train_mouse_tvae.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5b1035e4",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/andrewulmer/miniconda3/envs/mabe_2022/lib/python3.8/site-packages/tqdm/auto.py:22: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n",
      "  from .autonotebook import tqdm as notebook_tqdm\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "from tqdm import tqdm\n",
    "sys.path.append('./tvae')\n",
    "from train import *"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c798a5b",
   "metadata": {},
   "source": [
    "# Load videos and stack mice to perform mean-centering and SVD\n",
    "\n",
    "The TVAE accepts a sequence of frames as inputs. Before we split the videos into sequences, we are going to preprocess all the poses by normalizing the keypoint coordinates, mean-centering them, rotationally aligning the spine with the y-axis, and computing the singular value decomposition of the aligned pose. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "73a425e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "user_train = np.load('mouse_data/user_train.npy', allow_pickle=True).item()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "973fd405",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1600/1600 [00:00<00:00, 1927.55it/s]\n"
     ]
    }
   ],
   "source": [
    "# First we need to combine all the videos and normalize them to compute SVD\n",
    "from datasets.mouse_v1.preprocess import normalize\n",
    "\n",
    "full_dataset = []\n",
    "for i, (name, sequence) in enumerate(tqdm(user_train['sequences'].items())):\n",
    "    # Vectorizes each frame in the sequence\n",
    "    vec_seq = sequence['keypoints'].reshape(sequence['keypoints'].shape[0], -1)\n",
    "    full_dataset.append(normalize(vec_seq))\n",
    "           \n",
    "full_dataset = np.concatenate(full_dataset, axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9666e2c",
   "metadata": {},
   "source": [
    "The output of the last step is an array of each of the frames stacked on top of one another. Each of the 3 mice has 12 keypoints, with both x and y coordinates. So `full_dataset` will be `total_frames x 72`. \n",
    "\n",
    "The next step is to rotationally align each of the mice's poses such that the vector formed by the keypoint at the neck base and the keypoint at the tail base is aligned with the y-axis. The angle of rotation is stored and fed as an input to the model. After the poses are rotationally aligned, the mean of each mouse's pose is subtracted, and the singular value decomposition of the normalized, aligned, and mean-centered pose is computed. In a sense, we are trying to limit the relevant sources of variance that the TVAE representations will capture."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f9b3342d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Next we need to complete the rotation alignment and compute SVD\n",
    "from datasets.mouse_v1.preprocess import transform_to_svd_components\n",
    "_, svd, mean = transform_to_svd_components(full_dataset)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a736754",
   "metadata": {},
   "source": [
    "# Create sub-sequences with sliding window and complete preprocessing"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7157aa58",
   "metadata": {},
   "source": [
    "Next we iterate through each video and apply the preprocessing stack we developed in the last step. After each video is preprocessed, we pad the beginning and end of the video with repeat frames and create fixed-length sliding window sequences defined by `sub_seq_length` and `sliding_window` below. These sequences will be the inputs provided as inputs to the TVAE."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6caf64a2",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1600/1600 [01:19<00:00, 20.18it/s]\n"
     ]
    }
   ],
   "source": [
    "# Now we need to iterate through the videos, rotationally align, mean subtract, and apply SVD\n",
    "preprocessed_data = []\n",
    "sub_seq_length = 21\n",
    "sliding_window = 5\n",
    "for i, (name, sequence) in enumerate(tqdm(user_train['sequences'].items())):\n",
    "    # Preprocess sequences\n",
    "    vec_seq = sequence['keypoints'].reshape(sequence['keypoints'].shape[0], -1)\n",
    "    vec_seq = normalize(vec_seq)\n",
    "    \n",
    "    if i == 0: # Here for debugging - leave to demonstrate that preprocessing works\n",
    "        control = vec_seq\n",
    "        control = control.reshape(control.shape[0], -1)\n",
    "        control = np.pad(control, ((sub_seq_length//2, sub_seq_length-1-sub_seq_length//2), (0,0)), mode='edge')\n",
    "        control = np.stack([control[i:len(control)+i-sub_seq_length+1:sliding_window] for i in range(sub_seq_length)], axis=1)\n",
    "    \n",
    "    vec_seq, _, _ = transform_to_svd_components(\n",
    "            vec_seq,\n",
    "            svd_computer=svd,\n",
    "            mean=mean\n",
    "    )\n",
    "    \n",
    "    # Pads the beginning and end of the sequence with duplicate frames\n",
    "    vec_seq = vec_seq.reshape(vec_seq.shape[0], -1)\n",
    "    pad_vec = np.pad(vec_seq, ((sub_seq_length//2, sub_seq_length-1-sub_seq_length//2), (0,0)), mode='edge')\n",
    "    \n",
    "    # Converts sequence into [number of sub-sequences, frames in sub-sequence, x/y alternating keypoints]\n",
    "    sub_seqs = np.stack([pad_vec[i:len(pad_vec)+i-sub_seq_length+1:sliding_window] for i in range(sub_seq_length)], axis=1)\n",
    "    preprocessed_data.append(sub_seqs)\n",
    "        \n",
    "preprocessed_data = np.concatenate(preprocessed_data, axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9acf0db",
   "metadata": {},
   "source": [
    "# Postprocessing demonstration"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2aae2a16",
   "metadata": {},
   "source": [
    "This next cell demonstrates how to postprocess the pose and also serves as a sanity check to make sure the unalignment, SVD, and unnormalization give us back approximately the same pose we started with."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5ea84261",
   "metadata": {},
   "outputs": [
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       "\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": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Test postprocessing\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.animation import PillowWriter\n",
    "\n",
    "%matplotlib notebook\n",
    "\n",
    "from datasets.mouse_v1.preprocess import transform_svd_to_keypoints\n",
    "from datasets.mouse_v1.preprocess import unnormalize\n",
    "\n",
    "random_seq = preprocessed_data[20] # Cannot compare postprocessed/original pairs outside of first sequence (index 1800)\n",
    "random_seq = random_seq.reshape(-1, 3, 11)\n",
    "random_seq = transform_svd_to_keypoints(random_seq, svd, mean)\n",
    "random_seq = random_seq.reshape(random_seq.shape[0],-1)\n",
    "random_seq = unnormalize(random_seq.reshape(random_seq.shape[0],-1))\n",
    "\n",
    "control_seq = control[20] \n",
    "control_seq = control_seq.reshape(-1, 3, 12, 2)\n",
    "control_seq = control_seq[:,:,:10,:]\n",
    "control_seq = control_seq.reshape(control_seq.shape[0], -1)\n",
    "control_seq = unnormalize(control_seq)\n",
    "\n",
    "from celluloid import Camera\n",
    "fig = plt.figure()\n",
    "camera = Camera(fig)\n",
    "plt.xlim(0,850), plt.ylim(0,850)\n",
    "for i in range(0,21):\n",
    "    xvals = random_seq[i,::2]\n",
    "    yvals = random_seq[i,1::2]\n",
    "    plt.scatter(x=xvals, y=yvals, c='b')\n",
    "\n",
    "    xvals = control_seq[i,::2]\n",
    "    yvals = control_seq[i,1::2]\n",
    "    plt.scatter(x=xvals, y=yvals, c='g')\n",
    "    \n",
    "    camera.snap()\n",
    "    \n",
    "animation = camera.animate()\n",
    "writer = PillowWriter(fps=30)\n",
    "animation.save('test.gif', writer=writer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e17f52a",
   "metadata": {},
   "source": [
    "# Configure the model and training parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "625d9744",
   "metadata": {},
   "source": [
    "<!-- ![Screenshot%20from%202022-03-16%2016-02-04.png]() -->\n",
    "\n",
    "<div>\n",
    "<img src=\"tvae_diagram.png\" width=\"750\"/>\n",
    "</div>\n",
    "\n",
    "Above is the architecture that defines the trajectory variational autoencoder (TVAE) used here. The input to the model is comprised of states $s_{0}, ... , s_{\\tau}$ and actions that define the change from one state to the next $a_{0}, ... , a_{\\tau - 1}$. The encoder is a bi-directional GRU, the output of which, at each time step, is averaged and fed into fully-connected layers that produce a mean and variance which define a gaussian distribution (the posterior). A sample is then generated from the posterior and passed as an input, along with the initial state $s_{0}$ to the decoder. \n",
    "\n",
    "The decoder then \"rolls out\" each subsequent state by predicting a distribution of actions, and then sampling a single action used to act on the previous state i.e. $\\hat{s_1} = s_{0} + \\hat{a_{0}}, \\hat{s_2} = \\hat{s_1} + \\hat{a_1}, \\hat{s_3} = \\hat{s_2} + \\hat{a_2}$ etc. The output of each recurrent unit in the decoder is fed through fully-connected layers to produce the mean and variance of the gaussian distribution of actions. The reconstruction loss for a single trajectory is computed by taking the negative log-likelihood of the true action under the predicted distribution of actions and summing that across time. For more detail, the main computation of a forward pass through the model is completed in `./tvae/lib/models/core.py` in the method titled `forward`.\n",
    "\n",
    "\n",
    "In this application, the input trajectory will be a sequence of preprocessed poses, and we will treat the mean of the posterior as our embedding. Below are adjustable model and dataset configurations and their associated descriptions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c0a9ebe2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Example model arguments\n",
    "model_config = { \n",
    "    \"name\": \"tvae\",\n",
    "    \"z_dim\": 32,      # Dimensionality of the posterior / embedding\n",
    "    \"h_dim\": 256,     # Number of units to use in the fully-connected layers in the encoder and decoder\n",
    "    \"rnn_dim\": 256,   # Number of units to use in the recurrent encoder and decoder\n",
    "    \"num_layers\": 1,  # Number of layers to use in the recurrent encoder and decoder \n",
    "    \"state_dim\": 33,  # Dimensionality of the input states - we are only embedding single fly features for now\n",
    "    \"action_dim\": 33  # Dimensionality of the input actions\n",
    "}\n",
    "\n",
    "# Example training arguments\n",
    "train_config = { \n",
    "    \"batch_size\": 128,          # Batch size to use during training - higher = faster, but more GPU utilization\n",
    "    \"num_epochs_til_val\": 10,   # Checkpoints will be saved to ./checkpoints/{project_name}/ every num_epochs_til_val epochs \n",
    "    \"learning_rate\": 0.0002,    # Learning rate for the optimizer to use\n",
    "    \"num_epochs\": 300,          # Number of epochs to use\n",
    "    \"clip\": 10,                 # Higher means potentially faster but more unstable training\n",
    "    \"project_name\": 'test_mouse_jupyter_notebook'  # All checkpoints and loss logs will be saved to ./checkpoints/project_name/\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eca8b20f",
   "metadata": {},
   "source": [
    "# Split preprocessed data into training a validation sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d0411785",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Split the dataset into a training and testing set\n",
    "test_prop = 0.20\n",
    "test_len = int(len(preprocessed_data) * test_prop)\n",
    "np.random.shuffle(preprocessed_data)\n",
    "data_train = preprocessed_data[test_len:]\n",
    "data_test = preprocessed_data[:test_len]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f515b7b",
   "metadata": {},
   "source": [
    "# Create dataset object to train the TVAE using preprocessed data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b07d9e6d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from datasets import load_dataset\n",
    "\n",
    "# Device configurations\n",
    "device = torch.device('cuda:0')\n",
    "\n",
    "data_config = { \n",
    "    'name': 'mouse_v1',\n",
    "    'data_train': data_train,\n",
    "    'data_test': data_test,\n",
    "    'device': device,\n",
    "}   \n",
    "\n",
    "# build dataset and train / val split\n",
    "dataset = load_dataset(data_config)\n",
    "\n",
    "data_loader = DataLoader(\n",
    "                dataset,\n",
    "                batch_size=train_config['batch_size'],\n",
    "                shuffle = False\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1710a784",
   "metadata": {},
   "source": [
    "# Instantiate model and load most recent checkpoint if necessary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0f15f8bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# This will check and store the most recent checkpointed model in your project directory\n",
    "from util.checkpoint_handler import checkpoint_handler\n",
    "train_config = checkpoint_handler(train_config)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d9fab6b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the model\n",
    "model = TVAE(model_config)\n",
    "model = model.to(device)\n",
    "model.prepare_stage(train_config)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fb05a65",
   "metadata": {},
   "source": [
    "# Train the TVAE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6e8a4b2a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Train the model\n",
    "train_losses, val_losses = train(model, data_loader, train_config, device)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b51161c6",
   "metadata": {},
   "source": [
    "# Find best checkpoint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e372faec",
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(f'./checkpoints/{train_config[\"project_name\"]}/val_losses.txt', 'r') as myFile:\n",
    "    lines = myFile.readlines()\n",
    "    klds, nlls = [],[]\n",
    "    for i, line in enumerate(lines):\n",
    "        if 'NLL' in line:\n",
    "            nlls.append(float(line.split(' ')[-1]))\n",
    "        elif 'KLD' in line:\n",
    "            klds.append(float(line.split(' ')[-1]))\n",
    "\n",
    "best_ckpt = np.array(nlls).argmin()*10"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f836389f",
   "metadata": {},
   "source": [
    "# Visualize some reconstructions of the validation set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2ed4868b",
   "metadata": {},
   "outputs": [],
   "source": [
    "from reconstruct import *\n",
    "\n",
    "model.load_state_dict(torch.load(f'./checkpoints/{train_config[\"project_name\"]}/{best_ckpt}.pt'))\n",
    "\n",
    "data_loader.dataset.eval()\n",
    "model.eval()\n",
    "recons, originals, embeddings = reconstruct(model, data_loader, data_config['device'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b03572aa",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "random_seq = recons[200] # Cannot compare postprocessed/original pairs outside of first sequence (index 1800)\n",
    "random_seq = random_seq.reshape(-1, 3, 11)\n",
    "random_seq = transform_svd_to_keypoints(random_seq, svd, mean)\n",
    "random_seq = random_seq.reshape(random_seq.shape[0],-1)\n",
    "random_seq = unnormalize(random_seq.reshape(random_seq.shape[0],-1))\n",
    "\n",
    "original = originals[200]\n",
    "original = original.reshape(-1,3,11)\n",
    "original = transform_svd_to_keypoints(original, svd, mean)\n",
    "original = original.reshape(original.shape[0], -1)\n",
    "original = unnormalize(original.reshape(original.shape[0], -1))\n",
    "\n",
    "from celluloid import Camera\n",
    "fig = plt.figure()\n",
    "camera = Camera(fig)\n",
    "plt.xlim(0,850), plt.ylim(0,850)\n",
    "for i in range(0,21):\n",
    "    xvals = original[i,::2]\n",
    "    yvals = original[i,1::2]\n",
    "    \n",
    "    if i == 0: \n",
    "        plt.scatter(x=xvals, y=yvals, c='g', label = 'original')\n",
    "    else:\n",
    "        plt.scatter(x=xvals, y=yvals, c='g')\n",
    "\n",
    "    xvals = random_seq[i,::2]\n",
    "    yvals = random_seq[i,1::2]\n",
    "    \n",
    "    if i == 0:\n",
    "        plt.scatter(x=xvals, y=yvals, c='b', label='reconstruction')\n",
    "    else:\n",
    "        plt.scatter(x=xvals, y=yvals, c='b')\n",
    "\n",
    "    camera.snap()\n",
    "    \n",
    "plt.legend()\n",
    "animation = camera.animate()\n",
    "animation.save('test.gif', writer='imagemagick')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4eb5aa27",
   "metadata": {},
   "source": [
    "# Example submission\n",
    "This just iterates through all the sequences provided in sample clips, preprocesses them, produces embeddings for them, and then saves them in the correct dictionary format."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b805f109",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load best model checkpoint\n",
    "model.load_state_dict(torch.load(f'./checkpoints/{train_config[\"project_name\"]}/{best_ckpt}.pt'))\n",
    "\n",
    "# Load submission clips - you may have to delete some of the larger arrays above in order to prevent the kernel from dying\n",
    "submission_clips = np.load('mouse_data/submission_clips.npy',allow_pickle=True).item()\n",
    "submission = {\n",
    "    'frame_number_map': {},\n",
    "    'embeddings': []\n",
    "}\n",
    "\n",
    "# Now we need to iterate through the videos, rotationally align, mean subtract, and apply SVD\n",
    "sub_seq_length = 21\n",
    "sliding_window = 1\n",
    "start_idx = 0\n",
    "for i, (name, sequence) in enumerate(tqdm(submission_clips['sequences'].items())):\n",
    "    # Preprocess sequences\n",
    "    vec_seq = sequence['keypoints'].reshape(sequence['keypoints'].shape[0], -1)\n",
    "    vec_seq = normalize(vec_seq)\n",
    "    \n",
    "    vec_seq, _, _ = transform_to_svd_components(\n",
    "            vec_seq,\n",
    "            svd_computer=svd,\n",
    "            mean=mean\n",
    "    )\n",
    "    \n",
    "    # Pads the beginning and end of the sequence with duplicate frames\n",
    "    vec_seq = vec_seq.reshape(vec_seq.shape[0], -1)\n",
    "    pad_vec = np.pad(vec_seq, ((sub_seq_length//2, sub_seq_length-1-sub_seq_length//2), (0,0)), mode='edge')\n",
    "    \n",
    "    # Converts sequence into [number of sub-sequences, frames in sub-sequence, x/y alternating keypoints]\n",
    "    data_test = np.stack([pad_vec[i:len(pad_vec)+i-sub_seq_length+1:sliding_window] for i in range(sub_seq_length)], axis=1)\n",
    "    \n",
    "    # Device configurations\n",
    "    device = torch.device('cuda:0')\n",
    "\n",
    "    data_config = { \n",
    "        'name': 'mouse_v1',\n",
    "        'data_train': data_test,\n",
    "        'data_test': data_test,\n",
    "        'device': device,\n",
    "    }   \n",
    "   \n",
    "    # build dataset and train / val split\n",
    "    dataset = load_dataset(data_config)\n",
    "\n",
    "    data_loader = DataLoader(\n",
    "                    dataset,\n",
    "                    batch_size=train_config['batch_size'],\n",
    "                    shuffle = False\n",
    "    )\n",
    "    \n",
    "    data_loader.dataset.eval()\n",
    "    model.eval()\n",
    "    _, _, embeddings = reconstruct(model, data_loader, data_config['device'])\n",
    "    \n",
    "    end_idx = start_idx + len(embeddings)\n",
    "    submission['embeddings'].append(embeddings)\n",
    "    submission['frame_number_map'][name] = (start_idx, end_idx)\n",
    "    start_idx = end_idx\n",
    "       \n",
    "submission['embeddings'] = np.concatenate(submission['embeddings'], axis=0)\n",
    "np.save('test_mouse_tvae_submission.npy', submission)    "
   ]
  }
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