mnist_linearClassifier.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Importing libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reading data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<p>10 rows × 785 columns</p>\n",
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      ],
      "text/plain": [
       "   2  0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  ...    0.712  0.713  0.714  \\\n",
       "0  1  0    0    0    0    0    0    0    0    0  ...        0      0      0   \n",
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       "\n",
       "   0.715  0.716  0.717  0.718  0.719  0.720  0.721  \n",
       "0      0      0      0      0      0      0      0  \n",
       "1      0      0      0      0      0      0      0  \n",
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       "\n",
       "[10 rows x 785 columns]"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import os\n",
    "data = pd.read_csv('/home/rajendra/data/mnist_train.csv')\n",
    "data.head(10)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(449, 785)"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#data.plot(kind = 'line', x = 'Size', y = 'Price', figsize=(10,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "785"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cols = data.shape[1]\n",
    "cols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0, ..., 0, 0, 0],\n",
       "       [0, 0, 0, ..., 0, 0, 0],\n",
       "       [0, 0, 0, ..., 0, 0, 0],\n",
       "       ...,\n",
       "       [0, 0, 0, ..., 0, 0, 0],\n",
       "       [0, 0, 0, ..., 0, 0, 0],\n",
       "       [0, 0, 0, ..., 0, 0, 0]])"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array(data.iloc[:,1:cols])\n",
    "y = np.array(data.iloc[:, 0:1])\n",
    "x\n",
    "#data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((449, 784), (449, 1))"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape, y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Creating array of unique element in array y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3])"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.unique(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4,)"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.unique(y).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classes = np.unique(y).shape[0]\n",
    "classes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "rows = data.shape[0]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Inserting dummy variable(1 rows no. of times) in x, at 0th column(axis = 1), for easy calculation loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(449, 785)"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.insert(x,0,values = np.ones(rows), axis = 1)\n",
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0, ..., 0, 0, 0],\n",
       "       [1, 0, 0, ..., 0, 0, 0],\n",
       "       [1, 0, 0, ..., 0, 0, 0],\n",
       "       ...,\n",
       "       [1, 0, 0, ..., 0, 0, 0],\n",
       "       [1, 0, 0, ..., 0, 0, 0],\n",
       "       [1, 0, 0, ..., 0, 0, 0]])"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "parameters = x.shape[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Initialising  theta matrix with zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_theta = np.zeros((4, parameters))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 785)"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_theta.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# sigmoid Function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# \\\\(g(z) = sigmoid(z) = \\frac{1}{1 + exp(-z)}\\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1/(1 + np.exp(-z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ComputeCost or Error Function defined"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# \\\\(Cost=J(theta)=\\frac{1}{2m} * \\sum [first + second]   \\\\)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# \\\\(first + second = y*(-log(g(z))) + (1-y)*(-log(1-g(z)))\\\\)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### \\\\(where, z = x.theta^T = actual Output\\\\)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### first is error when expected output is 1 and second is error when expected output is 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "def computeCost(theta, x, y):\n",
    "    theta = np.matrix(theta)\n",
    "    x = np.matrix(x)\n",
    "    y = np.matrix(y)\n",
    "    \n",
    "    first = np.multiply(-y, np.log(sigmoid(x*theta.T)))\n",
    "    \n",
    "    second = np.multiply(-(1-y), np.log(1-sigmoid(x*theta.T)))\n",
    "    \n",
    "    cost = np.sum(first + second)\n",
    "    cost = cost/(2*len(x))\n",
    "    \n",
    "    return cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost = 1.3862943611198906\n"
     ]
    }
   ],
   "source": [
    "cost = computeCost(all_theta, x,  y)\n",
    "print(\"Cost = {}\" .format(cost))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gradient Function defined"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# \\\\(Grad = \\frac{d(J)}{d(theta)} = \\frac{c}{2m} * \\sum [X^T.error]\\\\)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# \\\\(error = g(z) - y\\\\)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### \\\\(where, z = x*theta^T\\\\)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### \\\\(c = learning rate\\\\) and m = len(x) = no. of rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "learning_rate = 1\n",
    "def gradient(theta, x, y):\n",
    "    \n",
    "    theta = np.matrix(theta)\n",
    "    x = np.matrix(x)\n",
    "    y = np.matrix(y)\n",
    "    \n",
    "    error = sigmoid(x*theta.T) - y\n",
    "    \n",
    "    grad = ((x.T*error)/(2*len(x)))\n",
    "    \n",
    "    grad = grad*learning_rate\n",
    "    \n",
    "    return grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gradient Descent, i.e minimising theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating one hot matrix(y_i, which is a column array) for each classes using x,y\n",
    "## and Calculating minimum theta i.e minimum value of computecost fuction using minimise Function(with initial theta as all 0's and args = (x,y_i), and jacobin = gradient)for each class "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import minimize\n",
    "def one_vs_all(x, y, classes, temp_theta): #finding an one hot matrix of each class(y_i) and using it to find min theta for that class(i.e gradient descent)\n",
    "    parameters = x.shape[1]\n",
    "    rows = x.shape[0]\n",
    "    \n",
    "    for i in range(0, classes):#calculating the ith column of one hot matrix and passing it into gradient descent\n",
    "        theta = np.zeros(parameters)\n",
    "        theta = temp_theta[i,:] #ith row of theta\n",
    "        \n",
    "        y_i = np.array([1 if label == i else 0 for label in y])\n",
    "        y_i = np.reshape(y_i, (rows, 1))\n",
    "        \n",
    "        #gradient descent\n",
    "        fmin = minimize(fun =computeCost, x0 = theta, args = (x, y_i), method = 'TNC', jac = gradient)\n",
    "        \n",
    "        all_theta[i,:] = fmin.x\n",
    "    return all_theta       \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.5/dist-packages/ipykernel_launcher.py:8: RuntimeWarning: divide by zero encountered in log\n",
      "  \n",
      "/usr/local/lib/python3.5/dist-packages/ipykernel_launcher.py:8: RuntimeWarning: invalid value encountered in multiply\n",
      "  \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.00526986  0.          0.         ...  0.          0.\n",
      "   0.        ]\n",
      " [-0.0135359   0.          0.         ...  0.          0.\n",
      "   0.        ]\n",
      " [-0.00288407  0.          0.         ...  0.          0.\n",
      "   0.        ]\n",
      " [ 0.02512358  0.          0.         ...  0.          0.\n",
      "   0.        ]]\n"
     ]
    }
   ],
   "source": [
    "#classes = 4\n",
    "min_theta = one_vs_all(x, y, classes, all_theta)\n",
    "print(min_theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "34.95410547491266"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "computeCost(min_theta, x, y )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predicted y for input x "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict_all(x, theta):\n",
    "    x = np.matrix(x)\n",
    "    theta = np.matrix(theta)\n",
    "    \n",
    "    h = sigmoid(x*theta.T)\n",
    "    h_argmax = np.argmax(h, axis = 1)\n",
    "    return h_argmax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculating Accuracy by comparing y_pred and y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = predict_all(x, min_theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n",
      "Training data =100.0%\n"
     ]
    }
   ],
   "source": [
    "correct = [1 if a == b else 0 for (a,b) in zip(y_pred,y)]\n",
    "print(correct)\n",
    "acc = (sum(map(int, correct))/float(len(correct)))\n",
    "print(\"Training data ={}%\" .format(acc*100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Testing->input png>rgb2gray>grarray>bw>ravel>reshape>insert dummy variable>predict fun called"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Input testing image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.image as mpimg\n",
    "img = mpimg.imread('/home/rajendra/data/test1.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## rgb2gray function defined, called and plotted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f14dcf599b0>"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def rgb2gray(rgb):\n",
    "    return np.dot(rgb[:,:,:3], [0.299, 0.587, 0.114])\n",
    "\n",
    "gray = rgb2gray(img)\n",
    "plt.imshow(gray, cmap = plt.get_cmap('gray'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## converted to grarray and then inverted it(bw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f14dcf0d8d0>"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grarray = np.asarray(gray)\n",
    "bw = (grarray < (grarray.mean()))*255\n",
    "plt.imshow(np.reshape(bw,(28,28)),cmap = plt.cm.gray)\n",
    "#bw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ravel and reshaped and inserted dummy variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "bw= bw.ravel()\n",
    "bw = bw.reshape(1,-1)\n",
    "brows = bw.shape[0]\n",
    "bw= np.insert(bw,0,values=np.ones(brows), axis = 1)\n",
    "#bw.shape\n",
    "#bw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## predict called"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[3]]\n"
     ]
    }
   ],
   "source": [
    "pred = predict_all(bw, min_theta)\n",
    "print(pred)"
   ]
  }
 ],
 "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}