main.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Hn0_iOUFy_w9"
   },
   "source": [
    "## Part 1: Implementation\n",
    "Implement spectral clustering function from scratch (for two clusters), taking as input the dataset. It must return the predicted clustering. Assume that the graph constructed is a fully connected graph. Use the normalized graph laplacian for this case.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "VYajkeo9BVu5"
   },
   "outputs": [],
   "source": [
    "from sklearn.cluster        import KMeans\n",
    "from sklearn.neighbors      import kneighbors_graph\n",
    "from scipy.spatial.distance import pdist, squareform\n",
    "from scipy.sparse.csgraph   import laplacian\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "\"\"\"Args:\n",
    "X: input samples, array (num, dim)\n",
    "n_clusters:   no. of clusters\n",
    "n_neighbours: neighborhood size\n",
    "\n",
    "Returns:\n",
    "Y: labels for samples, array (num,)\n",
    "\"\"\"\n",
    "def spectral_clustering(X, n_clusters=2, n_neighbors=10):\n",
    "    n, d = X.shape\n",
    "    A = kneighbors_graph(X, n_neighbors, mode='connectivity').toarray()\n",
    "    L = laplacian(A, normed=True)\n",
    "    w, v = np.linalg.eig(L)\n",
    "    w, v = w.real, v.real\n",
    "    i = np.argsort(w)\n",
    "    w, v = w[i], v[:,i]\n",
    "    Y = KMeans(n_clusters).fit_predict(v[:,:2])\n",
    "    return Y\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "D2txlZ8iyA1u"
   },
   "source": [
    "## Part 2: Clustering concentric circles\n",
    "Perform spectral clustering on the concentric circles dataset. Visualize the result by plotting it on a 2-d graph. Use different colours for different clusters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "EQJkpUzj1vSY"
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_circles \n",
    "\n",
    "CX, CY = make_circles(n_samples=200, shuffle=True,noise=0.05, random_state=1337, factor=0.5)\n",
    "# CX: input data points [n_samples, 2]\n",
    "# CY: true clusters [n_samples]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "3PKZWv1GAtKd"
   },
   "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 / mpl.ratio, fig.canvas.height / mpl.ratio);\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 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",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\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 src=\"data:image/png;base64,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\" width=\"600\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Part 2: Perform Spectral Clustering on the concentric circles dataset\n",
    "# Plot using colors from CY (true clusters) and CY_pred (predicted clusters)\n",
    "# Code in this cell should plot 2 subplots (true labels and predicted labels)\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib notebook\n",
    "\n",
    "C0 = CX[CY == 0]\n",
    "C1 = CX[CY == 1]\n",
    "\n",
    "DY = spectral_clustering(CX)\n",
    "D0 = CX[DY == 0]\n",
    "D1 = CX[DY == 1]\n",
    "\n",
    "fig = plt.figure(figsize=(6, 10))\n",
    "axi = fig.add_subplot(211)\n",
    "axi.scatter(C0[:,0], C0[:,1], label='Actual 0')\n",
    "axi.scatter(C1[:,0], C1[:,1], label='Actual 1')\n",
    "axi.title.set_text('Concentric circles dataset')\n",
    "\n",
    "axi = fig.add_subplot(212)\n",
    "axi.scatter(D0[:,0], D0[:,1], label='Predicted 0')\n",
    "axi.scatter(D1[:,0], D1[:,1], label='Predicted 1')\n",
    "axi.title.set_text('Predicted classes with Spectral clustering')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Y3Cy2CylyBpg"
   },
   "source": [
    "## Part 3: Evaluate accuracy\n",
    "Evaluate the accuracy of the clustering by comparing it with the true labels. Create two subplots (true vs predicted) with the color of each point showing the cluster label."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "-6GkKuI0BRrz"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy of Spectral clustering: 1.00\n"
     ]
    }
   ],
   "source": [
    "# Part 3: Report the accuracy of clustering\n",
    "ep = np.linalg.norm(DY - CY) / CY.shape[0]        # same class?\n",
    "en = np.linalg.norm((1 - DY) - CY) / CY.shape[0]  # reversed class?\n",
    "e = min(ep, en)                                         # it is ok if classes get reversed\n",
    "print('Accuracy of Spectral clustering: %.2f' % (1-e))  # accuracy = 1-error"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "Assignment 2",
   "provenance": [],
   "toc_visible": true
  },
  "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}