No_Fuss_DML_MNIST_Keras.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# No Fuss DML\n",
    "\n",
    "Implementation of NCA Loss for Distance metric learning using Keras form : https://arxiv.org/pdf/1703.07464.pdf\n",
    "Already applied it to various datasets, found it very useful especially when it's hard to mine hard negatives or triplets size is outrageously large.\n",
    "\n",
    "The technique can produce high quality embeddings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import keras\n",
    "from keras.datasets import mnist\n",
    "from keras.models import Model\n",
    "from keras.layers import Dense, Dropout, Flatten, Input, Reshape, Lambda, BatchNormalization\n",
    "from keras.layers import Conv2D, MaxPooling2D\n",
    "from keras.optimizers import RMSprop\n",
    "from keras.layers.embeddings import Embedding\n",
    "from keras import backend as K\n",
    "import numpy as np\n",
    "from keras_tqdm import TQDMNotebookCallback"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "img_rows, img_cols = 28, 28\n",
    "batch_size = 128\n",
    "num_classes = 10\n",
    "epochs = 5\n",
    "embedding_size = 64\n",
    "vis_sample_size = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "the data, shuffled and split between train and test sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "(x_train, y_train), (x_test, y_test) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pre process data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('x_train shape:', (60000, 28, 28, 1))\n",
      "(60000, 'train samples')\n",
      "(10000, 'test samples')\n"
     ]
    }
   ],
   "source": [
    "if K.image_data_format() == 'channels_first':\n",
    "    x_train = x_train.reshape(x_train.shape[0], 1, img_rows, img_cols)\n",
    "    x_test = x_test.reshape(x_test.shape[0], 1, img_rows, img_cols)\n",
    "    input_shape = (1, img_rows, img_cols)\n",
    "else:\n",
    "    x_train = x_train.reshape(x_train.shape[0], img_rows, img_cols, 1)\n",
    "    x_test = x_test.reshape(x_test.shape[0], img_rows, img_cols, 1)\n",
    "    input_shape = (img_rows, img_cols, 1)\n",
    "\n",
    "x_train = x_train.astype('float32')\n",
    "x_test = x_test.astype('float32')\n",
    "x_train /= 255\n",
    "x_test /= 255\n",
    "print('x_train shape:', x_train.shape)\n",
    "print(x_train.shape[0], 'train samples')\n",
    "print(x_test.shape[0], 'test samples')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model\n",
    "\n",
    "We will have two models one for training, the other to compute the embeddings (the useful one; just diffirent inputs/outputs and without proxy_layer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "inp_x = Input(shape=(28,28,1))\n",
    "inp_y = Input(shape=(1,))\n",
    "\n",
    "# Class proxy\n",
    "proxies_layer = Embedding(num_classes*2, embedding_size, name='emb_proxies', embeddings_initializer=keras.initializers.RandomNormal(mean=0.0, stddev=0.3, seed=7))\n",
    "proxies_output = proxies_layer(inp_y)\n",
    "proxies_output = Reshape((embedding_size,))(proxies_output)\n",
    "\n",
    "# Conv network\n",
    "x = Conv2D(32, kernel_size=(3, 3),\n",
    "        activation='relu',\n",
    "        input_shape=input_shape)(inp_x)\n",
    "x = Conv2D(64, (3, 3), activation='relu')(x)\n",
    "x = MaxPooling2D(pool_size=(2, 2))(x)\n",
    "x = Conv2D(64, (3, 3), activation='relu')(x)\n",
    "x = Conv2D(64, (3, 3), activation='relu')(x)\n",
    "x = MaxPooling2D(pool_size=(2, 2))(x)\n",
    "x = Flatten()(x)\n",
    "x = Dense(128, activation='relu')(x)\n",
    "x = BatchNormalization()(x)\n",
    "emb_img = Dense(embedding_size, activation='linear', name='embedding')(x)\n",
    "\n",
    "#proxies_layer.trainable = False\n",
    "\n",
    "# Training model\n",
    "model = Model(inputs=[inp_x, inp_y], outputs=[emb_img])\n",
    "to_be_used_model = Model(inputs=inp_x, outputs=emb_img)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## NCA Loss\n",
    "\n",
    "Maybe there is a more idiomatic way to implement nca loss in Keras/Tensorflow\n",
    "For more details about NCA look at http://www.cs.toronto.edu/~fritz/absps/nca.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from keras import backend as K\n",
    "import tensorflow as tf\n",
    "\n",
    "def expand_multiple_dims(x, axes, name=\"expand_multiple_dims\"):\n",
    "  with tf.name_scope(name):\n",
    "    for i in sorted(axes):\n",
    "      x = tf.expand_dims(x, axis=i, name=\"expand_axis_%i\" % i)\n",
    "    return x\n",
    "\n",
    "\n",
    "# Theano-like dimshuffle\n",
    "def dimshuffle(x, axes, name=\"dimshuffle\"):\n",
    "  with tf.name_scope(name):\n",
    "    assert all([i == \"x\" or isinstance(i, int) for i in axes])\n",
    "    real_axes = [i for i in axes if isinstance(i, int)]\n",
    "    bc_axes = [i for (i, j) in enumerate(axes) if j == \"x\"]\n",
    "    if x.get_shape().ndims is None:\n",
    "      x_shape = tf.shape(x)\n",
    "      x = tf.reshape(x, [x_shape[i] for i in range(max(real_axes) + 1)])  # will have static ndims\n",
    "    assert x.get_shape().ndims is not None\n",
    "\n",
    "    # First squeeze missing axes.\n",
    "    i = 0\n",
    "    while i < x.get_shape().ndims:\n",
    "      if i not in real_axes:\n",
    "        x = tf.squeeze(x, axis=i)\n",
    "        real_axes = [(j if (j < i) else (j - 1)) for j in real_axes]\n",
    "      else:\n",
    "        i += 1\n",
    "\n",
    "    # Now permute.\n",
    "    assert list(sorted(real_axes)) == list(range(x.get_shape().ndims))\n",
    "    if real_axes != list(range(x.get_shape().ndims)):\n",
    "      x = tf.transpose(x, real_axes)\n",
    "\n",
    "    # Now add broadcast dimensions.\n",
    "    if bc_axes:\n",
    "      x = expand_multiple_dims(x, bc_axes)\n",
    "    assert len(axes) == x.get_shape().ndims\n",
    "    return x\n",
    "\n",
    "def lookup(what, where, default=None):\n",
    "    \"\"\"Return ``where.what`` if what is a string, otherwise what. If not found\n",
    "    return ``default``.\"\"\"\n",
    "    if isinstance(what, (str, unicode)):\n",
    "        res = getattr(where, what, default)\n",
    "    else:\n",
    "        res = what\n",
    "    return res\n",
    "\n",
    "\n",
    "def l2(x, axis=None):    \n",
    "    return tf.norm(x, axis=axis, ord=2, keep_dims=False)\n",
    "\n",
    "def pairwise_diff(X, Y=None):\n",
    "    Y = X if Y is None else Y    \n",
    "    diffs = dimshuffle(K.transpose(X), (1, 0, 'x')) - dimshuffle(K.transpose(Y), ('x', 0, 1))    \n",
    "    return diffs\n",
    "\n",
    "\n",
    "def distance_matrix(X, Y=None, norm=l2):\n",
    "    diff = pairwise_diff(X, Y)\n",
    "    diff = distance_matrix_by_diff(diff, norm=norm)\n",
    "    return diff\n",
    "\n",
    "\n",
    "def distance_matrix_by_diff(diff, norm=l2):\n",
    "    diff = norm(diff, axis=1)\n",
    "    return diff\n",
    "\n",
    "def diagonal(x):\n",
    "    return tf.diag_part(x)\n",
    "\n",
    "def normalize_rowwise(mat):  \n",
    "    with tf.variable_scope(\"normalize_rowwise\"):\n",
    "        return mat / K.reshape(l2(mat,axis=1) + K.epsilon(), [-1,1])\n",
    "\n",
    "def nca_loss(embeddings, proxies_output, proxies_weights): # proxies_weights = proxy embedding raw matrix\n",
    "    \"\"\"Return the NCA loss for No Fuss DML.\n",
    "    For details, we refer you to 'Neighbourhood Component Analysis' by\n",
    "    J Goldberger, S Roweis, G Hinton, R Salakhutdinov (2004).\n",
    "    ----------\n",
    "    \"\"\"    \n",
    "    embeddings_normed = normalize_rowwise(embeddings)    \n",
    "    # Positive distances\n",
    "    target_proxies_normed = normalize_rowwise(proxies_output)        \n",
    "    positive_distances = diagonal(distance_matrix(target_proxies_normed, embeddings_normed))\n",
    "    numerator = K.exp(-positive_distances) \n",
    "    # Negative distances    \n",
    "    proxies_normed = normalize_rowwise(proxies_weights)    \n",
    "    all_distances = distance_matrix(embeddings_normed, proxies_normed)        \n",
    "    denominator = K.sum(K.exp(-all_distances), axis=1) - numerator        \n",
    "    # Compute ratio\n",
    "    loss_vector = -K.log(numerator) / (denominator+K.epsilon())\n",
    "    loss = K.mean(loss_vector)\n",
    "    return loss\n",
    "\n",
    "def loss(y_true, y_pred):\n",
    "    return  nca_loss(y_pred-0*y_true, proxies_output, proxies_layer.embeddings)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compile the model, RMSprop as optimizer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model.compile(loss=loss,optimizer='adadelta')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x7f387b20e8d0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit([x_train, y_train], np.zeros((x_train.shape[0],1)),\n",
    "          epochs=epochs,\n",
    "          verbose=0,\n",
    "          validation_data=([x_test, y_test], np.zeros((x_test.shape[0],1))),\n",
    "          batch_size=batch_size,\n",
    "          callbacks=[TQDMNotebookCallback(leave_inner=False)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Visualization\n",
    "\n",
    "Project produced embeddings on 2D plan using T-SNE, you can also use TensorBoard faster T-SNE a possibility to visualize in 3D\n",
    "\n",
    "Please this function will sample randomly a `vis_sample_size` points from test data. So yeah ! every time you will have different plot.\n",
    "\n",
    "(If it's not already done, please do yourself a favor and go read about t-sne https://distill.pub/2016/misread-tsne/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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R3XfoAY7O76RtZztvWPy6wQDbk+kBoLq8CoBUeHIrq/Gp8UxYUMXx37TTne2h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\nLk2SdI4MrJJGjWw2x4//pIO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xMu2HKes7Qq61gV1ffy+7vv4+dn39ffzm6x8v1FsQKQOr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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f37fd1b4c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.manifold import TSNE\n",
    "from matplotlib.pyplot import cm\n",
    "import scipy as sp\n",
    "from scipy import ndimage\n",
    "from scipy import misc\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def plot_embeddings(save=None):\n",
    "    colors=cm.rainbow(np.linspace(0,1,num_classes))    \n",
    "    sel = np.random.choice(x_test.shape[0], vis_sample_size, replace=False)\n",
    "    valid_set, valid_labels = x_test[sel,:], y_test[sel]\n",
    "    class_embeddings = np.array(to_be_used_model.predict(valid_set))\n",
    "\n",
    "\n",
    "    class_embeddings = TSNE(n_components=2, perplexity=45, verbose=0, n_iter=5000, learning_rate=10).fit_transform(class_embeddings)\n",
    "\n",
    "    plt.figure(figsize=(18,9))\n",
    "    for cls, color in zip(range(num_classes),colors):\n",
    "        current_points = class_embeddings[valid_labels==cls]\n",
    "        if save is not None:\n",
    "            plt.title('Iteration {}'.format(save))\n",
    "        plt.subplot(121).scatter(current_points[:,0], current_points[:,1],\n",
    "                    c=color, #valid_labels[valid_labels==cls],\n",
    "                    marker='${}$'.format(cls), s=100, linewidths=0.1, edgecolor='black')       \n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "plot_embeddings()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}