neural-discrete-representations.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "from tensorflow.python.framework import function\n",
    "\n",
    "# import tensorflow.contrib.eager as tfe\n",
    "# tfe.enable_eager_execution()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting /tmp/mnist/train-images-idx3-ubyte.gz\n",
      "Extracting /tmp/mnist/train-labels-idx1-ubyte.gz\n",
      "Extracting /tmp/mnist/t10k-images-idx3-ubyte.gz\n",
      "Extracting /tmp/mnist/t10k-labels-idx1-ubyte.gz\n"
     ]
    }
   ],
   "source": [
    "from tensorflow.examples.tutorials.mnist import input_data\n",
    "mnist = input_data.read_data_sets(\"/tmp/mnist\", one_hot=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "n_latents = 8\n",
    "k = 64\n",
    "batch_size = 32\n",
    "logdir = '/tmp/ndr/4'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "depth = 3\n",
    "width = 8\n",
    "\n",
    "def encoder(x):\n",
    "    for _ in range(depth):\n",
    "        x = tf.layers.conv2d(x, width, 4, 2, activation=tf.nn.elu, padding='SAME',kernel_initializer=tf.orthogonal_initializer())\n",
    "    return tf.layers.conv2d(x, width, 4, 2, padding='SAME',kernel_initializer=tf.orthogonal_initializer())\n",
    "\n",
    "\n",
    "def decoder(x):\n",
    "    for _ in range(depth):\n",
    "        x = tf.layers.conv2d_transpose(x, width, 4, 2, activation=tf.nn.elu, padding='SAME',kernel_initializer=tf.orthogonal_initializer())\n",
    "    return tf.layers.conv2d_transpose(x, 1, 4, 2, padding='SAME',kernel_initializer=tf.orthogonal_initializer())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def _copy_grad(unused_op, grad):\n",
    "    x = unused_op.inputs[0]\n",
    "    e = unused_op.inputs[1]\n",
    "#     dist = cosine_dist(x, e)\n",
    "#     _, idx = tf.nn.top_k(dist, 1)\n",
    "    # TODO. scatter grads into e.shape according to idx. \n",
    "    # will need to sum over the batch!?\n",
    "    # https://www.tensorflow.org/versions/r0.12/api_docs/python/state_ops/sparse_variable_updates\n",
    "    return tf.reshape(grad, (-1, n_latents)), tf.zeros(e.shape)\n",
    "\n",
    "@function.Defun(tf.float32, tf.float32, python_grad_func=_copy_grad)\n",
    "def lookup_fn(x, e):\n",
    "    dist = cosine_dist(x, e)\n",
    "    _, idx = tf.nn.top_k(dist, 1)\n",
    "    return tf.nn.embedding_lookup(e, tf.squeeze(idx))\n",
    "\n",
    "def lookup(x, e):\n",
    "    s = x.get_shape().as_list()\n",
    "    xflat = tf.reshape(x, (-1, n_latents))\n",
    "    \n",
    "    x_flat = lookup_fn(xflat, e)\n",
    "    dist = cosine_dist(xflat, e)  # these get recalculated, not nice!?\n",
    "    _, idx = tf.nn.top_k(dist, 1)\n",
    "    \n",
    "    x_flat.set_shape((batch_size, s[1]*s[2]*s[3]))\n",
    "    x_ = tf.reshape(x_flat, (batch_size,s[1],s[2],s[3]))\n",
    "    return x_,  tf.reshape(dist, (batch_size,s[1]*s[2], k, 1)), idx  # tf.argmax(idx, axis=1)\n",
    "\n",
    "# TODO. soft look up.\n",
    "# TODO. tok k, k not equal to 1, and average!?\n",
    "\n",
    "def cosine_dist(x, y):\n",
    "    x = tf.nn.l2_normalize(x, dim=1)\n",
    "    y = tf.nn.l2_normalize(y, dim=1)\n",
    "    return tf.matmul(x, y, transpose_b=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "tf.reset_default_graph()\n",
    "x = tf.placeholder_with_default(tf.random_normal((batch_size, 32, 32, 1)), \n",
    "                                shape=(batch_size, 32, 32, 1)) \n",
    "e = tf.get_variable(shape=(k, n_latents), \n",
    "                    dtype=tf.float32, \n",
    "                    name='embeddings',\n",
    "                    initializer=tf.orthogonal_initializer())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "z = encoder(x)\n",
    "e_, dist, idx = lookup(z, e)\n",
    "y = decoder(e_)\n",
    "# y = tf.nn.sigmoid(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6969\n",
      "Tensor(\"conv2d_4/BiasAdd:0\", shape=(32, 2, 2, 8), dtype=float32) Tensor(\"TopKV2:1\", shape=(128, 1), dtype=int32) Tensor(\"Reshape_2:0\", shape=(32, 4, 64, 1), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "print(np.sum([np.prod(var.get_shape().as_list()) for var in tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES)]))\n",
    "print(z, idx, dist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "reconstruction = tf.losses.mean_squared_error(x, y)\n",
    "matching_enc = tf.losses.mean_squared_error(z, tf.stop_gradient(e_))\n",
    "matching_emb = tf.losses.mean_squared_error(tf.stop_gradient(z), e_)\n",
    "orth = tf.losses.mean_squared_error(tf.eye(batch_size), tf.matmul(tf.layers.flatten(z), \n",
    "                                                                  tf.layers.flatten(z), \n",
    "                                                                  transpose_b=True))\n",
    "# added orthogonal regularsation onto z because I wanted\n",
    "# to ensure the encoder didnt collapse onto a small\n",
    "# subset of the vectors in e.\n",
    "# this is kinda cool?! trying to match two orthogonal spaces\n",
    "# the embeddings and the output of the encoder\n",
    "\n",
    "loss = reconstruction + matching_enc + 0.1*orth # # + matching_emb + "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "global_step =  tf.Variable(0, trainable=False, name='global_step')\n",
    "train_op = tf.train.AdamOptimizer(0.001).minimize(loss, global_step=global_step)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "summaries = tf.summary.merge([\n",
    "    tf.summary.scalar('reconstruction', reconstruction),\n",
    "    tf.summary.scalar('encoder_matching', matching_enc),\n",
    "    tf.summary.scalar('orth', orth),\n",
    "    tf.summary.scalar('loss', loss),\n",
    "    tf.summary.histogram('idx', idx),\n",
    "    tf.summary.histogram('embeddings', e),\n",
    "    tf.summary.image('inputs', x),\n",
    "    tf.summary.image('outputs', y),\n",
    "    tf.summary.image('dist', dist),\n",
    "])\n",
    "\n",
    "#     train_summaries = tf.summary.merge([train_summaries] +\n",
    "#             [tf.summary.image('class_{}'.format(i),\n",
    "#                               fetch_labels(x, idx, i))\n",
    "#              for i in range(k)])\n",
    "\n",
    "summarysaverhook = tf.train.SummarySaverHook(save_steps=50,\n",
    "                                      output_dir=logdir,\n",
    "                                      summary_op=summaries)\n",
    "\n",
    "hooks= [\n",
    "#     tf.train.StopAtStepHook(last_step=5000),\n",
    "    summarysaverhook\n",
    "        ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def preprocess(images):\n",
    "    images = images.reshape((-1, 28, 28, 1))\n",
    "    # pad the images so the are a power of two.\n",
    "    # works nicer with the encoder/decoder i wrote.\n",
    "    return np.pad(images, [(0,0), (2,2), (2,2), (0,0)], 'constant')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Create CheckpointSaverHook.\n",
      "INFO:tensorflow:Saving checkpoints for 1 into /tmp/ndr/4/model.ckpt.\n",
      " step: 100 loss: 0.0559INFO:tensorflow:global_step/sec: 30.8078\n",
      " step: 200 loss: 0.0558INFO:tensorflow:global_step/sec: 47.9623\n",
      " step: 300 loss: 0.0529INFO:tensorflow:global_step/sec: 48.0571\n",
      " step: 400 loss: 0.0470INFO:tensorflow:global_step/sec: 47.3686\n",
      " step: 500 loss: 0.0445INFO:tensorflow:global_step/sec: 45.7849\n",
      " step: 600 loss: 0.0452INFO:tensorflow:global_step/sec: 50.4072\n",
      " step: 700 loss: 0.0472INFO:tensorflow:global_step/sec: 48.3217\n",
      " step: 800 loss: 0.0430INFO:tensorflow:global_step/sec: 38.5889\n",
      " step: 900 loss: 0.0444INFO:tensorflow:global_step/sec: 37.6305\n",
      " step: 1000 loss: 0.0439INFO:tensorflow:global_step/sec: 34.7972\n",
      " step: 1100 loss: 0.0424INFO:tensorflow:global_step/sec: 46.1463\n",
      " step: 1200 loss: 0.0410INFO:tensorflow:global_step/sec: 45.8046\n",
      " step: 1300 loss: 0.0446INFO:tensorflow:global_step/sec: 46.9756\n",
      " step: 1400 loss: 0.0415INFO:tensorflow:global_step/sec: 48.4163\n",
      " step: 1500 loss: 0.0438INFO:tensorflow:global_step/sec: 44.6544\n",
      " step: 1600 loss: 0.0459INFO:tensorflow:global_step/sec: 51.8633\n",
      " step: 1700 loss: 0.0415INFO:tensorflow:global_step/sec: 46.6172\n",
      " step: 1800 loss: 0.0447INFO:tensorflow:global_step/sec: 45.7377\n",
      " step: 1900 loss: 0.0433INFO:tensorflow:global_step/sec: 47.6338\n",
      " step: 2000 loss: 0.0407INFO:tensorflow:global_step/sec: 46.2486\n",
      " step: 2100 loss: 0.0431INFO:tensorflow:global_step/sec: 50.0772\n",
      " step: 2200 loss: 0.0439INFO:tensorflow:global_step/sec: 46.0853\n",
      " step: 2300 loss: 0.0382INFO:tensorflow:global_step/sec: 41.2645\n",
      " step: 2400 loss: 0.0399INFO:tensorflow:global_step/sec: 40.4344\n",
      " step: 2500 loss: 0.0435INFO:tensorflow:global_step/sec: 46.7066\n",
      " step: 2600 loss: 0.0440INFO:tensorflow:global_step/sec: 44.4135\n",
      " step: 2700 loss: 0.0386INFO:tensorflow:global_step/sec: 40.1583\n",
      " step: 2800 loss: 0.0383INFO:tensorflow:global_step/sec: 38.1711\n",
      " step: 2900 loss: 0.0427INFO:tensorflow:global_step/sec: 42.3625\n",
      " step: 3000 loss: 0.0435INFO:tensorflow:global_step/sec: 44.6656\n",
      " step: 3100 loss: 0.0397INFO:tensorflow:global_step/sec: 43.555\n",
      " step: 3200 loss: 0.0435INFO:tensorflow:global_step/sec: 39.8638\n",
      " step: 3300 loss: 0.0396INFO:tensorflow:global_step/sec: 44.9152\n",
      " step: 3400 loss: 0.0395INFO:tensorflow:global_step/sec: 42.2248\n",
      " step: 3500 loss: 0.0410INFO:tensorflow:global_step/sec: 44.6674\n",
      " step: 3600 loss: 0.0450INFO:tensorflow:global_step/sec: 44.0795\n",
      " step: 3700 loss: 0.0426INFO:tensorflow:global_step/sec: 46.5901\n",
      " step: 3800 loss: 0.0443INFO:tensorflow:global_step/sec: 47.7807\n",
      " step: 3900 loss: 0.0411INFO:tensorflow:global_step/sec: 48.9744\n",
      " step: 4000 loss: 0.0382INFO:tensorflow:global_step/sec: 47.6262\n",
      " step: 4100 loss: 0.0366INFO:tensorflow:global_step/sec: 47.2312\n",
      " step: 4200 loss: 0.0420INFO:tensorflow:global_step/sec: 51.0079\n",
      " step: 4300 loss: 0.0427INFO:tensorflow:global_step/sec: 46.9004\n",
      " step: 4400 loss: 0.0391INFO:tensorflow:global_step/sec: 45.4641\n",
      " step: 4500 loss: 0.0419INFO:tensorflow:global_step/sec: 46.0442\n",
      " step: 4600 loss: 0.0434INFO:tensorflow:global_step/sec: 42.9318\n",
      " step: 4700 loss: 0.0420INFO:tensorflow:global_step/sec: 46.5501\n",
      " step: 4800 loss: 0.0397INFO:tensorflow:global_step/sec: 47.173\n",
      " step: 4900 loss: 0.0414INFO:tensorflow:global_step/sec: 44.1998\n",
      " step: 5000 loss: 0.0399INFO:tensorflow:global_step/sec: 47.3711\n",
      " step: 5100 loss: 0.0397INFO:tensorflow:global_step/sec: 47.8339\n",
      " step: 5200 loss: 0.0404INFO:tensorflow:global_step/sec: 40.0977\n",
      " step: 5300 loss: 0.0400INFO:tensorflow:global_step/sec: 42.8611\n",
      " step: 5400 loss: 0.0405INFO:tensorflow:global_step/sec: 42.4887\n",
      " step: 5500 loss: 0.0390INFO:tensorflow:global_step/sec: 44.6578\n",
      " step: 5600 loss: 0.0426INFO:tensorflow:global_step/sec: 45.5722\n",
      " step: 5700 loss: 0.0390INFO:tensorflow:global_step/sec: 44.6223\n",
      " step: 5800 loss: 0.0406INFO:tensorflow:global_step/sec: 44.7449\n",
      " step: 5900 loss: 0.0373INFO:tensorflow:global_step/sec: 43.6718\n",
      " step: 6000 loss: 0.0363INFO:tensorflow:global_step/sec: 44.2214\n",
      " step: 6100 loss: 0.0421INFO:tensorflow:global_step/sec: 45.5862\n",
      " step: 6200 loss: 0.0388INFO:tensorflow:global_step/sec: 43.0262\n",
      " step: 6300 loss: 0.0368INFO:tensorflow:global_step/sec: 42.562\n",
      " step: 6400 loss: 0.0412INFO:tensorflow:global_step/sec: 39.5892\n",
      " step: 6500 loss: 0.0368INFO:tensorflow:global_step/sec: 45.2398\n",
      " step: 6600 loss: 0.0398INFO:tensorflow:global_step/sec: 43.7667\n",
      " step: 6700 loss: 0.0377INFO:tensorflow:global_step/sec: 47.0642\n",
      " step: 6800 loss: 0.0403INFO:tensorflow:global_step/sec: 42.5834\n",
      " step: 6900 loss: 0.0407INFO:tensorflow:global_step/sec: 38.0501\n",
      " step: 7000 loss: 0.0367INFO:tensorflow:global_step/sec: 41.0992\n",
      " step: 7100 loss: 0.0394INFO:tensorflow:global_step/sec: 42.7573\n",
      " step: 7200 loss: 0.0381INFO:tensorflow:global_step/sec: 48.7841\n",
      " step: 7300 loss: 0.0420INFO:tensorflow:global_step/sec: 47.5289\n",
      " step: 7400 loss: 0.0390INFO:tensorflow:global_step/sec: 51.1691\n",
      " step: 7500 loss: 0.0369INFO:tensorflow:global_step/sec: 48.466\n",
      " step: 7600 loss: 0.0352INFO:tensorflow:global_step/sec: 45.3326\n",
      " step: 7700 loss: 0.0380INFO:tensorflow:global_step/sec: 47.186\n",
      " step: 7800 loss: 0.0368INFO:tensorflow:global_step/sec: 54.879\n",
      " step: 7900 loss: 0.0408INFO:tensorflow:global_step/sec: 48.4341\n",
      " step: 8000 loss: 0.0413INFO:tensorflow:global_step/sec: 44.1574\n",
      " step: 8100 loss: 0.0421INFO:tensorflow:global_step/sec: 41.184\n",
      " step: 8200 loss: 0.0392INFO:tensorflow:global_step/sec: 43.7059\n",
      " step: 8300 loss: 0.0375INFO:tensorflow:global_step/sec: 43.5561\n",
      " step: 8400 loss: 0.0420INFO:tensorflow:global_step/sec: 45.0752\n",
      " step: 8500 loss: 0.0391INFO:tensorflow:global_step/sec: 48.4233\n",
      " step: 8594 loss: 0.0381INFO:tensorflow:Saving checkpoints for 8594 into /tmp/ndr/4/model.ckpt.\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "with tf.train.MonitoredTrainingSession(checkpoint_dir=logdir,\n",
    "                                       hooks=hooks) as mon_sess:\n",
    "    while mnist.train.epochs_completed <5:\n",
    "        batch_x, batch_t = mnist.train.next_batch(batch_size)\n",
    "        batch_x = preprocess(batch_x)\n",
    "        step, l, _ = mon_sess.run([global_step, loss, train_op], feed_dict={x: batch_x})\n",
    "        print('\\r step: {} loss: {:.4f}'.format(step, l), end='', flush=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import mutual_info_score as mi\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Create CheckpointSaverHook.\n",
      "INFO:tensorflow:Restoring parameters from /tmp/ndr/4/model.ckpt-8594\n",
      "INFO:tensorflow:Saving checkpoints for 8594 into /tmp/ndr/4/model.ckpt.\n"
     ]
    }
   ],
   "source": [
    "t = []; t_ = []\n",
    "with tf.train.MonitoredTrainingSession(checkpoint_dir=logdir,\n",
    "                                       hooks=hooks) as mon_sess:\n",
    "    while mnist.test.epochs_completed <1:\n",
    "        batch_x, batch_t = mnist.test.next_batch(batch_size)\n",
    "        t.append(batch_t)\n",
    "        batch_x = preprocess(batch_x)\n",
    "        t_.append(mon_sess.run(idx, feed_dict={x: batch_x}))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((10016,), (10016, 4))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "targets = np.hstack([np.argmax(v, axis=1) for v in t])\n",
    "preds = np.vstack([v.reshape((batch_size, -1)) for v in t_])\n",
    "targets.shape, preds.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.3008667643560656"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ok, so the baseline performance is\n",
    "mi(targets, targets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.89740174897\n",
      "0.731570026919\n",
      "0.867416808441\n",
      "1.05419863176\n"
     ]
    }
   ],
   "source": [
    "# how well do our predictions align with the labels?\n",
    "for i in range(preds.shape[1]):\n",
    "    print(mi(targets, preds[:,i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.692182281675\n",
      "0.788856891283\n",
      "0.749627321016\n",
      "0.891907993292\n",
      "0.754533496026\n",
      "0.890050476551\n"
     ]
    }
   ],
   "source": [
    "# how well do the fmaps predict each other?\n",
    "# no, this is misleading. not doing the right thing!?\n",
    "for i in range(preds.shape[1]):\n",
    "    for j in range(preds.shape[1]):\n",
    "        if i > j:\n",
    "            print(mi(preds[:,i], preds[:,j]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import OneHotEncoder\n",
    "enc = OneHotEncoder(10, sparse=False)\n",
    "targets_one = enc.fit_transform(targets.reshape((-1, 1))) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Container object of 64 artists>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f719deda908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ZztPfr4E9gb3qx9NbXrN9p7mIWABcCmygul3MwcA7gbUtMY353tWI7qwj4qfA\nFZl5Qv08qD50z8jMj/Q0OW2XiBgB/mdmfrdl2O3ARzPztPr5TsBdwKsz87zeZKrtUf9IsQp4ZmZe\nUrfp3cBxmfntOuYg4FrgDzPzyt5lq05FxD3Au6i+GNm+DREROwBLgDcDpwA/z8x3uB1PfxHxfuDY\nzDx8jNds3waIiFOBIzPzqK3ENOZ717Q/4hMRM6l+Tfz+6LCsqrmLgSN7lZe6IyIeS/WLU2t73wdc\nge09nS2gOrq3pn6+GJjB5u18PXAztvO0ExF9EXEcMA+4HNu3aT4NnJ+ZP2gbfgS2cxMcUJ96fmNE\nfDkiHlMPdztuhhcAV0XEefWp51dHxOtGX2za965pX/gAuwH9VJVnq7uoGkrNshfVF2TbuyHqI7Sn\nA5dk5ui543sBG+udayvbeRqJiN+PiPupTqE4C3hRZl6H7dsYdUF7GHDSGC/vie083f0UeA3VKVBv\nAh4L/Dgi5uN23BSPozpaez3wp8BngTMi4lX164363jWj1wl0UTDG9SFqLNt7+joLOITNzxvfEtt5\nerkOOJTqiN5LgC9GxDO3Em/7TiMRsQ/VjxbPzsxNJaNiO08LmXlRy9NfR8SVwErgZcD6LYxm+04v\nfcCVmXlK/fyaiPg9qmLoy1sZb1q2cxOO+KwGhql+WWq1Bw+vTjX93Um1sdneDRARZwLHAH+Umbe3\nvHQnMKs+j7iV7TyNZOZQZi7PzKsz82SqC99PwPZtisXA7sCSiNgUEZuAo4ATImIjVVvOtp2bIzPv\nBW4AFuF23BR3UF2X1epaYN/6/0Z975r2hU/9K9MS4OjRYfWpM0cDl/UqL3VHZt5EtRG2tvdOVL2D\n2d7TSF30HAv8cWbe3PbyEmCIzdv5QKod8eWTlqQmWh8wG9u3KS4Gnkh1qtuh9eMqql+JR//fhO3c\nGHVHFo8HbsftuCkuBQ5qG3YQ1ZG9xn3vasqpbp8AzomIJcCVwNupLqI9u5dJqTP1ucOLqH5hAHhc\nRBwKrMnMW6hOrXhfRCwDVgAfAm4FvtODdNWBiDgL+AvghcBARIz+knRvZq7PzPsi4p+BT0TEWuB+\n4AzgUnsKmh4i4sPAf1L1sLkj8EqqowF/avs2Q2YOAEtbh0XEAHBPZl5bP7edp7GI+ChwPtWX4EcD\nf0dV7JzrdtwYpwGXRsRJwHlUBc3rqLqnH9WY712NKHwy87y6O9wPUh2K+wXwnMy8u7eZqUNHAD+k\nOnc0qe6HtPQlAAAFz0lEQVTRBHAO8L8z8yMRMQ/4HNW1Az8BnpeZG3uRrDryJqq2/VHb8P8FfLH+\n/+1Up7F+g+oowYVU93bS9LAnVVs+CrgX+CVV0TPa85ft20zt5/zbztPbPsBXgV2puq6+hKqr6nvq\n123faS4zr4qIFwGnUnVHfxNwQmae2xLTmO9djbiPjyRJkiRtzbS/xkeSJEmStsXCR5IkSVLjWfhI\nkiRJajwLH0mSJEmNZ+EjSZIkqfEsfCRJkiQ1noWPJEmSpMaz8JEkSZLUeBY+kiRJkhrPwkeSNC4R\nMRIRL+x1HuMREfvV+f5BD+Z9VD3vnSZ73pKkLbPwkSQREXtGxKci4saIWB8RKyPiuxHxJ12a32QU\nB9nFaU/leUuSxjCj1wlIknorIvYDLgPWAO8CfgXMBJ4LnAkc0o3ZUhUHsd0TiujPzOEtzEOSJMAj\nPpIk+AwwDDw5M7+dmcsy89rMPA34w7FGGOuITUQcWg/bt36+b33UaE1EPBARv4qI59aF1g/q0dZG\nxHBE/Es9TkTESRGxPCIGI+LnEfGSMeb73Ii4KiLWA0/bynt7fET8ICIGIuIXEbHZ+4mIp0fEj+t5\nrYyIT0bEvJbXXxkRP4uI+yLijoj4SkTs3jaNYyLi+noa3wf2b3t9zOWwlZwlSV1g4SNJj2ARsRB4\nDnBmZq5vfz0z79vK6GOdztU67CxgFvB04PeB9wIPADcDo8XMAcCjgBPq538LvAp4A9WRptOAL0XE\nM9rm84/19A4GfrmVHP8e+AhwKHAD8NWI6AOIiMcD/wl8vc7v5VRF1Kdaxp8JvA/4A+BYYD/gX0df\njIh9gG8C36nn8QXg1LYctrQcJEmTyFPdJOmRbRHVKWHXd2HajwG+kZlL6+crRl+IiDX1v3ePFlcR\nMQs4CTg6M68YHacuet4I/KRl2qdk5vfHkcNHM/PCevrvB35N9Z5vAE4EvpyZo4XO8oh4G/CjiHhz\nZm7MzLNbprWifv2KiJiXmYPAm4FlmfmeOua3dYcK72kZb4vLQZI0eSx8JOmRbfQ6mG5cjH8G8JmI\neA5wMfDNzPzVVuIXAfOA/4qI1utzZgJXtzxPYMk4c2id3x1U73cPqsLnUOCJEfGqlpjR+T4WuD4i\nFgPvr2MX8rszJfYFrqM64nQFm7u87XnpcpAkdYGnuknSI9tvqQqJgwvHG6n/thcoD8nMf6YqIL5I\ndYrXVRFx/FamuUP99xiqQmP0cQjw522xA+PMc1NrSvXf0c++HYDPUZ3GNjqvPwAOBG6sr/W5EFgH\nvAI4AnhRPe6s+u9oJw1bNMZy+Nk2loMkqQssfCTpESwz1wIXAcdHxNz21yNi5y2MejfVl/5HtQx7\n0hjTvy0zP5+ZLwU+Dry+fmlj/be/JXwpsAHYLzOXtz1uK3pj9ey38frVwO9l5k1jzG8IeAKwC3BS\nZl6amTcAe7ZNYynw1LZhRz4skc2Xwyf43XKQJE0SCx9J0l9TFSBXRsSLI2JRRDwhIv6GqpvrsSwD\nbgE+UMf/GfCO1oCIOC0i/jQi9o+Iw4E/pioUAFZSFSYviIjdImJ+Zj4AfAw4LSL+KiIeFxFPioi3\nRMRftk56nO9rW3H/BBxZ37/o0Pp9HBsRo9f83ExVoP1NRDy2vnnr+9qm8VnggIj4SEQcGBGvAF5d\nsBwkSZPEwkeSHuEycwVwOPBDqsLjV8D3qL6gv7k1tGWcIeA4qqMi1wDvBk5um3Q/1X2AlgIXUF0T\nc3w9/u1U186cCtxJ3ZNaZp4CfJCq44GlVL2uHQPcNFYe23prWxtWX2dzFFXPcj+mOgL0AeC2+vXV\nwGuAlwK/oeqw4J2bTSzzFqoe6o4FfkHVG91JbfPc4nKQJE2eyPTm0pIkSZKazSM+kiRJkhrPwkeS\nJElS41n4SJIkSWo8Cx9JkiRJjWfhI0mSJKnxLHwkSZIkNZ6FjyRJkqTGs/CRJEmS1HgWPpIkSZIa\nz8JHkiRJUuNZ+EiSJElqvP8Ptpq1RHgucU0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f719dd19128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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e8O2I2L9+3/ZtkPqfja+n2v+2sp3nvt8ADwF2qX+e3PKe7TvHRcT2wAXAJqrH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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f719dfbdc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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4FjAFuDgiZrTEfBr4M+DFwDOARwHfGuM81b67gPcCi+rXpcB3I+LQur/rt0Hq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\nkiRJkhrPwkeSJElS4/1/sD/fJkHzYAEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f71a88a4630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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+pdesWbNS+Re+8IWp/I9+9KNUvqurK5XPrqMAp556aip/xx13pPLZfcWKFStS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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f719dd19470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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IPYAxiqn8Acgi4W4E1nSrLg2EfSh+S3NvtwtR3/oYcElmfqnbhahv/Q5wTURc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\nUkUY0CRJkiSpIv4/gZRsNhydV+IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f71a3169c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Fs4ZXp1uAy2gWcJakMbcScKJXSZLUf3MKYVW1G0CSS2nGhM08aEKSJEmStIOexoRV1f36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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f71a314a0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Z = np.zeros((10, k))\n",
    "# how do the clusters correlate with the labels?\n",
    "for i in range(preds.shape[1]):\n",
    "    enc = OneHotEncoder(k, sparse=False)\n",
    "    preds_one = enc.fit_transform(preds[:,i].reshape((-1, 1))) \n",
    "    plt.figure(figsize=(10, 3))\n",
    "    plt.ylabel('Labels')\n",
    "    plt.xlabel('Cluster heads')\n",
    "    plt.title('Fmap position {}'.format(i))\n",
    "    M = np.dot(targets_one.T, preds_one[:, :64])\n",
    "    plt.imshow(M, interpolation='nearest', cmap='gray')\n",
    "    Z +=M\n",
    "plt.figure(figsize=(10, 3))\n",
    "plt.title('Total')\n",
    "plt.xlabel('Labels')\n",
    "plt.ylabel('Cluster heads')\n",
    "plt.imshow(Z, interpolation='nearest', cmap='gray')\n",
    "plt.figure(figsize=(10, 3))\n",
    "plt.xlabel('Labels')\n",
    "plt.ylabel('Correlation')\n",
    "plt.bar(range(10), (Z.sum(axis=1)-Z.sum(axis=1).mean())/Z.sum(axis=1).max())\n",
    "plt.figure(figsize=(10, 3))\n",
    "plt.xlabel('Cluster heads')\n",
    "plt.ylabel('Correlation')\n",
    "plt.bar(range(k), Z.sum(axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# it seems weird that one cluster head can correlate with many labels quite strongly\n",
    "# also that 5s are pretty much left out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AWnLbhjXqjWbWhKMjPRoNAADYDAhMAAAAF8DZRgAkAhMASJKcc4oaDdXr9cy6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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f71a85431d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# what does the dstribution of look ups look like?\n",
    "# hopefully not too asymetric\n",
    "plt.figure(figsize=(10, 6))\n",
    "_ = plt.hist(preds[:,0], bins=k, alpha=0.5)\n",
    "_ = plt.hist(preds[:,1], bins=k, alpha=0.5)\n",
    "_ = plt.hist(preds[:,2], bins=k, alpha=0.5)\n",
    "_ = plt.hist(preds[:,3], bins=k, alpha=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}