LCD-digits-dataset-NMF.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LCD digits dataset shows NMF parts-based decomposition\n",
    "\n",
    "This synthetic image dataset shows very nicely how NMF decompose images as the sums of their parts.  The collection of images is encoded as a 2d array of non-negative values.  Each row corresponds to an image, and each column corresponds to a pixel.  The non-negative entries represent the whiteness of the pixel, encoded here as a value between 0 and 1.\n",
    " \n",
    "See also the accompanying blog post http://building-babylon.net/2016/12/28/an-lcd-digit-dataset-for-illustrating-the-parts-based-representation-of-nmf/ .\n",
    "\n",
    "Released under Apache Licence v2.0.  I hope you find it useful."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "length = 4  # length of any LCD cell (\"stroke\")\n",
    "shape = (2 * length + 5, length + 4)  # shape of the images"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code for displaying a vector as an image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "def show_as_image(vector):\n",
    "    \"\"\"\n",
    "    Given a 1d vector representing an image, display that image in \n",
    "    black and white.  If there are negative values, then use red for \n",
    "    that pixel.\n",
    "    (displaying negative pixel values in red allows e.g. visual contrasting\n",
    "    of PCA and NMF components)\n",
    "    \"\"\"\n",
    "    bitmap = vector.copy().reshape(shape)  # make a square array\n",
    "    bitmap /= np.abs(vector).max()  # normalise (a copy!)\n",
    "    bitmap = bitmap[:,:,np.newaxis]\n",
    "    rgb_layers = [np.abs(bitmap)] + [bitmap.clip(0)] * 2\n",
    "    rgb_bitmap = np.concatenate(rgb_layers, axis=-1)\n",
    "    plt.figure(figsize=(2, 1))\n",
    "    plt.imshow(rgb_bitmap, interpolation='nearest')\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code for generating the images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  1.  1.  1.  1.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "def vertical_stroke(rightness, downness):\n",
    "    \"\"\"\n",
    "    Return a 2d numpy array representing an image with a single vertical stroke in it.\n",
    "    `rightness` and `downness` are values from [0, 1] and define the position of the vertical stroke.\n",
    "    \"\"\"\n",
    "    i = (downness * (length + 1)) + 2\n",
    "    j = rightness * (length + 1) + 1\n",
    "    x = np.zeros(shape=shape, dtype=np.float64)\n",
    "    for delta in range(length):\n",
    "        x[i + delta, j] = 1.\n",
    "    return x\n",
    "\n",
    "def horizontal_stroke(downness):\n",
    "    \"\"\"\n",
    "    Analogue to vertical_stroke, but it returns horizontal strokes.\n",
    "    `downness` is here a value in [0, 1, 2].\n",
    "    \"\"\"\n",
    "    i = (downness * (length + 1)) + 1\n",
    "    x = np.zeros(shape=shape, dtype=np.float64)\n",
    "    for j in range(length):\n",
    "        x[i, 2 + j] = 1.\n",
    "    return x\n",
    "\n",
    "print(horizontal_stroke(0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "strokes = [horizontal_stroke(k) for k in range(3)] + [vertical_stroke(k, l) for k in range(2) for l in range(2)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import random\n",
    "\n",
    "def random_composition():\n",
    "    \"\"\"\n",
    "    Return a random composition of 2, 3, 4, or 5 strokes as a single 2d numpy array.\n",
    "    (So not guaranteed to look like a real digit!)\n",
    "    \"\"\"\n",
    "    x = np.zeros(shape=shape, dtype=np.float64)\n",
    "    num_strokes = random.choice([2, 3, 4, 5])\n",
    "    sample = random.sample(strokes, num_strokes) # without replacement\n",
    "    for atom in sample:\n",
    "        x += atom\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  1.  1.  1.  1.  0.  0.]\n",
      " [ 0.  1.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  1.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  1.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  1.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  1.  1.  1.  1.  0.  0.]\n",
      " [ 0.  1.  0.  0.  0.  0.  1.  0.]\n",
      " [ 0.  1.  0.  0.  0.  0.  1.  0.]\n",
      " [ 0.  1.  0.  0.  0.  0.  1.  0.]\n",
      " [ 0.  1.  0.  0.  0.  0.  1.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.]]\n"
     ]
    }
   ],
   "source": [
    "bitmap = random_composition()\n",
    "print(bitmap)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEMAAABhCAYAAACNrhxOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAAYhJREFUeJzt3LFNw1AUQNH3EEWUlgVcUiJaBmAI5ssQGQBmoMwC9HSf\nIhS3sfXQtx1b3NOksOU8X1nfimwlW2uhq7tbD7AlxgBjgDHAGGAMMAaUYmTmMTOfM/O49EBLqM5/\nXzzeU0S8R8RbZn52T7e+x4g4RcRLRHyM7VSNMfx+nvpmurkhJmJU14zLHJNswGVqYzXGd/8cmzB5\nHt5NoLpm/Nkav4Yzc9bjeWWAMcAYYAwwBnTfTcbuGnOv9GvwygBjgDHAGGAMMAYYA4wBxgBjgDHA\nGGAMMAYYA4wBxgBjgDHAGGAMMAYYA7qfm4w9H/Ep/M4ZA4wBxgBjgDFg168kzP3dXhlgDDAGGAOM\nAcYAY4AxwBhgDDAGGAOMAcYAY4AxwBhgDDAGGAOMAcYAY8BirySswVcSFmQMMAYYA4wBxgBjgDHA\nGGAMqMY4LDrFeibPoxpj6J9jE4apjVl5xzszHyLiNa5/FLjH//k7xDXEubX2NbZTKcZ/4QIKxgBj\ngDHAGGAMMAb8AJimKhAh4kfnAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d3e0128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_as_image(bitmap.flatten())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(200, 104)\n"
     ]
    }
   ],
   "source": [
    "N = 200\n",
    "samples = [random_composition().flatten() for _ in range(N)]\n",
    "X = np.vstack(samples)\n",
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NMF learns the individual LCD cells"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.decomposition import NMF\n",
    "\n",
    "model = NMF(n_components=7)\n",
    "model.fit(X)\n",
    "X_transformed = model.transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d3e0160>"
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     "metadata": {},
     "output_type": "display_data"
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       "<matplotlib.figure.Figure at 0x1048477f0>"
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     "metadata": {},
     "output_type": "display_data"
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     "metadata": {},
     "output_type": "display_data"
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     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEMAAABhCAYAAACNrhxOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAAXVJREFUeJzt3DFOw0AQQNEZRBGl5QIuKREtB+AQnC+H4ABwBspcgJ5u\nKUzxm7VG2thxxH9NClvW+MtyLFvabK2FZnfXHmBPjAHGAGOAMcAYYAwoxcjMY2Y+Z+Zx7YHWUJ3/\nvni8p4j4iIi3zPwanm57jxFxioiXiPjs7VSNMf39nsZmuropFmJU7xnnS0yyA+eljdUYP+Nz7MLi\nefhvAsYAY4AxwBhgDDAGVJ9Au3rvUDNz9NCb88oAY4AxwBhgDDAGGAOMAcYAY4AxwBhgDDAGGAOM\nAcYAY4AxwBhgDDAGGAOGv5vc4veRHq8MMAYYA4wBxgBjgDHAGGAMMAYYA4wBxgBjgDHAGGAMMAYY\nA4wBxgBjgDHAGGAMMAYYA4wBxgBjgDHAGGAMMAYYA4wBxgBjgDHAGGAMqMY4rDrFdhbPoxpjGp9j\nF6aljVlZdzwzHyLiNeaFAm9xnb9DzCHeW2vfvZ1KMf4Lb6BgDDAGGAOMAcYAY8AvDJ8eBEUOVQQA\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fae0048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for component in model.components_:\n",
    "    show_as_image(component)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEMAAABhCAYAAACNrhxOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAAYZJREFUeJzt3LFNw0AUgOH3EEWUlgVcUiJaBmAI5ssQDAAzUGYBerqj\nMMVf4NMF+xxb/F+Twpbz/Ms6K3LkLKWERjfXHmBLjAHGAGOAMcAYYAxoipGZx8x8zMxj74F6aJ3/\ntvF4DxHxFhEvmfkxe7r13UfEKSKeIuJ9aqfWGMPP52neTFc3RCVG65pxXmKSDTjXNrbG+Jo/xyZU\nz8O7CbSuGRdb49dwZi56PK8MMAYYA4wBxoBud5OlV/rfTN2x/vrdXhlgDDAGGAOMAcYAY4AxwBhg\nDDAGGAOMAcYAY4AxwBhgDDAGGAOMAcYAY0C35yZr8Cl8R8YAY4AxwBhgDNj1rdW/JHRkDDAGGAOM\nAcYAY4AxwBhgDDAGGAOMAcYAY4AxwBhgDDAGGAOMAcYAY8Cun5v4l4SOjAHGAGOAMcAYYAwwBhgD\njAGtMQ5dp1hP9TxaYwzz59iEobYxW960lpl3EfEc44sC9/iev0OMIV5LKZ9TOzXF+C9cQMEYYAww\nBhgDjAHGgG9+hiQQGsUb9QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d2c6390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "digit7 = horizontal_stroke(0) + vertical_stroke(1, 0) + vertical_stroke(1, 1)\n",
    "show_as_image(digit7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.4930625 ,  0.54888887,  0.        ,  0.        ,  0.        ,\n",
       "         0.39639133,  0.        ]])"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.transform([digit7.flatten()])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Demonstration that PCA does not!\n",
    "\n",
    "The components that we obtain from PCA are dense and can not be interpreted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=7, random_state=None,\n",
       "  svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components=7)\n",
    "pca.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEMAAABhCAYAAACNrhxOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fb0ef60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEMAAABhCAYAAACNrhxOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111567e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEMAAABhCAYAAACNrhxOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d30f4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEMAAABhCAYAAACNrhxOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYvwXnkDBGGAMMAYYA4wBxoAvz68rluodCCEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10453b8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEMAAABhCAYAAACNrhxOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUDAGGAOMAcYAY4Ax4AvNyCh+jsKVcwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fea8080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEMAAABhCAYAAACNrhxOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\npZTGx9qrYvwXXkDBGGAMMAYYA4wBxoAvlGEvtjIt9mYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fb0abe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEMAAABhCAYAAACNrhxOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nY4AxwBhgDDAGfAKLeiZpqd0RvAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d31c128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for component in pca.components_:\n",
    "    show_as_image(component)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
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   "language": "python",
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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 },
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}