matrix_completion.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import glob\n",
    "import numpy as np\n",
    "%matplotlib notebook\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "512\n",
      "3395\n",
      "512\n"
     ]
    }
   ],
   "source": [
    "# users = list of all users\n",
    "# subs  = set of all subs (set to avoid duplicates)\n",
    "# activity = list of dictionary (key = sub , value = activity). ith list for ith user in users list\n",
    "\n",
    "users = []\n",
    "activity = []\n",
    "subs = set()\n",
    "for userDir in list(glob.iglob(\"users/*\")):\n",
    "    try:\n",
    "        with open(userDir+\"/subreddits30.csv\") as file:\n",
    "            userSubs = file.read().split('\\n')\n",
    "            tempDir = {}\n",
    "            for row in userSubs[1:-1]:\n",
    "                sub = row.split(',')[0]\n",
    "                score =  row.split(',')[1]\n",
    "                subs.add(sub)\n",
    "                tempDir[sub] = score\n",
    "            activity.append(tempDir)\n",
    "            users.append(userDir.split('/')[-1])\n",
    "    except:\n",
    "        pass\n",
    "subs = list(subs)\n",
    "print(len(users))\n",
    "print(len(subs))\n",
    "print(len(activity))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(512, 3395)\n"
     ]
    }
   ],
   "source": [
    "# matrix = row is user, column is sub, value is activity. Sparse with many zeros\n",
    "\n",
    "matrix = np.zeros((len(users),len(subs)))\n",
    "for idx,act in enumerate(activity):\n",
    "    for k,v in act.items():\n",
    "        matrix[idx][subs.index(k)] = v\n",
    "print(matrix.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# trying to cap max activity value\n",
    "# min max normalization\n",
    "\n",
    "# matrix[matrix>100] = 100\n",
    "# matrix = matrix/np.max(matrix,axis=1)[:,None]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(512, 3395)\n",
      "(512, 512)\n",
      "(512,)\n",
      "(512, 3395)\n"
     ]
    },
    {
     "data": {
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       "window.mpl = {};\n",
       "\n",
       "\n",
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       "    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",
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       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
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       "\n",
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       "            }\n",
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       "\n",
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       "\n",
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       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
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       "        '<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",
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       "\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 overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f68ca783780>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# SVD to get low rank structure. VT rows represent sub vectore. U rows represent users. \n",
    "U, S, VT = np.linalg.svd(matrix,full_matrices=False)\n",
    "matrixReconstruct = (U * S) @ VT\n",
    "print(matrix.shape)\n",
    "print(U.shape)\n",
    "print(S.shape)\n",
    "print(VT.shape)\n",
    "plt.plot(S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# remove less relevant dimnsions and preprocces to make row order for faster calculation\n",
    "U = U[:,:100]\n",
    "V = VT[:100]\n",
    "V = V.T.copy()\n",
    "matrixT = matrix.T.copy()\n",
    "matrixReconstructT = matrixReconstruct.T.copy()\n",
    "usersnp = np.array(users)\n",
    "subsnp = np.array(subs)\n",
    "random_user = np.random.randint(U.shape[0])\n",
    "random_sub = np.random.randint(V.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ukpolitics\n",
      "['ukpolitics' 'LabourUK' 'marvelstudios' 'MarvelStudiosSpoilers'\n",
      " 'HouseOfCards' 'syriancivilwar' 'coaxedintoasnafu' 'ufl'\n",
      " 'LiveFromNewYork' 'suits']\n"
     ]
    }
   ],
   "source": [
    "# pick random sub and find 10 closest subs (including that sub) using rank approximation\n",
    "close_subs = np.argsort(np.sum((V-V[random_sub])**2,axis=1))[:10]\n",
    "print(subsnp[random_sub])\n",
    "print(subsnp[close_subs])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ukpolitics\n",
      "['ukpolitics' 'LabourUK' 'marvelstudios' 'MarvelStudiosSpoilers'\n",
      " 'HouseOfCards' 'syriancivilwar' 'television' 'coaxedintoasnafu' 'ufl'\n",
      " 'TwentyFour']\n"
     ]
    }
   ],
   "source": [
    "# pick random sub and find 10 closest subs (including that sub) using original matrix\n",
    "close_subs = np.argsort(np.sum((matrixT-matrixT[random_sub])**2,axis=1))[:10]\n",
    "print(subsnp[random_sub])\n",
    "print(subsnp[close_subs])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ukpolitics\n",
      "['ukpolitics' 'LabourUK' 'marvelstudios' 'MarvelStudiosSpoilers'\n",
      " 'HouseOfCards' 'syriancivilwar' 'television' 'coaxedintoasnafu' 'ufl'\n",
      " 'suits']\n"
     ]
    }
   ],
   "source": [
    "# pick random sub and find 10 closest subs (including that sub) using reconstructed matrix\n",
    "close_subs = np.argsort(np.sum((matrixReconstructT-matrixReconstructT[random_sub])**2,axis=1))[:10]\n",
    "print(subsnp[random_sub])\n",
    "print(subsnp[close_subs])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fish_EyeMouth\n",
      "['Fish_EyeMouth' 'Maedhre' 'CJnella91' 'jonyprepperisrael' 'ashamedseesaw'\n",
      " 'Montiexx' 'purpleandorange1522' 'muhy_men' 'Baconboi212121' 'DogfaceZed']\n"
     ]
    }
   ],
   "source": [
    "# pick random user and find 10 closest user( including that user) using rank approximation\n",
    "close_users = np.argsort(np.sum((U-U[random_user])**2,axis=1))[:10]\n",
    "print(usersnp[random_user])\n",
    "print(usersnp[close_users])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fish_EyeMouth\n",
      "['Fish_EyeMouth' 'Maedhre' 'ashamedseesaw' 'jonyprepperisrael' 'Montiexx'\n",
      " 'Robotman6900' 'CJnella91' 'Waterkoker' 'Baconboi212121' 'DogfaceZed']\n"
     ]
    }
   ],
   "source": [
    "# pick random user and find 10 closest users (including that user) using original matrix\n",
    "close_users = np.argsort(np.sum((matrix-matrix[random_user])**2,axis=1))[:10]\n",
    "print(usersnp[random_user])\n",
    "print(usersnp[close_users])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fish_EyeMouth\n",
      "['Fish_EyeMouth' 'Maedhre' 'ashamedseesaw' 'jonyprepperisrael' 'Montiexx'\n",
      " 'Robotman6900' 'CJnella91' 'Waterkoker' 'Baconboi212121' 'DogfaceZed']\n"
     ]
    }
   ],
   "source": [
    "# pick random user and find 10 closest users (including that user) using reconstructed matrix\n",
    "close_users = np.argsort(np.sum((matrixReconstruct-matrixReconstruct[random_user])**2,axis=1))[:10]\n",
    "print(usersnp[random_user])\n",
    "print(usersnp[close_users])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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