ALS_demo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([[5,0,4,0,3,3],\n",
    "            [0,4,0,0,3,0],\n",
    "            [3,0,0,3,0,0],\n",
    "            [0,4,0,5,0,1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[5, 0, 4, 0, 3, 3],\n",
       "        [0, 4, 0, 0, 3, 0],\n",
       "        [3, 0, 0, 3, 0, 0],\n",
       "        [0, 4, 0, 5, 0, 1]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q = np.asmatrix(x)\n",
    "Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "W = Q>0.01\n",
    "W[W == True] = 1\n",
    "W[W == False] = 0\n",
    "# To be consistent with our Q matrix\n",
    "W = W.astype(np.float64, copy=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "lambda_ = 0.1\n",
    "n_factors = 3\n",
    "m, n = Q.shape\n",
    "n_iterations = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.random.rand(m, n_factors) \n",
    "Y = np.random.rand(n_factors, n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_error(Q, X, Y, W):\n",
    "    return np.sum((W * (Q - np.dot(X, Y)))**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[1., 0., 1., 0., 1., 1.],\n",
       "        [0., 1., 0., 0., 1., 0.],\n",
       "        [1., 0., 0., 1., 0., 0.],\n",
       "        [0., 1., 0., 1., 0., 1.]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "shapes (1,) and (6,3) not aligned: 1 (dim 0) != 6 (dim 0)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-27-c705fa0f3275>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mii\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn_iterations\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mu\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mWu\u001b[0m \u001b[1;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mW\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 4\u001b[1;33m         \u001b[0mX\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mu\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msolve\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mY\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdiag\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mWu\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mY\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mlambda_\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0meye\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn_factors\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mY\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdiag\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mWu\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mQ\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mu\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      5\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mWi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mW\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      6\u001b[0m         \u001b[0mY\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msolve\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdiag\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mWi\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mX\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mlambda_\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0meye\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn_factors\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdiag\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mWi\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mQ\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: shapes (1,) and (6,3) not aligned: 1 (dim 0) != 6 (dim 0)"
     ]
    }
   ],
   "source": [
    "weighted_errors = []\n",
    "for ii in range(n_iterations):\n",
    "    for u, Wu in enumerate(W):\n",
    "        X[u,:] = np.linalg.solve(np.dot(Y,d np.dot(np.diag(Wu), Y.T)) + lambda_ * np.eye(n_factors),np.dot(Y, np.dot(np.diag(Wu), Q[u].T))).T\n",
    "    for i, Wi in enumerate(W.T):\n",
    "        Y[:,i] = np.linalg.solve(np.dot(X.T, np.dot(np.diag(Wi), X)) + lambda_ * np.eye(n_factors),np.dot(X.T, np.dot(np.diag(Wi), Q[:, i])))\n",
    "    weighted_errors.append(get_error(Q, X, Y, W))\n",
    "    print('{}th iteration is completed'.format(ii))\n",
    "weighted_Q_hat = np.dot(X,Y)\n",
    "print('Error of rated movies: {}'.format(get_error(Q, X, Y, W)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(weighted_errors);\n",
    "plt.xlabel('Iteration Number');\n",
    "plt.ylabel('Mean Squared Error');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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