, ci_x] += ndimage.sum(g * (1 - f_b[m]), bin0[m], bin_labels) + \\\n",
    "                    ndimage.sum(g * f_b[m], bin1[m], bin_labels)\n",
    "        \n",
    "        n_blks_x = self.n_cells_x + 1 - self.blk_size\n",
    "        n_blks_y = self.n_cells_y + 1 - self.blk_size\n",
    "        features = np.zeros((n_blks_x, n_blks_y, self.blk_size ** 2 * self.n_bins))\n",
    "        for bi_x in range(n_blks_x):\n",
    "            for bi_y in range(n_blks_y):\n",
    "                blk = hist[bi_y:bi_y+self.blk_size, bi_x:bi_x+self.blk_size].copy()\n",
    "                blk_norm = norm(blk.flatten())\n",
    "                if blk_norm > 0:\n",
    "                    blk /= blk_norm\n",
    "                np.clip(blk, None, self.clip_val, out=blk)\n",
    "                blk_norm = norm(blk.flatten())\n",
    "                if blk_norm > 0:\n",
    "                    blk /= blk_norm\n",
    "                features[bi_x, bi_y] = blk.ravel()\n",
    "        return features.flatten()\n",
    "\n",
    "hog = HogFeatures((25, 50))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**To test you implementation test data is availabe.**\n",
    "\n",
    "The array `image` is the input, and `steps` contains the values of the inner variables of the HOG algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of bins: 9\n",
      "Cell size: 8\n",
      "Block size: 2\n",
      "Unsigned directions: True\n",
      "Clip value: 0.2\n"
     ]
    }
   ],
   "source": [
    "image, steps = mllab.pca.hog_test_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/bohn/anaconda3/lib/python3.6/site-packages/scipy/ndimage/measurements.py:431: FutureWarning: Conversion of the second argument of issubdtype from `int` to `np.signedinteger` is deprecated. In future, it will be treated as `np.int64 == np.dtype(int).type`.\n",
      "  safe = ((np.issubdtype(dt, int) and dt.itemsize <= int_size) or\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=None, random_state=None,\n",
       "  svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hog_train_features = []\n",
    "for i in range(int_train_features.shape[0]):\n",
    "    hog_train_features.append(hog.extract(int_train_features[i]))\n",
    "hog_train_features = np.array(hog_train_features)\n",
    "hog_train_pca = PCA()\n",
    "hog_train_pca.fit(hog_train_features)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/bohn/anaconda3/lib/python3.6/site-packages/scipy/ndimage/measurements.py:431: FutureWarning: Conversion of the second argument of issubdtype from `int` to `np.signedinteger` is deprecated. In future, it will be treated as `np.int64 == np.dtype(int).type`.\n",
      "  safe = ((np.issubdtype(dt, int) and dt.itemsize <= int_size) or\n"
     ]
    }
   ],
   "source": [
    "hog_test_features = []\n",
    "for i in range(int_test_features.shape[0]):\n",
    "    hog_test_features.append(hog.extract(int_test_features[i]))\n",
    "hog_test_features = np.array(hog_test_features)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "35\n",
      "60\n",
      "85\n",
      "110\n",
      "135\n",
      "160\n",
      "185\n",
      "210\n",
      "235\n",
      "260\n",
      "285\n",
      "310\n",
      "335\n"
     ]
    }
   ],
   "source": [
    "hog_n_used_pcs = np.arange(10,360,25)\n",
    "hog_train_scores = np.zeros(len(hog_n_used_pcs))\n",
    "hog_test_scores = np.zeros(len(hog_n_used_pcs))\n",
    "\n",
    "hog_train_pca_features = hog_train_pca.transform(hog_train_features)\n",
    "hog_test_pca_features = hog_train_pca.transform(hog_test_features)\n",
    "\n",
    "for i, q in enumerate(hog_n_used_pcs):\n",
    "    svc = LinearSVC()\n",
    "    print(q)\n",
    "    svc.fit(hog_train_pca_features[:,:q], int_train_labels)\n",
    "    hog_train_scores[i] = svc.score(hog_train_pca_features[:,:q], int_train_labels)\n",
    "    hog_test_scores[i] = svc.score(hog_test_pca_features[:,:q], int_test_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb3cd7d8780>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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w6sWraluKq/w+tjKXm3UHcisGOXx7+AQA3ROjuPWCbozvk8LI7gmEhQSd6RIi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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb3cc4a0f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,10))\n",
    "plt.plot(hog_n_used_pcs, hog_train_scores, 'o-', label='training scores')\n",
    "plt.plot(hog_n_used_pcs, hog_test_scores, 'o-', label='testing scores')\n",
    "plt.xlabel('number of used pc'); plt.ylabel('accuracy');plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}