pose_autoencoder.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setup and load data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n",
      "['ffmpeg', 'ffmpeg_file', 'imagemagick', 'imagemagick_file', 'html']\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "from functions.functions import *\n",
    "from functions.plotting import *\n",
    "from functions.autoencoder import *\n",
    "from keras import backend as K\n",
    "from keras.callbacks import TerminateOnNaN, ModelCheckpoint\n",
    "from keras.models import model_from_json\n",
    "from livelossplot.keras import PlotLossesCallback\n",
    "import livelossplot\n",
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "import os\n",
    "import glob\n",
    "from itertools import combinations\n",
    "import matplotlib\n",
    "plt.rcParams['animation.ffmpeg_path'] = './ffmpeg' # for using html5 video in Jupyter notebook\n",
    "print(matplotlib.animation.writers.list()) # check that ffmpeg is loaded. if it's not there, use .to_jshtml() instead of .to_html5_video()."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GPUs found: 0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "setup_gpus()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Files loaded: ['data/rnn_data/mariel_betternot_and_retrograde.npy', 'data/rnn_data/mariel_knownbetter.npy']\n"
     ]
    }
   ],
   "source": [
    "data = load_data('data/rnn_data/mariel_*')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Check out the real data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting from frame 6131...\n"
     ]
    },
    {
     "data": {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame = np.random.randint(0,data.full.X.shape[1]-50)\n",
    "print(\"Starting from frame {}...\".format(frame))\n",
    "\n",
    "HTML(animate(data.full.X[:,frame:,:], frames=100))\n",
    "# HTML(animate(data.selected.X[:,frame:,:], frames=100, edges=data.selected.edges, colors='black'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Build the autoencoder for poses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the training dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training set size: (53, 14859, 3)\n",
      "Test set size: (53, 3715, 3)\n"
     ]
    }
   ],
   "source": [
    "# X_train = data.selected.X    # 15 joints\n",
    "X_train = data.full.X[:,:int(data.full.X.shape[1]*.8),:]    # 53 joints (80% train)\n",
    "X_test = data.full.X[:,int(data.full.X.shape[1]*.8):,:]    # 53 joints (20% test)\n",
    "print(\"Training set size: {}\".format(X_train.shape))\n",
    "print(\"Test set size: {}\".format(X_test.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train without adding random (x,y) offsets:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From /Users/mnp3/miniconda3/envs/choreo/lib/python3.7/site-packages/tensorflow/python/framework/op_def_library.py:263: colocate_with (from tensorflow.python.framework.ops) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Colocations handled automatically by placer.\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_3 (InputLayer)         (None, 53, 3)             0         \n",
      "_________________________________________________________________\n",
      "model_1 (Model)              (None, 2)                 14530     \n",
      "_________________________________________________________________\n",
      "model_2 (Model)              (None, 53, 3)             14687     \n",
      "=================================================================\n",
      "Total params: 29,217\n",
      "Trainable params: 29,217\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n",
      "WARNING:tensorflow:From /Users/mnp3/miniconda3/envs/choreo/lib/python3.7/site-packages/tensorflow/python/ops/math_ops.py:3066: to_int32 (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Use tf.cast instead.\n",
      "Epoch 1/50\n",
      "14859/14859 [==============================] - 1s 79us/step - loss: 0.1967: 0s - loss: 0.\n",
      "Epoch 2/50\n",
      "14859/14859 [==============================] - 1s 42us/step - loss: 0.0355\n",
      "Epoch 3/50\n",
      "14859/14859 [==============================] - 1s 50us/step - loss: 0.0143\n",
      "Epoch 4/50\n",
      "14859/14859 [==============================] - 1s 45us/step - loss: 0.0132\n",
      "Epoch 5/50\n",
      "14859/14859 [==============================] - 1s 41us/step - loss: 0.0118: 0s - loss: 0.01\n",
      "Epoch 6/50\n",
      "14859/14859 [==============================] - 1s 50us/step - loss: 0.0099\n",
      "Epoch 7/50\n",
      "14859/14859 [==============================] - 1s 41us/step - loss: 0.0083\n",
      "Epoch 8/50\n",
      "14859/14859 [==============================] - 1s 40us/step - loss: 0.0074\n",
      "Epoch 9/50\n",
      "14859/14859 [==============================] - 1s 46us/step - loss: 0.0070\n",
      "Epoch 10/50\n",
      "14859/14859 [==============================] - 1s 40us/step - loss: 0.0068\n",
      "Epoch 11/50\n",
      "14859/14859 [==============================] - 1s 45us/step - loss: 0.0067\n",
      "Epoch 12/50\n",
      "14859/14859 [==============================] - 1s 35us/step - loss: 0.0066\n",
      "Epoch 13/50\n",
      "14859/14859 [==============================] - 1s 48us/step - loss: 0.0066\n",
      "Epoch 14/50\n",
      "14859/14859 [==============================] - 1s 40us/step - loss: 0.0066\n",
      "Epoch 15/50\n",
      "14859/14859 [==============================] - 1s 36us/step - loss: 0.0066\n",
      "Epoch 16/50\n",
      "14859/14859 [==============================] - 1s 42us/step - loss: 0.0066\n",
      "Epoch 17/50\n",
      "14859/14859 [==============================] - 1s 46us/step - loss: 0.0066\n",
      "Epoch 18/50\n",
      "14859/14859 [==============================] - 0s 33us/step - loss: 0.0065\n",
      "Epoch 19/50\n",
      "14859/14859 [==============================] - 1s 38us/step - loss: 0.0065\n",
      "Epoch 20/50\n",
      "14859/14859 [==============================] - 1s 44us/step - loss: 0.0065\n",
      "Epoch 21/50\n",
      "14859/14859 [==============================] - 1s 34us/step - loss: 0.0065\n",
      "Epoch 22/50\n",
      "14859/14859 [==============================] - 0s 33us/step - loss: 0.0065\n",
      "Epoch 23/50\n",
      "14859/14859 [==============================] - 1s 41us/step - loss: 0.0065\n",
      "Epoch 24/50\n",
      "14859/14859 [==============================] - 1s 42us/step - loss: 0.0065\n",
      "Epoch 25/50\n",
      "14859/14859 [==============================] - 1s 56us/step - loss: 0.0065\n",
      "Epoch 26/50\n",
      "14859/14859 [==============================] - 1s 41us/step - loss: 0.0065\n",
      "Epoch 27/50\n",
      "14859/14859 [==============================] - 1s 39us/step - loss: 0.0065\n",
      "Epoch 28/50\n",
      "14859/14859 [==============================] - 1s 38us/step - loss: 0.0065\n",
      "Epoch 29/50\n",
      "14859/14859 [==============================] - 1s 38us/step - loss: 0.0065\n",
      "Epoch 30/50\n",
      "14859/14859 [==============================] - 1s 37us/step - loss: 0.0065\n",
      "Epoch 31/50\n",
      "14859/14859 [==============================] - 1s 39us/step - loss: 0.0065\n",
      "Epoch 32/50\n",
      "14859/14859 [==============================] - 1s 46us/step - loss: 0.0065\n",
      "Epoch 33/50\n",
      "14859/14859 [==============================] - 1s 34us/step - loss: 0.0065\n",
      "Epoch 34/50\n",
      "14859/14859 [==============================] - 1s 57us/step - loss: 0.0064\n",
      "Epoch 35/50\n",
      "14859/14859 [==============================] - 1s 56us/step - loss: 0.0064\n",
      "Epoch 36/50\n",
      "14859/14859 [==============================] - 1s 39us/step - loss: 0.0064\n",
      "Epoch 37/50\n",
      "14859/14859 [==============================] - 1s 49us/step - loss: 0.0064\n",
      "Epoch 38/50\n",
      "14859/14859 [==============================] - 1s 34us/step - loss: 0.0064\n",
      "Epoch 39/50\n",
      "14859/14859 [==============================] - 1s 34us/step - loss: 0.0064\n",
      "Epoch 40/50\n",
      "14859/14859 [==============================] - 1s 43us/step - loss: 0.0064\n",
      "Epoch 41/50\n",
      "14859/14859 [==============================] - 1s 38us/step - loss: 0.0064\n",
      "Epoch 42/50\n",
      "14859/14859 [==============================] - 0s 34us/step - loss: 0.0064\n",
      "Epoch 43/50\n",
      "14859/14859 [==============================] - 1s 34us/step - loss: 0.0064\n",
      "Epoch 44/50\n",
      "14859/14859 [==============================] - 1s 36us/step - loss: 0.0064\n",
      "Epoch 45/50\n",
      "14859/14859 [==============================] - 0s 33us/step - loss: 0.0063\n",
      "Epoch 46/50\n",
      "14859/14859 [==============================] - 1s 37us/step - loss: 0.0063\n",
      "Epoch 47/50\n",
      "14859/14859 [==============================] - 1s 38us/step - loss: 0.0063\n",
      "Epoch 48/50\n",
      "14859/14859 [==============================] - 1s 36us/step - loss: 0.0063\n",
      "Epoch 49/50\n",
      "14859/14859 [==============================] - 1s 39us/step - loss: 0.0063\n",
      "Epoch 50/50\n",
      "14859/14859 [==============================] - 1s 47us/step - loss: 0.0062\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x180f20990>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ae_nooffset = Autoencoder(n_verts=X_train.shape[0], latent_dim=2, n_layers=2, n_units=64, relu=True, dropout=False, add_random_offsets=False)\n",
    "ae_nooffset.model.summary()\n",
    "X_T = X_train.transpose((1,0,2))\n",
    "ae_nooffset.model.fit(X_T, X_T, batch_size = 128, epochs = 50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Real data in blue, autoencoded predictions in orange (we want these to be very similar):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Seeding with frame 168\n"
     ]
    },
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_frames = 100\n",
    "frame = np.random.randint(0,X_test.shape[1]-n_frames)\n",
    "print(\"Seeding with frame {}\".format(frame))\n",
    "nooffset_predictions = ae_nooffset.get_predictions(X_test, start_frame=frame, n_frames=n_frames)\n",
    "HTML(animate_ghost(X_test[:,frame:,:], nooffset_predictions, frames=n_frames, ghost_shift=0.2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train with adding random (x,y) offsets to the input data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_6 (InputLayer)         (None, 53, 3)             0         \n",
      "_________________________________________________________________\n",
      "model_4 (Model)              (None, 32)                16480     \n",
      "_________________________________________________________________\n",
      "model_5 (Model)              (None, 53, 3)             16607     \n",
      "=================================================================\n",
      "Total params: 33,087\n",
      "Trainable params: 33,087\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n",
      "Epoch 1/50\n",
      "14859/14859 [==============================] - 1s 74us/step - loss: 0.2180\n",
      "Epoch 2/50\n",
      "14859/14859 [==============================] - 1s 38us/step - loss: 0.0367\n",
      "Epoch 3/50\n",
      "14859/14859 [==============================] - 1s 36us/step - loss: 0.0140\n",
      "Epoch 4/50\n",
      "14859/14859 [==============================] - 1s 39us/step - loss: 0.0129\n",
      "Epoch 5/50\n",
      "14859/14859 [==============================] - 1s 35us/step - loss: 0.0119\n",
      "Epoch 6/50\n",
      "14859/14859 [==============================] - 1s 35us/step - loss: 0.0107\n",
      "Epoch 7/50\n",
      "14859/14859 [==============================] - 0s 32us/step - loss: 0.0091\n",
      "Epoch 8/50\n",
      "14859/14859 [==============================] - 1s 42us/step - loss: 0.0071\n",
      "Epoch 9/50\n",
      "14859/14859 [==============================] - 0s 31us/step - loss: 0.0050\n",
      "Epoch 10/50\n",
      "14859/14859 [==============================] - 0s 30us/step - loss: 0.0034\n",
      "Epoch 11/50\n",
      "14859/14859 [==============================] - 1s 39us/step - loss: 0.0026\n",
      "Epoch 12/50\n",
      "14859/14859 [==============================] - 0s 31us/step - loss: 0.0022\n",
      "Epoch 13/50\n",
      "14859/14859 [==============================] - 0s 34us/step - loss: 0.0020\n",
      "Epoch 14/50\n",
      "14859/14859 [==============================] - 1s 46us/step - loss: 0.0019\n",
      "Epoch 15/50\n",
      "14859/14859 [==============================] - 0s 31us/step - loss: 0.0019\n",
      "Epoch 16/50\n",
      "14859/14859 [==============================] - 1s 34us/step - loss: 0.0018\n",
      "Epoch 17/50\n",
      "14859/14859 [==============================] - 0s 31us/step - loss: 0.0018\n",
      "Epoch 18/50\n",
      "14859/14859 [==============================] - 0s 30us/step - loss: 0.0018\n",
      "Epoch 19/50\n",
      "14859/14859 [==============================] - 1s 34us/step - loss: 0.0018\n",
      "Epoch 20/50\n",
      "14859/14859 [==============================] - 0s 29us/step - loss: 0.0018\n",
      "Epoch 21/50\n",
      "14859/14859 [==============================] - 0s 29us/step - loss: 0.0017\n",
      "Epoch 22/50\n",
      "14859/14859 [==============================] - 1s 39us/step - loss: 0.0017\n",
      "Epoch 23/50\n",
      "14859/14859 [==============================] - 1s 41us/step - loss: 0.0017\n",
      "Epoch 24/50\n",
      "14859/14859 [==============================] - 1s 45us/step - loss: 0.0017\n",
      "Epoch 25/50\n",
      "14859/14859 [==============================] - 1s 45us/step - loss: 0.0017\n",
      "Epoch 26/50\n",
      "14859/14859 [==============================] - 1s 41us/step - loss: 0.0017\n",
      "Epoch 27/50\n",
      "14859/14859 [==============================] - 1s 48us/step - loss: 0.0016\n",
      "Epoch 28/50\n",
      "14859/14859 [==============================] - 1s 38us/step - loss: 0.0016\n",
      "Epoch 29/50\n",
      "14859/14859 [==============================] - 1s 39us/step - loss: 0.0016\n",
      "Epoch 30/50\n",
      "14859/14859 [==============================] - 0s 33us/step - loss: 0.0016\n",
      "Epoch 31/50\n",
      "14859/14859 [==============================] - 0s 34us/step - loss: 0.0016\n",
      "Epoch 32/50\n",
      "14859/14859 [==============================] - 1s 58us/step - loss: 0.0015\n",
      "Epoch 33/50\n",
      "14859/14859 [==============================] - 1s 48us/step - loss: 0.0015\n",
      "Epoch 34/50\n",
      "14859/14859 [==============================] - 1s 37us/step - loss: 0.0015\n",
      "Epoch 35/50\n",
      "14859/14859 [==============================] - 1s 34us/step - loss: 0.0015\n",
      "Epoch 36/50\n",
      "14859/14859 [==============================] - 1s 35us/step - loss: 0.0014\n",
      "Epoch 37/50\n",
      "14859/14859 [==============================] - 0s 30us/step - loss: 0.0014\n",
      "Epoch 38/50\n",
      "14859/14859 [==============================] - 1s 42us/step - loss: 0.0014\n",
      "Epoch 39/50\n",
      "14859/14859 [==============================] - 1s 41us/step - loss: 0.0013\n",
      "Epoch 40/50\n",
      "14859/14859 [==============================] - 1s 49us/step - loss: 0.0013\n",
      "Epoch 41/50\n",
      "14859/14859 [==============================] - 1s 53us/step - loss: 0.0013\n",
      "Epoch 42/50\n",
      "14859/14859 [==============================] - 1s 50us/step - loss: 0.0012: 0s - l\n",
      "Epoch 43/50\n",
      "14859/14859 [==============================] - 1s 40us/step - loss: 0.0012\n",
      "Epoch 44/50\n",
      "14859/14859 [==============================] - 1s 39us/step - loss: 0.0012\n",
      "Epoch 45/50\n",
      "14859/14859 [==============================] - 1s 42us/step - loss: 0.0011\n",
      "Epoch 46/50\n",
      "14859/14859 [==============================] - 1s 38us/step - loss: 0.0011\n",
      "Epoch 47/50\n",
      "14859/14859 [==============================] - 1s 41us/step - loss: 0.0011\n",
      "Epoch 48/50\n",
      "14859/14859 [==============================] - 1s 48us/step - loss: 0.0011\n",
      "Epoch 49/50\n",
      "14859/14859 [==============================] - 1s 44us/step - loss: 0.0010\n",
      "Epoch 50/50\n",
      "14859/14859 [==============================] - 1s 42us/step - loss: 0.0010\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x1354bbf50>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ae_withoffset = Autoencoder(n_verts=X_train.shape[0], latent_dim=32, n_layers=2, n_units=64, relu=True, dropout=False, add_random_offsets=False)\n",
    "ae_withoffset.model.summary()\n",
    "X_T = X_train.transpose((1,0,2))\n",
    "ae_withoffset.model.fit(X_T, X_T, batch_size = 128, epochs = 50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Real data in blue, autoencoded predictions in orange (we want these to be very similar):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Seeding with frame 2641\n"
     ]
    },
    {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_frames = 100\n",
    "frame = np.random.randint(0,X_test.shape[1]-n_frames)\n",
    "print(\"Seeding with frame {}\".format(frame)) \n",
    "withoffset_predictions = ae_withoffset.get_predictions(X_test, start_frame=frame, n_frames=n_frames)\n",
    "HTML(animate_ghost(X_test[:,frame:,:], withoffset_predictions, frames=n_frames, ghost_shift=0.2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compare predictions with and without (x,y) offsets:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Seeding with frame 1454\n"
     ]
    },
    {
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       "ZjU5LjEwLjEwMA==\n",
       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_frames = 100\n",
    "frame = np.random.randint(0,X_test.shape[1]-n_frames)\n",
    "print(\"Seeding with frame {}\".format(frame)) \n",
    "nooffset_predictions = ae_nooffset.get_predictions(X_test, start_frame=frame, n_frames=n_frames)\n",
    "withoffset_predictions = ae_withoffset.get_predictions(X_test, start_frame=frame, n_frames=n_frames)\n",
    "HTML(animate_ghost(nooffset_predictions, withoffset_predictions, frames=n_frames, ghost_shift=0.2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_pose(x, ax=None, lim=(-0.5, 0.5), center=False, colors=None):\n",
    "    if ax is None:\n",
    "        fig = plt.figure()\n",
    "        ax = p3.Axes3D(fig)\n",
    "    if center:\n",
    "        x = x-x.mean(axis=0)\n",
    "    ax.set_xlim(*lim)\n",
    "    ax.set_ylim(*lim)\n",
    "    ax.set_zlim(*lim)\n",
    "    ax.scatter(x[:,0], x[:,1], x[:,2], c=colors)\n",
    "    return ax\n",
    "\n",
    "def plot_stick(x, edges, ax=None, fig=None, subplot=None, lim=(-0.5,0.5), center=False, colors=None):\n",
    "    if subplot is not None:\n",
    "        if fig is None:\n",
    "            fig = plt.figure()\n",
    "        ax = fig.add_subplot(*subplot, projection='3d')\n",
    "    if ax is None:\n",
    "        if fig is None:\n",
    "            fig = plt.figure()\n",
    "        ax = p3.Axes3D(fig)\n",
    "    if center:\n",
    "        x = x-x.mean(axis=0)\n",
    "    ax.set_xlim(*lim)\n",
    "    ax.set_ylim(*lim)\n",
    "    ax.set_zlim(*lim)\n",
    "    #ax.scatter(x[:,0], x[:,1], x[:,2])\n",
    "    for ie,e in enumerate(edges):\n",
    "        if colors is not None:\n",
    "            c = colors[ie]\n",
    "        else:\n",
    "            c = None\n",
    "        ax.plot(np.linspace(x[e[0],0],x[e[1],0],10),np.linspace(x[e[0],1],x[e[1],1],10),np.linspace(x[e[0],2],x[e[1],2],10), color=c)\n",
    "    return ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras import layers\n",
    "# Simple autoencoder to learn single-frame poses\n",
    "# Parameters:\n",
    "#   X: input dataset (used to determine shapes)\n",
    "#   n_units: A tuple of 1 or more integers indicating the number of Dense layer units for each dense layer desired.\n",
    "#   add_noise: if True, add unit gaussian noise to each of the encoded layer outputs.\n",
    "#\n",
    "# The returned model requires no target values during training/evaluation\n",
    "# (since the target values are the same as the inputs).\n",
    "def mk_pose_ae(X, n_units=(32,), add_noise=True):\n",
    "    K.clear_session()\n",
    "    \n",
    "    # Define an activation for hidden layers\n",
    "    def s(L):\n",
    "        return layers.PReLU()(L)\n",
    "    \n",
    "    H = encoder_input = layers.Input((X.shape[1], X.shape[2]))\n",
    "    \n",
    "    # Shift the (x,y) values of the input so that it is centered at zero.\n",
    "    # The z-coordinate is left unchanged.\n",
    "    offsets = layers.Lambda(lambda x: K.constant([[[1,1,0]]])*K.mean(x,axis=1,keepdims=True))(encoder_input)\n",
    "    H = layers.Subtract()([H, offsets])\n",
    "    \n",
    "    # Flatten vertices before feeding into dense networks.\n",
    "    H = layers.Reshape((X.shape[1]*X.shape[2],))(H)\n",
    "    \n",
    "    # Create the specified number and size of Dense layers.\n",
    "    for nu in n_units:\n",
    "        H = layers.Dense(nu)(H)\n",
    "        H = s(H)\n",
    "    \n",
    "    # add unit gaussian noise to the latent space, if requested.\n",
    "    if add_noise:\n",
    "        R = K.random_normal(K.shape(H), 0, 1)\n",
    "        H = layers.Lambda(lambda x: x+R)(H)\n",
    "    \n",
    "    # Decoder layers progressively scale the latent space back to\n",
    "    # original input size.\n",
    "    for nu in n_units[::-1][1:]:\n",
    "        H = layers.Dense(nu)(H)\n",
    "        H = s(H)\n",
    "    \n",
    "    # Final dense output layer with tanh activation for (-1,1) range.\n",
    "    H = layers.Dense((X.shape[1]*X.shape[2]), activation='tanh')(H)\n",
    "    H = layers.Reshape((X.shape[1],X.shape[2]))(H)\n",
    "    \n",
    "    # restore the subtracted (x,y) offset before outputting\n",
    "    H = layers.Add()([H, offsets])\n",
    "    decoder_output = H\n",
    "    \n",
    "    autoencoder = Model(encoder_input, decoder_output)\n",
    "    \n",
    "    # Define the autoencoder loss as the pointwise mean squared error of the\n",
    "    # output relative to the input.\n",
    "    ae_loss = K.mean(K.sum(K.square(decoder_output-encoder_input), axis=-1))\n",
    "    autoencoder.add_loss(ae_loss)\n",
    "    \n",
    "    # compile model without target y values (loss is defined by input and output layers only).\n",
    "    autoencoder.compile(optimizer='adam')\n",
    "    \n",
    "    return autoencoder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "__________________________________________________________________________________________________\n",
      "Layer (type)                    Output Shape         Param #     Connected to                     \n",
      "==================================================================================================\n",
      "input_1 (InputLayer)            (None, 53, 3)        0                                            \n",
      "__________________________________________________________________________________________________\n",
      "lambda_1 (Lambda)               (None, 1, 3)         0           input_1[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "subtract_1 (Subtract)           (None, 53, 3)        0           input_1[0][0]                    \n",
      "                                                                 lambda_1[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "reshape_1 (Reshape)             (None, 159)          0           subtract_1[0][0]                 \n",
      "__________________________________________________________________________________________________\n",
      "dense_1 (Dense)                 (None, 32)           5120        reshape_1[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "p_re_lu_1 (PReLU)               (None, 32)           32          dense_1[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "lambda_2 (Lambda)               (None, 32)           0           p_re_lu_1[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "dense_2 (Dense)                 (None, 159)          5247        lambda_2[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "reshape_2 (Reshape)             (None, 53, 3)        0           dense_2[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "add_1 (Add)                     (None, 53, 3)        0           reshape_2[0][0]                  \n",
      "                                                                 lambda_1[0][0]                   \n",
      "==================================================================================================\n",
      "Total params: 10,399\n",
      "Trainable params: 10,399\n",
      "Non-trainable params: 0\n",
      "__________________________________________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Instantiate network with whatever parameters you like!\n",
    "\n",
    "n_units = (32,)\n",
    "add_noise = True\n",
    "\n",
    "auto = mk_pose_ae(X_train.transpose((1,0,2)), n_units=n_units, add_noise=add_noise)\n",
    "auto.summary()\n",
    "\n",
    "# these will get populated after each call to fit() by the values in the\n",
    "# built-in History callback.\n",
    "losses = []\n",
    "val_losses = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 14859 samples, validate on 3715 samples\n",
      "Epoch 1/50\n",
      "14859/14859 [==============================] - 1s 47us/step - loss: 0.6697 - val_loss: 0.4745\n",
      "Epoch 2/50\n",
      "14859/14859 [==============================] - 0s 28us/step - loss: 0.3423 - val_loss: 0.2475\n",
      "Epoch 3/50\n",
      "14859/14859 [==============================] - 0s 28us/step - loss: 0.1912 - val_loss: 0.1343\n",
      "Epoch 4/50\n",
      "14859/14859 [==============================] - 1s 35us/step - loss: 0.1025 - val_loss: 0.0695\n",
      "Epoch 5/50\n",
      "14859/14859 [==============================] - 0s 28us/step - loss: 0.0539 - val_loss: 0.0379\n",
      "Epoch 6/50\n",
      "14859/14859 [==============================] - 0s 31us/step - loss: 0.0310 - val_loss: 0.0236\n",
      "Epoch 7/50\n",
      "14859/14859 [==============================] - 0s 29us/step - loss: 0.0204 - val_loss: 0.0169\n",
      "Epoch 8/50\n",
      "14859/14859 [==============================] - 0s 33us/step - loss: 0.0153 - val_loss: 0.0135\n",
      "Epoch 9/50\n",
      "14859/14859 [==============================] - 0s 30us/step - loss: 0.0126 - val_loss: 0.0120\n",
      "Epoch 10/50\n",
      "14859/14859 [==============================] - 0s 29us/step - loss: 0.0111 - val_loss: 0.0109\n",
      "Epoch 11/50\n",
      "14859/14859 [==============================] - 0s 29us/step - loss: 0.0101 - val_loss: 0.0104\n",
      "Epoch 12/50\n",
      "14859/14859 [==============================] - 0s 30us/step - loss: 0.0095 - val_loss: 0.0096\n",
      "Epoch 13/50\n",
      "14859/14859 [==============================] - 0s 31us/step - loss: 0.0090 - val_loss: 0.0093\n",
      "Epoch 14/50\n",
      "14859/14859 [==============================] - 0s 32us/step - loss: 0.0086 - val_loss: 0.0090\n",
      "Epoch 15/50\n",
      "14859/14859 [==============================] - 0s 28us/step - loss: 0.0084 - val_loss: 0.0088\n",
      "Epoch 16/50\n",
      "14859/14859 [==============================] - 0s 32us/step - loss: 0.0081 - val_loss: 0.0085\n",
      "Epoch 17/50\n",
      "14859/14859 [==============================] - 1s 34us/step - loss: 0.0079 - val_loss: 0.0085\n",
      "Epoch 18/50\n",
      "14859/14859 [==============================] - 0s 30us/step - loss: 0.0077 - val_loss: 0.0083\n",
      "Epoch 19/50\n",
      "14859/14859 [==============================] - 1s 35us/step - loss: 0.0075 - val_loss: 0.0081\n",
      "Epoch 20/50\n",
      "14859/14859 [==============================] - 1s 36us/step - loss: 0.0073 - val_loss: 0.0079\n",
      "Epoch 21/50\n",
      "14859/14859 [==============================] - 0s 33us/step - loss: 0.0072 - val_loss: 0.0079\n",
      "Epoch 22/50\n",
      "14859/14859 [==============================] - 0s 28us/step - loss: 0.0071 - val_loss: 0.0077\n",
      "Epoch 23/50\n",
      "14859/14859 [==============================] - 0s 27us/step - loss: 0.0070 - val_loss: 0.0076\n",
      "Epoch 24/50\n",
      "14859/14859 [==============================] - 0s 27us/step - loss: 0.0069 - val_loss: 0.0075\n",
      "Epoch 25/50\n",
      "14859/14859 [==============================] - 0s 27us/step - loss: 0.0067 - val_loss: 0.0073\n",
      "Epoch 26/50\n",
      "14859/14859 [==============================] - 0s 26us/step - loss: 0.0066 - val_loss: 0.0073\n",
      "Epoch 27/50\n",
      "14859/14859 [==============================] - 0s 28us/step - loss: 0.0065 - val_loss: 0.0072\n",
      "Epoch 28/50\n",
      "14859/14859 [==============================] - 0s 26us/step - loss: 0.0064 - val_loss: 0.0071\n",
      "Epoch 29/50\n",
      "14859/14859 [==============================] - 0s 28us/step - loss: 0.0063 - val_loss: 0.0069\n",
      "Epoch 30/50\n",
      "14859/14859 [==============================] - 0s 26us/step - loss: 0.0062 - val_loss: 0.0069\n",
      "Epoch 31/50\n",
      "14859/14859 [==============================] - 0s 28us/step - loss: 0.0061 - val_loss: 0.0068\n",
      "Epoch 32/50\n",
      "14859/14859 [==============================] - 0s 26us/step - loss: 0.0060 - val_loss: 0.0067\n",
      "Epoch 33/50\n",
      "14859/14859 [==============================] - 0s 28us/step - loss: 0.0059 - val_loss: 0.0067\n",
      "Epoch 34/50\n",
      "14859/14859 [==============================] - 0s 31us/step - loss: 0.0058 - val_loss: 0.0064\n",
      "Epoch 35/50\n",
      "14859/14859 [==============================] - 0s 32us/step - loss: 0.0057 - val_loss: 0.0063\n",
      "Epoch 36/50\n",
      "14859/14859 [==============================] - 0s 33us/step - loss: 0.0056 - val_loss: 0.0064\n",
      "Epoch 37/50\n",
      "14859/14859 [==============================] - 0s 31us/step - loss: 0.0056 - val_loss: 0.0062\n",
      "Epoch 38/50\n",
      "14859/14859 [==============================] - 0s 29us/step - loss: 0.0055 - val_loss: 0.0062\n",
      "Epoch 39/50\n",
      "14859/14859 [==============================] - 0s 30us/step - loss: 0.0054 - val_loss: 0.0062\n",
      "Epoch 40/50\n",
      "14859/14859 [==============================] - 1s 36us/step - loss: 0.0053 - val_loss: 0.0061\n",
      "Epoch 41/50\n",
      "14859/14859 [==============================] - 1s 36us/step - loss: 0.0053 - val_loss: 0.0060\n",
      "Epoch 42/50\n",
      "14859/14859 [==============================] - 0s 31us/step - loss: 0.0052 - val_loss: 0.0059\n",
      "Epoch 43/50\n",
      "14859/14859 [==============================] - 0s 25us/step - loss: 0.0051 - val_loss: 0.0059\n",
      "Epoch 44/50\n",
      "14859/14859 [==============================] - 0s 27us/step - loss: 0.0050 - val_loss: 0.0058\n",
      "Epoch 45/50\n",
      "14859/14859 [==============================] - 0s 25us/step - loss: 0.0050 - val_loss: 0.0057\n",
      "Epoch 46/50\n",
      "14859/14859 [==============================] - 0s 26us/step - loss: 0.0049 - val_loss: 0.0057\n",
      "Epoch 47/50\n",
      "14859/14859 [==============================] - 0s 27us/step - loss: 0.0048 - val_loss: 0.0056\n",
      "Epoch 48/50\n",
      "14859/14859 [==============================] - 1s 36us/step - loss: 0.0048 - val_loss: 0.0055\n",
      "Epoch 49/50\n",
      "14859/14859 [==============================] - 0s 30us/step - loss: 0.0047 - val_loss: 0.0056\n",
      "Epoch 50/50\n",
      "14859/14859 [==============================] - 0s 28us/step - loss: 0.0047 - val_loss: 0.0054\n"
     ]
    }
   ],
   "source": [
    "# specify training parameters and fit the model.\n",
    "# Note: subjectively, it seems that a loss of 2e-3 looks fairly convincing.\n",
    "batch_size = 128\n",
    "epochs = 50\n",
    "learning_rate = 3e-4\n",
    "\n",
    "K.set_value(auto.optimizer.lr, learning_rate)\n",
    "\n",
    "auto.fit(X_train.transpose((1,0,2)), None, validation_data=(X_test.transpose((1,0,2)), None), epochs=epochs, batch_size=batch_size)\n",
    "\n",
    "losses.extend(auto.history.history['loss'])\n",
    "val_losses.extend(auto.history.history['val_loss'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(53, 3715, 3)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using frame # [3424]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 720x432 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot losses and some example auto-encoded poses from the validation set\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.plot(losses, label='train')\n",
    "plt.plot(val_losses, label='val')\n",
    "plt.yscale('log')\n",
    "plt.xlabel('epoch')\n",
    "plt.ylabel('loss')\n",
    "plt.legend()\n",
    "\n",
    "n_sample = 1\n",
    "itest = np.random.randint(0,X_test.shape[1],n_sample)\n",
    "print(\"Using frame # {}\".format(itest))\n",
    "xtest = X_test.transpose((1,0,2))[itest]\n",
    "ytest = auto.predict(xtest)\n",
    "for i in range(n_sample):\n",
    "    fig = plt.figure(figsize=(10,6))\n",
    "    plt.suptitle(\"Validation frame %d\"% itest[i])\n",
    "    plot_pose(xtest[i]-xtest[i].mean(axis=0), center=True, colors='magenta')\n",
    "    plot_pose(ytest[i]-ytest[i].mean(axis=0), center=True, colors='red')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "choreo",
   "language": "python",
   "name": "choreo"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}