03-mnist-synthetic-dataset.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Synthethic Dataset\n",
    "\n",
    "### Creating a synthetic dataset of multi-digit images from the MNIST dataset \n",
    "\n",
    "---\n",
    "\n",
    "This notebook explains my approach to creating a synthetic dataset of 64x64 images of digit sequences from the MNIST Handwritten Digit Database. The resulting dataset is fairly simple compared to the original SVHN dataset, but it allows us to quickly develop and experiment with model architectures for recognizing multiple digits in a single image.\n",
    "\n",
    "Our resulting dataset consists of 50,000 greyscale images of size 64 x 64 where we have 10,000 examples for each possible sequence length. We randomly select the images that are concatenated from the original MNIST dataset. These images are then scaled down to 12 x 12 pixels (since 5 x 12 < 64) this allows us to fit up to 5 images horizontally. These images are then concatenated and centered both horizontally and vertically in the resulting image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (16.0, 4.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading the MNIST dataset\n",
    "\n",
    "Let's load the MNIST dataset using the ``sklearn.datasets`` package for convinience."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original Shape\n",
      "((70000, 784), (70000,))\n",
      "\n",
      "New Shape\n",
      "(70000, 28, 28)\n"
     ]
    }
   ],
   "source": [
    "from sklearn import datasets, preprocessing\n",
    "\n",
    "# Fetch the MNIST dataset from mldata.org\n",
    "mnist = datasets.fetch_mldata('MNIST original')\n",
    "\n",
    "# Extract the data and labels\n",
    "X, y = mnist.data.astype(float), mnist.target.astype(int)\n",
    "\n",
    "print(\"Original Shape\")\n",
    "print(X.shape, y.shape)\n",
    "\n",
    "# Reshape the original dataset which is flat to 28x28 images\n",
    "X = X.reshape(len(X), 28, 28)\n",
    "\n",
    "print(\"\\nNew Shape\")\n",
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's implement a few helper functions to help us to visually explore our data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD+CAYAAAD1VNNvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIkEp/CJBKfwiQf0fzl8fsgvtRXMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119f38250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_image(img):\n",
    "    \"\"\"Helper function for displaying a single image\n",
    "    \"\"\"\n",
    "    plt.imshow(img, interpolation='nearest')\n",
    "\n",
    "def plot_images(img, labels, nrows, ncols):\n",
    "    \"\"\"Helper function used to display digits\n",
    "    \"\"\"\n",
    "    plt.figure(figsize=(min(16, ncols*2), min(16, nrows*2)))\n",
    "    for i in range(nrows * ncols):\n",
    "        plt.subplot(nrows, ncols, i+1)\n",
    "        # Reshape every image to a square array 2d array\n",
    "        if img[i].shape == (64, 64, 1):\n",
    "            plt.imshow(img[i,:,:,0], interpolation='nearest')\n",
    "        else:\n",
    "            plt.imshow(img[i], interpolation='nearest')\n",
    "        plt.xticks([]); plt.yticks([])\n",
    "        plt.title(labels[i])\n",
    "        \n",
    "\n",
    "# Display a single image\n",
    "plot_image(X[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot a few more digits to get a better sense of what the data looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA4sAAADECAYAAAA29bRHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\noM6iiIiIiIiIOPw/qFktfo+kz14AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119f20f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot 2 rows with 16 digits each\n",
    "plot_images(X, y, 2, 16)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks like our dataset is ordered by label, let's randomly sort the arrays to view some of the other numbers as well"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA4sAAADECAYAAAA29bRHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13b93abd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.utils import shuffle\n",
    "\n",
    "# Shuffle the dataset\n",
    "X, y = shuffle(X, y)\n",
    "\n",
    "# Plot 2 rows with 16 digits each\n",
    "plot_images(X, y, 2, 16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating the synthetic dataset\n",
    "\n",
    "Let's create a synthetic dataset consisting of sequences of up to 5 digits using the MNIST dataset. Let's start by specifying the new dimensions, the maximum number of digits and the size of our new dataset for convenience."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Height and width of our new synthethic images\n",
    "height, width = 64, 64\n",
    "\n",
    "# Maximum number of digits\n",
    "max_digits = 5\n",
    "\n",
    "# Scale the origina images down to 45% (12x12 pixels)\n",
    "scale = 0.45\n",
    "\n",
    "# New height and width of the scaled images\n",
    "new_height, new_width = 12, 12\n",
    "\n",
    "# We create a new dataset with 50,000 images\n",
    "dataset_size = 50000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Concatenating the images and labels\n",
    "\n",
    "Here is a simple function to concatenate a set of images into a single larger image and center the digit sequence within the new image. The following bulletpoints outline the procedure:\n",
    "\n",
    "* By scaling the image to 45% we get a 12 x 12 image\n",
    "* If we concatenate, say 3 images our resulting image will be 12 x 36 pixels\n",
    "* To center this image horizontally we must calculate the padding on each side, which is (64 - 36) / 2 = 14\n",
    "* To center it vertically we know that our new image is 64 pixels high and that our scaled images are 12 x 12 pixels. This means that we must pad the image with (64 - 12) / 2 = 26 pixels vertically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAEACAYAAAB8u6CyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d5f2f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.misc import imresize\n",
    "\n",
    "def concat_images(images):\n",
    "    \"\"\" Scales, concatenates and centers a sequence of digits in an image\n",
    "    \"\"\"\n",
    "    # Keep this\n",
    "    num_digits = len(images)    \n",
    "    \n",
    "    # Initialize a numpy array for the new image\n",
    "    new_image = np.zeros(shape=(height, width), dtype=\"uint8\")\n",
    "    \n",
    "    # Calculate the horizontal and vertical padding\n",
    "    y_pad = (height - new_height) / 2\n",
    "    x_pad = (width - num_digits * new_width) / 2\n",
    "    \n",
    "    # For every image passed to the function\n",
    "    for i in range(num_digits):\n",
    "                         \n",
    "        # Scale down the original image\n",
    "        scaled = imresize(images[i], scale)\n",
    "        \n",
    "        # Calculate the starting position\n",
    "        x_offset = x_pad + (i*new_width)\n",
    "        \n",
    "        # Add the scaled image to the new image\n",
    "        new_image[y_pad:height-y_pad, x_offset:x_offset+new_width] = scaled\n",
    "        \n",
    "    # Return the newly centered image\n",
    "    return new_image\n",
    "\n",
    "\n",
    "# Concatenate image 0 through 5 to a single image\n",
    "plot_image(concat_images(X[0:5]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also need a new label structure for our newly created images. Let's represent each label as a list where each element represents the digit in the sequence. For sequences with less than 5 digits we use 10 as a filler to represent missing values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 6, 2, 2, 0])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def concat_labels(labels, num_images=5):\n",
    "    \"\"\" Concatenates a set of set of labels into a single numpy array\n",
    "    \"\"\"\n",
    "    new_label = np.zeros(num_images, dtype=int)\n",
    "    for i in range(num_images):\n",
    "        if i < len(labels):\n",
    "            new_label[i] = labels[i]\n",
    "        else:\n",
    "            new_label[i] = 10\n",
    "    return new_label\n",
    "\n",
    "\n",
    "# Concatenate the labels for image 0 through 5\n",
    "concat_labels(y[:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's test the function to see that we are able to generate some images with different number of digits and that our new labels match the images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 6, 2, 2, 0])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAEACAYAAAB8u6CyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11dce0410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display images 0 through 5\n",
    "plot_image(concat_images(X[:5]))\n",
    "\n",
    "# Print the label for the new image\n",
    "concat_labels(y[:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3,  6,  2, 10, 10])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAEACAYAAAB8u6CyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n8IsEpfCLBKXwiwSl8IsE9b/lK11jTMQneQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e43f110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display images 0 through 3\n",
    "plot_image(concat_images(X[:3]))\n",
    "\n",
    "# Print the labels for the new image\n",
    "concat_labels(y[:3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3, 10, 10, 10, 10])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAEACAYAAAB8u6CyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11da3f190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display the first image\n",
    "plot_image(concat_images(X[:1]))\n",
    "\n",
    "# Print the new label\n",
    "concat_labels(y[:1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dataset generator\n",
    "\n",
    "Let's write a simple function that will help us to generate our synthetic dataset. The function will create an even number of samples for the different digit sequence length. E.g, if we want to create 50,000 images we will get 10,000 images with a single digit, 20,000 images with 2 digits etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Images', (50000, 64, 64, 1))\n",
      "('Labels', (50000, 5))\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "def generate_digit_sequences(data, labels, n):\n",
    "    \"\"\" Helper function for automatically generating a new dataset of digit sequences\n",
    "    \"\"\"\n",
    "    # Initialize numpy arrays\n",
    "    X = np.zeros(shape=(n, height, width), dtype='uint8')\n",
    "    y = np.zeros(shape=(n, max_digits), dtype=np.int32)\n",
    "    \n",
    "    # Number of training examples of each sequence length\n",
    "    n_samples = n / max_digits\n",
    "    \n",
    "    # For every possible digit sequence length\n",
    "    for i in range(1, max_digits+1):\n",
    "        \n",
    "        # Pick n_samples images\n",
    "        for j in range((i-1)*n_samples, i*n_samples):\n",
    "            \n",
    "            # Select i random digits from the original dataset\n",
    "            selection = random.sample(range(0, len(data)), i)\n",
    "            \n",
    "            # Concatenate the digits and labels from\n",
    "            X[j] = concat_images(data[selection])\n",
    "            y[j] = concat_labels(labels[selection])\n",
    "            \n",
    "    # Add an additional dimension to the image array\n",
    "    X = np.expand_dims(X, axis=3)\n",
    "            \n",
    "    # Return the new dataset\n",
    "    return X, y\n",
    "\n",
    "\n",
    "# Generate a synthetic dataset of digit sequences with 50,000 new images\n",
    "X_new, y_new = generate_digit_sequences(X, y, dataset_size)\n",
    "\n",
    "print(\"Images\", X_new.shape)\n",
    "print(\"Labels\", y_new.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Class Balance and sequence lengths\n",
    "\n",
    "Let's verify that our dataset is fairly balanced in terms of the individual digits (0-9) and that we actually generated a dataset with an even distribution of digit sequence lengths."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA7oAAAEKCAYAAAA8USkxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSZKkWjHRlSRJkiTViomuJEmSJKlW/j+NQVYH7XYVEgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e568c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot a histogram showing the class distribution\n",
    "plt.subplot2grid((1, 2), (0, 0))\n",
    "plt.hist(y_new.flatten())\n",
    "plt.title(\"Class Distribution (10 = empty)\")\n",
    "\n",
    "# Plot a histogram showing the sequence length distribution\n",
    "plt.subplot2grid((1, 2), (0, 1))\n",
    "plt.hist((y_new != 10).sum(1), color='r', bins=5)\n",
    "plt.xlim(1, 5)\n",
    "plt.title(\"Sequence Length Distribution\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The histogram looks ok. As expected we have an overweight of 10's that are used to represent missing numbers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sanity Check\n",
    "\n",
    "Let's do a sanity check of our dataset to make sure that our images looks ok and that our labels match the images."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA4sAAAFmCAYAAADEVg8WAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSZIkSQUGi5IkSZKkAoNFSZIkSVLB/wdB9IqpIGLj2gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e1c0610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Shuffle the examples before visualizing\n",
    "X_new, y_new = shuffle(X_new, y_new, random_state=0)\n",
    "\n",
    "# Plot 3 rows of 8 images from the new dataset\n",
    "plot_images(X_new, y_new, 3, 8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training, Test and Validation Sets\n",
    "\n",
    "Let's split our dataset and create a training, test and validation set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Training', (37500, 64, 64, 1), (37500, 5))\n",
      "('Test', (10000, 64, 64, 1), (10000, 5))\n",
      "('Validation', (2500, 64, 64, 1), (2500, 5))\n"
     ]
    }
   ],
   "source": [
    "from sklearn.cross_validation import train_test_split\n",
    "\n",
    "# Create a training and test set\n",
    "X_train, X_test, y_train, y_test = train_test_split(X_new, y_new)\n",
    "\n",
    "# Select some random images to be used in our validation set\n",
    "idx = np.random.choice(range(0, len(X_test)), size=int(len(X_test)*0.20), replace=False)\n",
    "\n",
    "# Construct our validation set and remove the images from the test set\n",
    "X_val, y_val = X_test[idx], y_test[idx]\n",
    "\n",
    "# Remove the validation samples from the testset\n",
    "X_test = np.delete(X_test, idx, axis=0)\n",
    "y_test = np.delete(y_test, idx, axis=0)\n",
    "\n",
    "print(\"Training\", X_train.shape, y_train.shape)\n",
    "print(\"Test\", X_test.shape, y_test.shape)\n",
    "print('Validation', X_val.shape, y_val.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Storing the Data\n",
    "\n",
    "Let's store our new datasets in a h5py file that we will use as model input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import h5py\n",
    "\n",
    "# Create file\n",
    "h5f = h5py.File('data/MNIST_synthetic.h5', 'w')\n",
    "\n",
    "# Store the datasets\n",
    "h5f.create_dataset('train_dataset', data=X_train)\n",
    "h5f.create_dataset('train_labels', data=y_train)\n",
    "h5f.create_dataset('test_dataset', data=X_test)\n",
    "h5f.create_dataset('test_labels', data=y_test)\n",
    "h5f.create_dataset('valid_dataset', data=X_val)\n",
    "h5f.create_dataset('valid_labels', data=y_val)\n",
    "\n",
    "# Close the file\n",
    "h5f.close()"
   ]
  }
 ],
 "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": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}