Dimension_Reduction_Dictionary_learning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dictionary Learning is a dimensionality reduction technique to reduce high dimensions into a **sparse representation** of input data, often used in denoising of images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "import skimage\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import load_digits\n",
    "from sklearn.decomposition import DictionaryLearning\n",
    "digits = load_digits()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "NUM_IMAGES = 48"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample = digits.data[:NUM_IMAGES,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(48, 64)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 48 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,10))\n",
    "\n",
    "for i in range(NUM_IMAGES):\n",
    "    ax = fig.add_subplot(6,8,i+1, xticks=[],yticks = [])\n",
    "    ax.imshow(sample[i].reshape(8,8),\n",
    "              cmap='Blues_r',\n",
    "              interpolation = 'nearest')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "dict_learn = DictionaryLearning(n_components = 36, \n",
    "                                fit_algorithm='lars', # optomization algo\n",
    "                               transform_algorithm='lasso_lars')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_dict = dict_learn.fit_transform(sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(48, 36)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_dict.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# visualise the sparse representation of the first transformed image\n",
    "resized = skimage.transform.resize(X_dict[0].reshape(6,6),(8,8))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fec6ea1cfd0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.imshow(resized, cmap=\"Blues_r\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## look at the sparse representations of all 48 images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x720 with 48 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,10))\n",
    "\n",
    "for i in range(NUM_IMAGES):\n",
    "    ax = fig.add_subplot(6,8,i+1, xticks=[],yticks = [])\n",
    "    ax.imshow(X_dict[i].reshape(6,6),\n",
    "              cmap='Blues_r',\n",
    "              interpolation = 'nearest')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(36, 64)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dict_learn.components_.shape\n",
    "\n",
    "# original size: 8 x 8 = 64\n",
    "# sparse code: 6 x 6 = 36"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## get the original image from the sparse representation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "original = np.matmul(X_dict,dict_learn.components_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(48, 64)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "original.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fec6df547b8>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "# first image\n",
    "plt.imshow(original[0].reshape(8,8),cmap='Blues_r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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",
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 },
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