FMML_Aug22_M1Lab4_LinearAlgebra.ipynb

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  "metadata": {
    "colab": {
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      "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/harika136/IIIT_IHUB_HYD/blob/main/FMML_Aug22_M1Lab4_LinearAlgebra.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: Amit Pandey [amit.pandey@research.iiit.ac.in]\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": 38,
      "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",
        "      #print(start)\n",
        "      end = np.expand_dims(end,0)\n",
        "      #print(end)\n",
        "    #print(\"\\n\",len(start))\n",
        "    #print(\"\\n start is:\", start)\n",
        "    nan = np.ones(len(start))*np.nan\n",
        "    #print(\"\\n\",nan)\n",
        "\n",
        "    x = np.stack((start[:,0], end[:,0], nan)).T.reshape(-1)\n",
        "    #print(\"\\n x is:\",x)\n",
        "    y = np.stack((start[:,1], end[:,1], nan)).T.reshape(-1)\n",
        "    #print(\"\\n y is:\",y)\n",
        "    return x, y\n",
        "\n",
        "  def parallellines(axis, addend, lines, unit):\n",
        "    #print(\"addend:\",addend)\n",
        "    addend = np.repeat(np.expand_dims(addend,0), lines*2, 0) \n",
        "    #print(\"\\nnew addend:\", addend)\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",
        "  #print(\"\\n x axis\", xaxis)\n",
        "  yaxis = transform[1]\n",
        "  #print(\"\\n y axis\", yaxis)\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": 39,
      "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. To be a basis all that is required is linear independence and they must span the space. 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": "3824f88a-b43e-4315-aa1f-a286f30c4f35"
      },
      "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": 40,
      "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": "FV7bAEopoENU",
        "outputId": "33c6de10-925b-4833-f085-b2d3197a14bb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 130
        }
      },
      "source": [
        "## IMPORTANT : IF T IS A NON STANDARD BASIS / COORDINATE SYSTEM, AND P IS VECTOR/COORDINATE OF A POINT IN THIS T SYSTEM, THEN COORDINATE OF P IN STANDARD BASIS\n",
        "## SYSTEM IS : PSTANDARD = T*P [* DENOTES MATRIX MULTIPLICATION]\n",
        "\n",
        "\n",
        "## AND IF Pnonstandard = T^-1 * Pstandard\n",
        "\n",
        "https://towardsdatascience.com/essential-math-for-data-science-basis-and-change-of-basis-f7af2348d463\n",
        "\n",
        "https://math.stackexchange.com/questions/165563/change-to-standard-basis"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "error",
          "ename": "SyntaxError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-41-a59452d3bb20>\"\u001b[0;36m, line \u001b[0;32m7\u001b[0m\n\u001b[0;31m    https://towardsdatascience.com/essential-math-for-data-science-basis-and-change-of-basis-f7af2348d463\u001b[0m\n\u001b[0m           ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "taCUcAMEpBlt"
      },
      "source": [
        "## EACH COLUMN OF T == BASIS MATRIX IS THE iTH AND jTH VECTOR (IMAGINE AS X AND Y AXIS EQUIVALENT OF NON STANDARD SYSTEM)\n",
        "\n",
        "## FOR STANDARD SYSTEM ==> iTH VECTOR == X AXIS == [1 0] AND jTH VECTOR == Y AXIS == [0 1]\n"
      ],
      "execution_count": 42,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 633
        },
        "id": "E0A2Bc36qHg0",
        "outputId": "640d77c6-5ace-4d10-da73-6d3810310fce"
      },
      "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": 43,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:40: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
            "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jSuTaeSDQoYK",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 667
        },
        "outputId": "5b17f83a-5b21-42b1-bf83-efe50ee0fa61"
      },
      "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": 44,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:40: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
            "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:40: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
            "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 667
        },
        "id": "uQ927lleopa5",
        "outputId": "4f121f66-56a9-49e2-e78e-0d75b2db4521"
      },
      "source": [
        "\n",
        "fig, ax = plotGrid(T0.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": 45,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:40: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
            "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:40: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
            "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "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": "cab7f643-1f44-4728-9518-747cb70b6645"
      },
      "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": 47,
      "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": "b6d2861d-45d5-44f0-b967-d6e2129a8dd2"
      },
      "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": 48,
      "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": 49,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RzF-9mGxUkWC"
      },
      "source": [
        "Get the MNIST dataset:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rLioX9fTr6wF"
      },
      "source": [
        "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",
        "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",
        "  #print(img2)\n",
        "  img2 = img2>0\n",
        "  #print(img2)\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",
        "\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"
      ],
      "execution_count": 50,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bHz5BVmLUjzb"
      },
      "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": 51,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I7qGVrlnQCUy"
      },
      "source": [
        "Let us plot the samples and see what they look like:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DnqAj7lprnZs",
        "outputId": "2b4c60e5-ae1d-4c78-fe51-96946255229e"
      },
      "source": [
        "train_feats.shape #248 samples and 2 is the number of features == holes and bound"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(248, 2)"
            ]
          },
          "metadata": {},
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6RPqsTMFDNG8",
        "outputId": "55faea3c-8590-48e3-e78c-0636252747b0"
      },
      "source": [
        "train_feats"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
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              "       [  0,  45]])"
            ]
          },
          "metadata": {},
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "19ZAP2jvDZ19",
        "outputId": "ea09e880-3347-4a0e-f274-f78949282275"
      },
      "source": [
        "train_y"
      ],
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 0, 0, 2, 2, 1, 2, 0, 2, 3, 1, 3, 0, 0, 3, 3, 0, 0, 3, 2, 2, 1,\n",
              "       3, 0, 1, 3, 2, 3, 2, 1, 3, 1, 2, 0, 1, 2, 0, 3, 2, 0, 3, 0, 2, 2,\n",
              "       2, 0, 0, 0, 3, 0, 3, 3, 0, 1, 0, 3, 3, 2, 1, 3, 0, 3, 3, 0, 2, 2,\n",
              "       3, 3, 2, 1, 1, 0, 2, 1, 1, 2, 3, 0, 2, 0, 1, 0, 1, 3, 1, 2, 3, 3,\n",
              "       1, 2, 1, 2, 1, 3, 0, 2, 1, 3, 0, 1, 3, 2, 1, 2, 1, 1, 2, 0, 1, 1,\n",
              "       0, 0, 3, 0, 2, 2, 0, 1, 3, 2, 1, 0, 0, 2, 1, 2, 0, 2, 2, 2, 2, 1,\n",
              "       3, 3, 0, 1, 0, 2, 1, 2, 3, 2, 3, 1, 0, 1, 1, 1, 0, 3, 0, 2, 2, 2,\n",
              "       1, 2, 1, 0, 1, 3, 3, 1, 0, 0, 3, 2, 3, 3, 1, 2, 1, 2, 3, 1, 2, 2,\n",
              "       3, 2, 0, 3, 3, 2, 0, 2, 3, 1, 2, 2, 1, 2, 2, 3, 1, 1, 0, 3, 1, 1,\n",
              "       2, 0, 1, 3, 0, 3, 0, 2, 2, 0, 2, 2, 0, 3, 0, 0, 0, 3, 3, 2, 2, 2,\n",
              "       2, 3, 1, 2, 2, 0, 0, 2, 2, 1, 0, 3, 3, 0, 1, 1, 1, 0, 0, 0, 3, 1,\n",
              "       2, 0, 3, 3, 3, 1], dtype=uint8)"
            ]
          },
          "metadata": {},
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "saRzHfi9QAGd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "outputId": "ceb78878-697b-4464-b6c6-317a65a6a11e"
      },
      "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": 55,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-100.0, 300.0)"
            ]
          },
          "metadata": {},
          "execution_count": 55
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qf6ZCx7ctB_k"
      },
      "source": [
        "## Elongated in the x direction, as range of values features can take is different, we generally dont like this in ml models."
      ],
      "execution_count": 56,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hCb4DikQP1ck"
      },
      "source": [
        "Check the baseline accuracy on the test set:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bEs6cXR_tbRg"
      },
      "source": [
        "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)"
      ],
      "execution_count": 57,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rxVr6bd9PzlI",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ddb24d61-e93c-4d4e-8728-539831c301d9"
      },
      "source": [
        "test_pred = NN(train_feats, train_y, test_feats)\n",
        "acc = Accuracy(test_y, test_pred)\n",
        "print('Baseline accuracy = ', acc)"
      ],
      "execution_count": 58,
      "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": 59,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HgV9_M8dFO0z"
      },
      "source": [],
      "execution_count": 59,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iRH4VckHZaWv",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "outputId": "c77c4e22-baf6-4f83-eb95-9e774f0a0112"
      },
      "source": [
        "fig, ax = plotData(train_feats_t, train_y)\n",
        "ax.set_xlim(xlim)\n",
        "ax.set_ylim(ylim)"
      ],
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-100.0, 300.0)"
            ]
          },
          "metadata": {},
          "execution_count": 60
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "id": "6j76AQrYFPm9",
        "outputId": "095e16f1-9efa-4704-b640-f2f13f4d6e6b"
      },
      "source": [
        "transform = np.array([[0.5,-0.5],[0,4.5]])\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\n",
        "\n",
        "fig, ax = plotData(train_feats_t, train_y)\n",
        "ax.set_xlim(xlim)\n",
        "ax.set_ylim(ylim)"
      ],
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-100.0, 300.0)"
            ]
          },
          "metadata": {},
          "execution_count": 61
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0DD4K9KitqSG"
      },
      "source": [
        "## observe how the plot has changed. Since the values of the transformation matrix were chosen in such a way that it brings about this elongation in y direction - ie along bound.\n",
        "## you can play with these values"
      ],
      "execution_count": 62,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "l9fknczfZdYF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2b11448c-056a-4bff-dd7d-d84779b6125b"
      },
      "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": 63,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy after transform =  0.7857142857142857\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",
      "source": [
        "### **ANSWER FOR QUESTION 1**"
      ],
      "metadata": {
        "id": "gDtcHfyKZ8L7"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "GETTING THE DATA SET"
      ],
      "metadata": {
        "id": "qudMThQmaJe9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from keras.datasets import mnist\n",
        "#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()"
      ],
      "metadata": {
        "id": "7wlMr4TOaTMS"
      },
      "execution_count": 64,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "FUNCTION TO TRANSFORM THE DATA\n",
        "\n"
      ],
      "metadata": {
        "id": "lm2DjS1TadGh"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def tranformDataSet(transform, train_feats, test_feats):\n",
        "  train_feats_t = np.matmul(train_feats, transform)\n",
        "  test_feats_t = np.matmul(test_feats, transform)\n",
        "  return train_feats_t, test_feats_t"
      ],
      "metadata": {
        "id": "tZXhBI9panjG"
      },
      "execution_count": 65,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "FUNCTION TO CHECK THE ACCURACY"
      ],
      "metadata": {
        "id": "yYSeA1J_azGJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def checkAccuracy(train_fests_t, test_feats_t, train_y, test_y):\n",
        "  test_pred = NN(train_feats_t, train_y, test_feats_t)\n",
        "  acc = Accuracy(test_y, test_pred)\n",
        "  return acc"
      ],
      "metadata": {
        "id": "he0O87j2a7q5"
      },
      "execution_count": 66,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "FUNCTION TO MAKE APPLY THE TRANSFORMATION AS WELL AS GETTING THE ACCURACY"
      ],
      "metadata": {
        "id": "nNOQkmRUbD8A"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def getAccuracy(train_X, train_y, test_X, test_y, featurelist, transformlist):\n",
        "  listtest = []\n",
        "  listtrain = []\n",
        "  accuracyList = []\n",
        "  # for i in range(-5,6):\n",
        "  #   transformlist.append(np.array([[i, i+1], [i-1, i]]))\n",
        "  for feature in featurelist:\n",
        "    if feature == \"boundary\":\n",
        "      listtrain.append(np.array([getBoundaryPixels(i).sum() for i in train_X]))\n",
        "      listtest.append(np.array([getBoundaryPixels(i).sum() for i in test_X]))\n",
        "    if feature == \"hole\":\n",
        "      listtrain.append(np.array([getHolePixels(i).sum() for i in train_X]))\n",
        "      listtest.append(np.array([getHolePixels(i).sum() for i in test_X]))\n",
        "    if feature == \"hull\":\n",
        "      listtrain.append(np.array([getHullPixels(i).sum() for i in train_X]))\n",
        "      listtest.append(np.array([getHullPixels(i).sum() for i in test_X]))\n",
        "    if feature == \"sum\":\n",
        "      listtrain.append(np.sum(train_X, (1,2))/(28*28))\n",
        "      listtest.append(np.sum(test_X, (1,2))/(28*28))\n",
        "  train_feats = np.vstack(tuple(j for j in listtrain)).transpose()\n",
        "  test_feats = np.vstack(tuple(j for j in listtest)).transpose()\n",
        "  # train_fests_t, test_feats_t = tranformDataSet(np.array([[0.5,-0.5],[0,2.5]]), train_feats, test_feats)\n",
        "  # accuracyList.append(checkAccuracy(train_fests_t, test_feats_t, train_y, test_y))\n",
        "  for i in transformlist:\n",
        "    train_fests_t, test_feats_t = tranformDataSet(i, train_feats, test_feats)\n",
        "    accuracyList.append(checkAccuracy(train_fests_t, test_feats_t, train_y, test_y))\n",
        "  return accuracyList"
      ],
      "metadata": {
        "id": "HEJqb2pSbLvT"
      },
      "execution_count": 67,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "NOW LET US CHECK FOR ACCURACIES OBTAINED FOR DIFFERENT VALUES OF TRANSFORMATION MATRICES"
      ],
      "metadata": {
        "id": "MNHCITCLbgMy"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "featurelist = ['hole','boundary']\n",
        "transformlist = [np.array([[0.25,-0.25],[0,4.5]]), \n",
        "                 np.array([[0.85,-0.25], [0, 4.0]]),\n",
        "                 np.array([[1,-0.25], [0, 4.0]]),\n",
        "                 np.array([[0.25,-0.25], [0, 4.0]]),\n",
        "                 np.array([[0.25,-0.85], [0, 4.5]]),\n",
        "                 np.array([[0.25,-0.25], [0, 3.0]]),\n",
        "                 np.array([[0.25,-0.25],[0,-4.5]]),\n",
        "                 np.array([[-0.25,-0.25],[0,-4.5]]),\n",
        "                 ]\n",
        "accuracyList = getAccuracy(train_X, train_y, test_X, test_y, featurelist, transformlist)\n",
        "for i in range(len(transformlist)):\n",
        "  print(f\"matrics = {transformlist[i]} accuracy = {accuracyList[i]}\")"
      ],
      "metadata": {
        "id": "fTurqDUsbnim",
        "outputId": "713eea6b-2b75-4ba6-881d-424d125f44d3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "matrics = [[ 0.25 -0.25]\n",
            " [ 0.    4.5 ]] accuracy = 0.5952380952380952\n",
            "matrics = [[ 0.85 -0.25]\n",
            " [ 0.    4.  ]] accuracy = 0.6190476190476191\n",
            "matrics = [[ 1.   -0.25]\n",
            " [ 0.    4.  ]] accuracy = 0.5714285714285714\n",
            "matrics = [[ 0.25 -0.25]\n",
            " [ 0.    4.  ]] accuracy = 0.5952380952380952\n",
            "matrics = [[ 0.25 -0.85]\n",
            " [ 0.    4.5 ]] accuracy = 0.7142857142857143\n",
            "matrics = [[ 0.25 -0.25]\n",
            " [ 0.    3.  ]] accuracy = 0.35714285714285715\n",
            "matrics = [[ 0.25 -0.25]\n",
            " [ 0.   -4.5 ]] accuracy = 0.2857142857142857\n",
            "matrics = [[-0.25 -0.25]\n",
            " [ 0.   -4.5 ]] accuracy = 0.2857142857142857\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **ANSWER FOR QUESTION 2**"
      ],
      "metadata": {
        "id": "zDRHWOgubveK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "featurelist = [\"hull\",'sum']\n",
        "transformlist = [np.array([[0.25,-0.25],[0,2.5]]), \n",
        "                 np.array([[0.85,-0.25], [0, 2.0]]),\n",
        "                 np.array([[1,-0.25], [0, 2.0]]),\n",
        "                 np.array([[0.25,-0.25], [0, 2.0]]),\n",
        "                 np.array([[0.25,-0.85], [0, 2.5]]),\n",
        "                 np.array([[0.25,-0.25], [0, 3.0]]),\n",
        "                 np.array([[0.25,-0.25],[0,-2.5]]),\n",
        "                 np.array([[30,20],[0,-20.5]]),\n",
        "                 ]\n",
        "accuracyList = getAccuracy(train_X, train_y, test_X, test_y, featurelist, transformlist)\n",
        "for i in range(len(transformlist)):\n",
        "  print(f\"matrics = {transformlist[i]} accuracy = {accuracyList[i]}\")"
      ],
      "metadata": {
        "id": "mSFCQrHCb4pl",
        "outputId": "fdea2c2e-bb00-472b-a9ee-d622e4e3d85e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "matrics = [[ 0.25 -0.25]\n",
            " [ 0.    2.5 ]] accuracy = 0.2857142857142857\n",
            "matrics = [[ 0.85 -0.25]\n",
            " [ 0.    2.  ]] accuracy = 0.2857142857142857\n",
            "matrics = [[ 1.   -0.25]\n",
            " [ 0.    2.  ]] accuracy = 0.2857142857142857\n",
            "matrics = [[ 0.25 -0.25]\n",
            " [ 0.    2.  ]] accuracy = 0.2857142857142857\n",
            "matrics = [[ 0.25 -0.85]\n",
            " [ 0.    2.5 ]] accuracy = 0.2857142857142857\n",
            "matrics = [[ 0.25 -0.25]\n",
            " [ 0.    3.  ]] accuracy = 0.2857142857142857\n",
            "matrics = [[ 0.25 -0.25]\n",
            " [ 0.   -2.5 ]] accuracy = 0.2857142857142857\n",
            "matrics = [[ 30.   20. ]\n",
            " [  0.  -20.5]] accuracy = 0.23809523809523808\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": 70,
      "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": 71,
      "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": "33b4401b-5f20-40d2-bee0-ecc0dd2bfddf"
      },
      "source": [
        "fig, ax = plotData(train_feats_rescaled, train_y)\n"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "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": "cfb08bf7-aa66-4634-8dbf-a205bd9a157a"
      },
      "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": 73,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy after transform =  0.8095238095238095\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": "97ZaxoTZgTwR"
      },
      "source": [],
      "execution_count": 73,
      "outputs": []
    }
  ]
}