HW5 Q2 - NNMF.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#initialize matrices\n",
    "X = np.zeros(shape = (3012, 8447)) #counts, words by docs\n",
    "W = np.random.uniform(1, 2, size = (3012, 25))\n",
    "H = np.random.uniform(1, 2, size = (25, 8447))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#define divergence objective\n",
    "def divergence_objective(X, W, H):\n",
    "    WH_log = np.log(W @ H + 10**(-16))\n",
    "    #print(np.multiply(X, WH_log).sum())\n",
    "    #return(-1*np.subtract(np.multiply(X, WH_log).sum(), (W @ H).sum())) #add 10**(-16) before taking log to avoid error\n",
    "    return(-1*np.sum(np.subtract(np.multiply(X, WH_log), (W @ H)))) #add 10**(-16) before taking log to avoid error\n",
    "    #return(np.sum(np.add(np.multiply(X, np.log(1/np.add(np.matmul(W,H), 10**(-16)))), np.matmul(W,H)))) #add 10**(-16) before taking log to avoid error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with open(\"/Users/rebecca.peyser/Documents/Columbia_DSI/machinelearning/HW/Homework 5/hw5-data/nyt_data.txt\") as f:\n",
    "    articles = f.read().splitlines()\n",
    "splitoncomma = [article.split(',') for article in articles]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8447\n",
      "163\n",
      "151\n"
     ]
    }
   ],
   "source": [
    "print(len(splitoncomma))\n",
    "print(len(splitoncomma[0]))\n",
    "print(len(splitoncomma[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "doc_idx = 0\n",
    "for article in splitoncomma:\n",
    "    for word in article:\n",
    "        word, count = word.split(':')\n",
    "        X[int(word)-1, doc_idx] = count\n",
    "    doc_idx += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "obj = []\n",
    "for t in np.arange(100):\n",
    "    #update H\n",
    "    W_norm = np.divide(np.transpose(W), np.add(np.sum(np.transpose(W), axis = 1)[:,None], 10**(-16))) #add 10**(-16) to the denominator to avoid dividing by 0\n",
    "    purple = np.divide(X, np.add(np.matmul(W, H), 10**(-16))) #add 10**(-16) to the denominator to avoid dividing by 0\n",
    "    H = np.multiply(H, np.dot(W_norm, purple))\n",
    "    \n",
    "    #update W\n",
    "    purple = np.divide(X, np.add(np.matmul(W, H), 10**(-16))) #add 10**(-16) to the denominator to avoid dividing by 0\n",
    "    H_norm = np.transpose(np.divide(H, np.add(np.sum(H, axis = 1)[:,None], 10**(-16)))) #add 10**(-16) to the denominator to avoid dividing by 0\n",
    "    W = np.multiply(W, np.dot(purple, H_norm))\n",
    "    \n",
    "    #value of objective function\n",
    "    obj.append(divergence_objective(X, W, H))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
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3FEePn5yw3tBAP6uXXOZQMSs5SbsiYrhePbdM7BRupZjZVHjMxE4zmYF5Tx82M3CY2AQa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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bfd7f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter((np.arange(100)+1), obj)\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}