Module1_Lab4_FMML20210660.ipynb

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  "metadata": {
    "colab": {
      "name": " Lab4_LinearAlgebra_FMML20210660",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/SreenadhSingamaneni/IIITH-FMML20210660/blob/main/Module1_Lab4_FMML20210660.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mU9LZjQxiQT2"
      },
      "source": [
        "# Transforming data using linear algebra\n",
        "\n",
        "FMML Module 1, Lab 4<br>\n",
        " Module Coordinator: Thrupthi Ann John thrupthi.ann@research.iiit.ac.in <br>\n",
        " Release date: 25 October 2021 <br>\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KBe4ZA32UTbv"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from keras.datasets import mnist"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7mqG-dafVpya"
      },
      "source": [
        "#@title\n",
        "\n",
        "from IPython.display import Latex as lt\n",
        "#Plotting functions \n",
        "#(You DON'T need to understand how these functions)\n",
        "\n",
        "# function to plot a grid \n",
        "def plotGrid(transform, unit, linestyle = ':', fig=None, ax=None):\n",
        "  lim1 = -100\n",
        "  lim2 = 100\n",
        "  def mat2xy(start, end):\n",
        "    if len(start.shape)==1:\n",
        "      start = np.expand_dims(start,0)\n",
        "      end = np.expand_dims(end,0)\n",
        "    nan = np.ones(len(start))*np.nan\n",
        "    x = np.stack((start[:,0], end[:,0], nan)).T.reshape(-1)\n",
        "    y = np.stack((start[:,1], end[:,1], nan)).T.reshape(-1)\n",
        "    return x, y\n",
        "\n",
        "  def parallellines(axis, addend, lines, unit):\n",
        "    addend = np.repeat(np.expand_dims(addend,0), lines*2, 0) \n",
        "    unit = np.expand_dims(np.arange(-lines, lines)*unit,1)\n",
        "    unit = unit-lines\n",
        "    addend = addend*unit\n",
        "    lines = np.expand_dims(axis,0) + addend\n",
        "    return np.concatenate((lines, lines*-1))\n",
        "\n",
        "  if fig is None:\n",
        "    fig, ax = plt.subplots(figsize=(10,10))\n",
        "  transform = transform.astype(np.float)\n",
        "  xaxis = transform[0]\n",
        "  yaxis = transform[1]\n",
        "    \n",
        "  # plot lines parallel to the x axis\n",
        "  lines1= parallellines(xaxis*lim1, yaxis, 100,unit )\n",
        "  lines2 = parallellines(xaxis*lim2, yaxis, 100,unit )\n",
        "  x,y = mat2xy(lines1, lines2)\n",
        "  plt.plot(x,y, linestyle+'k', linewidth=0.5)\n",
        "  # plot x axis\n",
        "  x,y = mat2xy(xaxis*lim1, xaxis*lim2)\n",
        "  plt.plot(x,y,linestyle, color = '#440077')\n",
        "\n",
        "  # plot  lines parallel to the y axis\n",
        "  lines1= parallellines(yaxis*lim1, xaxis, 100,unit)\n",
        "  lines2 = parallellines(yaxis*lim2, xaxis, 100,unit)\n",
        "  x,y = mat2xy(lines1, lines2)\n",
        "  plt.plot(x,y, linestyle+'k', linewidth=0.5)\n",
        "  # plot y axis\n",
        "  x,y = mat2xy(yaxis*lim1, yaxis*lim2)\n",
        "  plt.plot(x,y,linestyle, color= '#aa5500')\n",
        "\n",
        "  return fig, ax\n",
        "\n",
        "def plotData(X, y, xlabel = 'hole', ylabel = 'bound', fig=None, ax = None):\n",
        "\n",
        "  if fig is None:\n",
        "    fig, ax = plt.subplots()\n",
        "  for ii in range(nclasses):\n",
        "    plt.scatter(X[y==ii,0], X[y==ii, 1])\n",
        "  plt.legend([str(i) for i in range(nclasses)])\n",
        "  plt.xlabel(xlabel)\n",
        "  plt.ylabel(ylabel)\n",
        "  lim2 = X.max() \n",
        "  lim1 = X.min() \n",
        "  add = abs(lim1-lim2)/5\n",
        "  return fig, ax\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9d5dmEXxaktp"
      },
      "source": [
        "# Matrix transformations on data\n",
        "\n",
        "A 2D coordinate system is defined by its basis vectors, i and j. In the standard coordinate system (Let us call it T0), the basis vectors are\n",
        "\n",
        "$$\\begin{equation}\n",
        "i = \\left\\{  \\begin{aligned}1 \\\\ 0 \\end{aligned} \\right\\} \n",
        "\\end{equation}$$\n",
        "and\n",
        "$$\\begin{equation} j = \\left\\{ \\begin{aligned} 0 \\\\ 1\\end{aligned} \\right\\} \\end{equation}$$\n",
        "\n",
        "We can use any two vectors as basis vectors for a new coordinate system as long as they are not colinear. For example, let us call this new coordinate system T1:\n",
        "\n",
        "$$\\begin{equation}\n",
        "i = \\left\\{  \\begin{aligned}1 \\\\ -1 \\end{aligned} \\right\\} \n",
        "\\end{equation}$$\n",
        "and\n",
        "$$\\begin{equation} j = \\left\\{ \\begin{aligned} 0 \\\\ 2 \\end{aligned} \\right\\} \\end{equation}$$\n",
        "\n",
        "Suppose we have a point [a,b] in the T1 coordinate system. Its representation in the standard system T0 can be obtained by the following matrix multiplication:\n",
        "\n",
        "$$ \\begin{equation} \n",
        "\\left\\{  \\begin{aligned}a' \\\\ b' \\end{aligned} \\right\\} = \n",
        "\\left\\{  \\begin{aligned}&1 & 0 \\\\ -&1 & 2 \\end{aligned} \\right\\}\n",
        "\\left\\{  \\begin{aligned}a \\\\ b \\end{aligned} \\right\\}\n",
        "\\end{equation}$$\n",
        "where the columns of the matrix are the basis vectors of T1. \n",
        "\n",
        "Let us see this in action:\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "K8SCFKqfbM-l",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f3cbab1e-cc9f-4618-ba52-43ee872db588"
      },
      "source": [
        "T0 = np.array([[1,0],[0,1]])\n",
        "T1 = np.array([[1,0], [-1,2]])\n",
        "\n",
        "data1 = np.array([5,4]) # the data in T1 coordinate system\n",
        "data0 = np.matmul(T1, data1) # the data in T0 coordinate system\n",
        "\n",
        "print('Data in T0 = ', data0)\n",
        "print('Data in T1 = ', data1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Data in T0 =  [5 3]\n",
            "Data in T1 =  [5 4]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kIfEWZ1RQeve"
      },
      "source": [
        "We can visualize this below. T0 is shown with dotted lines and T1 is shown with solid lines. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jSuTaeSDQoYK",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 578
        },
        "outputId": "0fab76db-a453-42b5-db9d-4821932e1ddb"
      },
      "source": [
        "fig, ax = plotGrid(T1.T, 1,'-') # custom plotting function, no need to understand this\n",
        "plotGrid(T0.T, 1, fig=fig, ax=ax) # custom plotting function, no need to understand this\n",
        "plt.scatter(data0[0], data0[1])\n",
        "ax.set_xlim(-10,10)\n",
        "ax.set_ylim(-10,10)\n",
        "ax.set_xticks([]);\n",
        "ax.set_yticks([]);\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nUb3oYWIgdya"
      },
      "source": [
        "Look at the coordinates of the blue dot. In T0 (dotted lines), the position is [5,3] where it is [5,4] in T1. Feel free to experiment with different data points and coordinate systems. \n",
        "\n",
        "Remember that we can achieve the same thing by post-multiplying the transpose of the transformation matrix to the data. This will come in handy when transforming multiple data points at once:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SD4pqOMndf-4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8bdac7c2-6752-4933-b4d4-ef06ec300850"
      },
      "source": [
        "data0_a = np.matmul(T1, data1)\n",
        "data0_b = np.matmul(data1, T1.T)\n",
        "print(data0_a)\n",
        "print(data0_b)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[5 3]\n",
            "[5 3]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z-Kui3dSESPm"
      },
      "source": [
        "Why is transforming data useful? Data transformations cause the distance between data points to change. This will affect distance-based algorithms such as nearest neighbour"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nE0NbpYIC9ou",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "bbd0a543-513a-43f2-89e1-571a3f13109d"
      },
      "source": [
        "# let us define 3 points in T1\n",
        "A1 = np.array([3,3])\n",
        "B1 = np.array([2,-5])\n",
        "C1 = np.array([1,-1])\n",
        "\n",
        "# the corresponding points in T0:\n",
        "A0 = np.matmul(T1, A1)\n",
        "B0 = np.matmul(T1, B1)\n",
        "C0 = np.matmul(T1, C1)\n",
        "\n",
        "# function to calculate Euclidean distance:\n",
        "def dist(a, b):\n",
        "  diff = a-b\n",
        "  sq = diff*diff\n",
        "  return np.sqrt(sq.sum())\n",
        "\n",
        "# distance between the points in T1\n",
        "print('Distance between A and B in T1 = ', dist(A1, B1))\n",
        "print('Distance between B and C in T1 = ', dist(B1, C1))\n",
        "print('Distance between A and C in T1 = ', dist(A1, C1))\n",
        "\n",
        "print('')\n",
        "# distnace between the points in T0\n",
        "print('Distance between A and B in T0 = ', dist(A0, B0))\n",
        "print('Distance between B and C in T0 = ', dist(B0, C0))\n",
        "print('Distance between A and C in T0 = ', dist(A0, C0))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Distance between A and B in T1 =  8.06225774829855\n",
            "Distance between B and C in T1 =  4.123105625617661\n",
            "Distance between A and C in T1 =  4.47213595499958\n",
            "\n",
            "Distance between A and B in T0 =  15.033296378372908\n",
            "Distance between B and C in T0 =  9.055385138137417\n",
            "Distance between A and C in T0 =  6.324555320336759\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YE95JMniUtDm"
      },
      "source": [
        "We see that in T1, B and C are the closest whereas in T0, A and C are the closest. These kinds of changes will affect the predictions returned by the nearest neighbour algorithm. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PFbpTSBdV29C"
      },
      "source": [
        "# Transformations on MNIST\n",
        "\n",
        "Let us experiment with a subset of the MNIST dataset. We will extract two features from the database for our experiment. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kMvUzC2GUawS"
      },
      "source": [
        "Functions for nearest neighbour, accuracy and feature extraction. (from previous labs)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "22ayl0sViF5-"
      },
      "source": [
        "#@title\n",
        "\n",
        "def NN1(traindata, trainlabel, query):\n",
        "  diff  = traindata - query  # find the difference between features. Numpy automatically takes care of the size here \n",
        "  sq = diff*diff # square the differences\n",
        "  dist = sq.sum(1) # add up the squares\n",
        "  label = trainlabel[np.argmin(dist)] # our predicted label is the label of the training data which has the least distance from the query\n",
        "  return label\n",
        "\n",
        "def NN(traindata, trainlabel, testdata):\n",
        "  # we will run nearest neighbour for each sample in the test data \n",
        "  # and collect the predicted classes in an array using list comprehension\n",
        "  predlabel = np.array([NN1(traindata, trainlabel, i) for i in testdata])\n",
        "  return predlabel\n",
        "\n",
        "def Accuracy(gtlabel, predlabel):\n",
        "  assert len(gtlabel)==len(predlabel), \"Length of the groundtruth labels and predicted labels should be the same\"\n",
        "  correct = (gtlabel==predlabel).sum() # count the number of times the groundtruth label is equal to the predicted label.\n",
        "  return correct/len(gtlabel)\n",
        "\n",
        "def cumArray(img):\n",
        "  img2 = img.copy()\n",
        "  for ii in range(1, img2.shape[1]):\n",
        "    img2[ii,:] = img2[ii,:] + img2[ii-1,:]  # for every row, add up all the rows above it.\n",
        "  img2 = img2>0\n",
        "  return img2\n",
        "\n",
        "def getHolePixels(img):\n",
        "  im1 = cumArray(img)\n",
        "  im2 = np.rot90(cumArray(np.rot90(img)), 3) # rotate and cumulate it again for differnt direction\n",
        "  im3 = np.rot90(cumArray(np.rot90(img, 2)), 2)\n",
        "  im4 = np.rot90(cumArray(np.rot90(img, 3)), 1)\n",
        "  hull =  im1 & im2 & im3 & im4 # this will create a binary image with all the holes filled in.\n",
        "  hole = hull & ~ (img>0) # remove the original digit to leave behind the holes\n",
        "  return hole\n",
        "\n",
        "def getHullPixels(img):\n",
        "  im1 = cumArray(img)\n",
        "  im2 = np.rot90(cumArray(np.rot90(img)), 3) # rotate and cumulate it again for differnt direction\n",
        "  im3 = np.rot90(cumArray(np.rot90(img, 2)), 2)\n",
        "  im4 = np.rot90(cumArray(np.rot90(img, 3)), 1)\n",
        "  hull =  im1 & im2 & im3 & im4 # this will create a binary image with all the holes filled in.\n",
        "  return hull\n",
        "\n",
        "def minus(a, b):\n",
        "  return a & ~ b\n",
        "\n",
        "def getBoundaryPixels(img):\n",
        "  img = img.copy()>0  # binarize the image\n",
        "  rshift = np.roll(img, 1, 1)\n",
        "  lshift = np.roll(img, -1 ,1)\n",
        "  ushift = np.roll(img, -1, 0)\n",
        "  dshift = np.roll(img, 1, 0)\n",
        "  boundary = minus(img, rshift) | minus(img, lshift) | minus(img, ushift) | minus(img, dshift)\n",
        "  return boundary\n",
        "\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RzF-9mGxUkWC"
      },
      "source": [
        "Get the MNIST dataset:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bHz5BVmLUjzb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "405e1a83-07f2-446f-d010-1171cb7d004a"
      },
      "source": [
        "#loading the dataset\n",
        "(train_X, train_y), (test_X, test_y) = mnist.load_data()\n",
        "train_X = train_X/255\n",
        "test_X = test_X/255\n",
        "\n",
        "nclasses = 4\n",
        "\n",
        "# get only for the first 4 classes\n",
        "train_X = train_X[train_y<nclasses]\n",
        "train_y = train_y[train_y<nclasses]\n",
        "test_X = test_X[test_y<nclasses]\n",
        "test_y = test_y[test_y<nclasses]\n",
        "\n",
        "train_X = train_X[::100].copy() # We are only taking a subset of the training set\n",
        "train_y = train_y[::100].copy() # do the same to the labels\n",
        "test_X = test_X[::100].copy() # taking a subset of the test set. This code takes every 500th sample\n",
        "test_y = test_y[::100].copy()\n",
        "\n",
        "# get all the features\n",
        "train_hole = np.array([getHolePixels(i).sum() for i in train_X])\n",
        "test_hole = np.array([getHolePixels(i).sum() for i in test_X])\n",
        "train_bound = np.array([getBoundaryPixels(i).sum() for i in train_X])\n",
        "test_bound = np.array([getBoundaryPixels(i).sum() for i in test_X])\n",
        "# train_hull = np.array([getHullPixels(i).sum() for i in train_X])\n",
        "# test_hull = np.array([getHullPixels(i).sum() for i in test_X])\n",
        "# train_sum = np.sum(train_X, (1,2))/(28*28)\n",
        "# test_sum = np.sum(test_X, (1,2))/(28*28)\n",
        "\n",
        "# create the train and test set by combining the appropriate features\n",
        "train_feats = np.vstack((train_hole,train_bound)).transpose()\n",
        "test_feats = np.vstack((test_hole, test_bound)).transpose()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n",
            "11493376/11490434 [==============================] - 0s 0us/step\n",
            "11501568/11490434 [==============================] - 0s 0us/step\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I7qGVrlnQCUy"
      },
      "source": [
        "Let us plot the samples and see what they look like:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "saRzHfi9QAGd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "outputId": "1acdf23b-3aae-4935-997f-57cd7fd3a163"
      },
      "source": [
        "# fix limits of x and y axis so that we can see what is going on\n",
        "xlim=[-100,300]\n",
        "ylim=[-100,300]\n",
        "fig, ax = plotData(train_feats, train_y)\n",
        "ax.set_xlim(xlim)\n",
        "ax.set_ylim(ylim)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-100.0, 300.0)"
            ]
          },
          "metadata": {},
          "execution_count": 11
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hCb4DikQP1ck"
      },
      "source": [
        "Check the baseline accuracy on the test set:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rxVr6bd9PzlI",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "97d9bb62-f617-4c62-98a0-797fc875c94e"
      },
      "source": [
        "test_pred = NN(train_feats, train_y, test_feats)\n",
        "acc = Accuracy(test_y, test_pred)\n",
        "print('Baseline accuracy = ', acc)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Baseline accuracy =  0.7619047619047619\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nl8Noo8pZRek"
      },
      "source": [
        "Let us try transforming the features and checking their accuracy:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8dUPWRsEZKwo"
      },
      "source": [
        "transform = np.array([[0.5,-0.5],[0,2.5]])\n",
        "\n",
        "train_feats_t = np.matmul(train_feats, transform)\n",
        "test_feats_t = np.matmul(test_feats, transform)  # whatever transform we are applying to the training set should be applied to the test set also"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iRH4VckHZaWv",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "outputId": "abcf4bb3-7c28-4fe2-e11f-0d489ff9c283"
      },
      "source": [
        "fig, ax = plotData(train_feats_t, train_y)\n",
        "ax.set_xlim(xlim)\n",
        "ax.set_ylim(ylim)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-100.0, 300.0)"
            ]
          },
          "metadata": {},
          "execution_count": 14
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "l9fknczfZdYF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4391c08a-e572-4215-c277-173d535c3a8b"
      },
      "source": [
        "test_pred = NN(train_feats_t, train_y, test_feats_t)\n",
        "acc = Accuracy(test_y, test_pred)\n",
        "print('Accuracy after transform = ', acc)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy after transform =  0.8095238095238095\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OFBQlAnNZ3on"
      },
      "source": [
        "## Questions:\n",
        "1. Experiment with different transformation matrices and check the accuracy\n",
        "2. Will the same transform used for these two features also work for other features?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l2jYBRGO2x5I"
      },
      "source": [
        "**1st answer :**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HHemljPH24Ee",
        "outputId": "52b879a8-a107-4c39-dbdc-f090d9ae29bb"
      },
      "source": [
        "#1\n",
        "transform = np.array([[5,3],[6,7]])\n",
        "train_feats_t = np.matmul(train_feats, transform)\n",
        "test_feats_t = np.matmul(test_feats, transform) \n",
        "test_pred = NN(train_feats_t, train_y, test_feats_t)\n",
        "acc = Accuracy(test_y, test_pred)\n",
        "print('Accuracy after transform = ', acc)\n",
        "\n",
        "#2\n",
        "transform = np.array([[0.4,0.7],[0.3,1.6]])\n",
        "train_feats_t = np.matmul(train_feats, transform)\n",
        "test_feats_t = np.matmul(test_feats, transform) \n",
        "test_pred = NN(train_feats_t, train_y, test_feats_t)\n",
        "acc = Accuracy(test_y, test_pred)\n",
        "print('Accuracy after transform = ', acc)\n",
        "\n",
        "#3\n",
        "transform = np.array([[1,1],[-2,-2]])\n",
        "train_feats_t = np.matmul(train_feats, transform)\n",
        "test_feats_t = np.matmul(test_feats, transform) \n",
        "test_pred = NN(train_feats_t, train_y, test_feats_t)\n",
        "acc = Accuracy(test_y, test_pred)\n",
        "print('Accuracy after transform = ', acc)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy after transform =  0.7142857142857143\n",
            "Accuracy after transform =  0.7857142857142857\n",
            "Accuracy after transform =  0.5476190476190477\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HwXycF613qLm"
      },
      "source": [
        "**2nd answer:** i have tested with sum and hull and yes it works "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZAQSZnws3t4c",
        "outputId": "259f57f0-4b7b-4a3a-b6e9-5c8cd9ff1db4"
      },
      "source": [
        "(train_X, train_y), (test_X, test_y) = mnist.load_data()\n",
        "train_X = train_X/255\n",
        "test_X = test_X/255\n",
        "\n",
        "nclasses = 4\n",
        "\n",
        "train_X = train_X[train_y<nclasses]\n",
        "train_y = train_y[train_y<nclasses]\n",
        "test_X = test_X[test_y<nclasses]\n",
        "test_y = test_y[test_y<nclasses]\n",
        "\n",
        "train_X = train_X[::100].copy() \n",
        "train_y = train_y[::100].copy() \n",
        "test_X = test_X[::100].copy() \n",
        "test_y = test_y[::100].copy()\n",
        "\n",
        "train_hull = np.array([getHullPixels(i).sum() for i in train_X])\n",
        "test_hull = np.array([getHullPixels(i).sum() for i in test_X])\n",
        "train_sum = np.sum(train_X, (1,2))/(28*28)\n",
        "test_sum = np.sum(test_X, (1,2))/(28*28)\n",
        "\n",
        "train_feats = np.vstack((train_hull,train_sum)).transpose()\n",
        "test_feats = np.vstack((test_hull, test_sum)).transpose()\n",
        "\n",
        "test_pred = NN(train_feats, train_y, test_feats)\n",
        "acc = Accuracy(test_y, test_pred)\n",
        "print('Accuracy after transform = ', acc)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy after transform =  0.6666666666666666\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "36TOA47xak20"
      },
      "source": [
        "# Data normalization\n",
        "\n",
        "Sometimes the features of our data have vastly different scales. This will cause the learning algorithm to give more importance to certain features, reducing its performance. Data normalization is a method in which we transform the features so that they have similar scales. \n",
        "\n",
        "Three commonly used feature scaling techniques are rescaling, mean normalization and z-score normalization. Here, we will talk about the simplest one: rescaling. \n",
        "\n",
        "$$\\begin{equation}\n",
        "x' = \\frac {x -min(x)} { max(x) - min(x)}\n",
        "\\end{equation}$$\n",
        "\n",
        "\n",
        "\n",
        "For more information, see [this page](https://towardsdatascience.com/data-normalization-in-machine-learning-395fdec69d02)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ni19QKDLZzeo"
      },
      "source": [
        "def rescale(data):\n",
        "  return (data - data.min())/(data.max() - data.min())"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8k83ZMtKeZrQ"
      },
      "source": [
        "We have to apply the rescaling to each feature individually. Also remember to apply the same transform we are using on the train set to the test set. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1JLOPwhvehpR"
      },
      "source": [
        "train_feats_rescaled_x = rescale(train_feats[:,0])\n",
        "train_feats_rescaled_y = rescale(train_feats[:,1])\n",
        "train_feats_rescaled = np.stack((train_feats_rescaled_x, train_feats_rescaled_y),1)\n",
        "\n",
        "test_feats_rescaled_x = rescale(test_feats[:,0])\n",
        "test_feats_rescaled_y = rescale(test_feats[:,1])\n",
        "test_feats_rescaled = np.stack((test_feats_rescaled_x, test_feats_rescaled_y),1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_h8GD9qJyZEb"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RaZVy9vxfKwX"
      },
      "source": [
        "Let us plot the rescaled features:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LXyatpwZevOH",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "outputId": "8ed81430-a80f-4dc3-8ca9-68a03252bcef"
      },
      "source": [
        "fig, ax = plotData(train_feats_rescaled, train_y)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZjBgxE6zglsL"
      },
      "source": [
        "This type of rescaling makes all the features between 0 and 1. \n",
        "\n",
        "Let us calculate the accuracy obtained by this transform:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hKQnsj-KgNZc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "20ebdf26-f775-4410-baa9-4237b9c46b9a"
      },
      "source": [
        "test_pred = NN(train_feats_rescaled, train_y, test_feats_rescaled)\n",
        "acc = Accuracy(test_y, test_pred)\n",
        "print('Accuracy after transform = ', acc)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy after transform =  0.6428571428571429\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7qYX90Gqg-jO"
      },
      "source": [
        "All 2D linear transformations can be repreented by a transformation matrix. So what is the matrix associated with the rescaling function? Actually, we cannot represent rescaling with a matrix multiplication, because it is not a linear transform. Rescaling involves shifting the origin of the data, which is not allowed under linear transformations.\n",
        "\n",
        "We can represent rescaling as a matrix multiplication followed by a vector addition. Let our first feature vector be called X and second feature vector be called Y. Suppose we want to rescale a data point [a,b]\n",
        "\n",
        "$$ \\begin{equation}\n",
        " \\left\\{  \\begin{aligned}a' \\\\ b' \\end{aligned} \\right\\} = \n",
        " \\left\\{  \\begin{aligned} \\frac{a - min(X)}{max(X) - min(X)} \\\\ \\frac{b - min(Y)}{max(Y) - min(Y)} \\end{aligned} \\right\\} =\n",
        " \\left\\{  \\begin{aligned}&\\frac{1}{max(X)-min(X)} &0\\\\ &0 &\\frac{1}{max(Y)-min(Y)} \\end{aligned} \n",
        " \\right\\}\\left\\{  \\begin{aligned}a \\\\ b \\end{aligned} \\right\\} + \n",
        " \\left\\{  \\begin{aligned} \\frac{ -min(X)}{max(X) - min(X)} \\\\ \\frac{-min(Y)}{max(Y) - min(Y)} \\end{aligned} \\right\\}\n",
        "\\end{equation}$$\n",
        "\n",
        "You can verify this yourself if you wish, though it is not necessary. \n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7KwEVhqs7p2X"
      },
      "source": [
        "def rescale2(x,y,a,b):# x,y are features , a,b are data points\n",
        "  a1=np.array([\n",
        "              [1 / x.max() - x.min() , 0],\n",
        "              [0, 1 / y.max() - y.min()] \n",
        "              ])\n",
        "  a2=np.array([a,b])\n",
        "  r=np.matmul(a1,a2)\n",
        "  a3= np.array([\n",
        "             [-x.min()/(x.max()-x.min())],\n",
        "             [ -y.min()/(y.max()-y.min())]\n",
        "            ])\n",
        "  return (r+a3)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TNZc6QzngNVJ"
      },
      "source": [
        "\n",
        "  #i dont understand what to replace in place of a,b \n",
        "  "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9N7wqVvFyRVX"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}