FMML_M1L4.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Gani69/Fmml/blob/main/FMML_M1L4.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\n",
        "\n",
        "Matrix transformations are at the heart of many machine learning algorithms. In this lab, we'll visualize the effect of some simple transformations on a unit square and then visualize it using the MNIST dataset. We also see what data normalization means and how it can help in improving the accuracy of machine learning models."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "KBe4ZA32UTbv"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from keras.datasets import mnist"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "cellView": "form",
        "id": "7mqG-dafVpya"
      },
      "outputs": [],
      "source": [
        "# You don't need to understand these functions\n",
        "\n",
        "\n",
        "def plotGrid(transform, unit, linestyle=\":\", fig=None, ax=None):\n",
        "    lim1 = -100\n",
        "    lim2 = 100\n",
        "\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=(5, 5))\n",
        "    transform = transform.astype(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",
        "\n",
        "def plotData(X, y, xlabel=\"hole\", ylabel=\"bound\", fig=None, ax=None):\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",
        "    return fig, ax"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9d5dmEXxaktp"
      },
      "source": [
        "## Matrix transformations on data\n",
        "\n",
        "Note: This lab involves a lot of matrix operations. If you are not familiar with them, please go through the resources given in class before proceeding. You can also review Khan Academy's excellent linear algebra [resources](https://www.khanacademy.org/math/linear-algebra/matrix-transformations).\n",
        "\n",
        "A 2D coordinate system is defined by its basis vectors, i and j. Any point in this 2D space can be represented as a linear combination of these basis vectors. For example, the point (a,b) can be represented as:\n",
        "\n",
        "$$\\begin{equation}\n",
        "\\left\\{  \\begin{aligned}a \\\\ b \\end{aligned} \\right\\} = a\\left\\{  \\begin{aligned}1 \\\\ 0 \\end{aligned} \\right\\} + b\\left\\{  \\begin{aligned}0 \\\\ 1 \\end{aligned} \\right\\} = a\\hat{i} + b\\hat{j}\n",
        "\\end{equation}$$\n",
        "\n",
        "A matrix can be used to perform a linear transformation on the basis vectors. The new basis vectors $\\hat{i}$ and $\\hat{j}$ are given by the product of the matrix and the basis vectors of the standard coordinate system.\n",
        "\n",
        "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",
        "\n",
        "Let us see this in action:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "K8SCFKqfbM-l",
        "outputId": "024b35ba-8b94-4598-ee88-401793680fdb"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Data in T0 =  [5 3]\n",
            "Data in T1 =  [5 4]\n"
          ]
        }
      ],
      "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)"
      ]
    },
    {
      "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",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 320
        },
        "id": "jSuTaeSDQoYK",
        "outputId": "acf9a26a-f62a-4ca1-87b9-49556e3e5591"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "fig, ax = plotGrid(T1.T, 1, \"-\")\n",
        "plotGrid(T0.T, 1, fig=fig, ax=ax)\n",
        "\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",
        "plt.show()"
      ]
    },
    {
      "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",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SD4pqOMndf-4",
        "outputId": "d2817a0a-ce88-40ba-8874-4bfd61abf07a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[5 3]\n",
            "[5 3]\n"
          ]
        }
      ],
      "source": [
        "data0_a = np.matmul(T1, data1)\n",
        "data0_b = np.matmul(data1, T1.T)\n",
        "print(data0_a)\n",
        "print(data0_b)"
      ]
    },
    {
      "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",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nE0NbpYIC9ou",
        "outputId": "97ed55a0-b84b-4494-9dd5-43820ec152a7"
      },
      "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"
          ]
        }
      ],
      "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",
        "\n",
        "def dist(a, b):\n",
        "    # function to calculate Euclidean distance between two points\n",
        "    diff = a - b\n",
        "    sq = diff * diff\n",
        "    return np.sqrt(sq.sum())\n",
        "\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))"
      ]
    },
    {
      "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. We will then transform the data using a transformation matrix and visualize the data in the new coordinate system. We will also see how normalization can help in improving the accuracy of the model. We will reuse previous labs code for this."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "cellView": "form",
        "id": "22ayl0sViF5-"
      },
      "outputs": [],
      "source": [
        "def NN1(traindata, trainlabel, query):\n",
        "    \"\"\"\n",
        "    This function takes in the training data, training labels and a query point\n",
        "    and returns the predicted label for the query point using the nearest neighbour algorithm\n",
        "\n",
        "    traindata: numpy array of shape (n,d) where n is the number of samples and d is the number of features\n",
        "    trainlabel: numpy array of shape (n,) where n is the number of samples\n",
        "    query: numpy array of shape (d,) where d is the number of features\n",
        "\n",
        "    returns: the predicted label for the query point which is the label of the training data which is closest to the query point\n",
        "    \"\"\"\n",
        "    diff = (\n",
        "        traindata - query\n",
        "    )  # 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)]\n",
        "    return label\n",
        "\n",
        "\n",
        "def NN(traindata, trainlabel, testdata):\n",
        "    \"\"\"\n",
        "    This function takes in the training data, training labels and test data\n",
        "    and returns the predicted labels for the test data using the nearest neighbour algorithm\n",
        "\n",
        "    traindata: numpy array of shape (n,d) where n is the number of samples and d is the number of features\n",
        "    trainlabel: numpy array of shape (n,) where n is the number of samples\n",
        "    testdata: numpy array of shape (m,d) where m is the number of test samples and d is the number of features\n",
        "\n",
        "    returns: the predicted labels for the test data which is the label of the training data which is closest to each test point\n",
        "    \"\"\"\n",
        "    predlabel = np.array([NN1(traindata, trainlabel, i) for i in testdata])\n",
        "    return predlabel\n",
        "\n",
        "\n",
        "def Accuracy(gtlabel, predlabel):\n",
        "    \"\"\"\n",
        "    This function takes in the ground-truth labels and predicted labels\n",
        "    and returns the accuracy of the classifier\n",
        "\n",
        "    gtlabel: numpy array of shape (n,) where n is the number of samples\n",
        "    predlabel: numpy array of shape (n,) where n is the number of samples\n",
        "\n",
        "    returns: the accuracy of the classifier which is the number of correct predictions divided by the total number of predictions\n",
        "    \"\"\"\n",
        "    assert len(gtlabel) == len(\n",
        "        predlabel\n",
        "    ), \"Length of the ground-truth labels and predicted labels should be the same\"\n",
        "    correct = (\n",
        "        gtlabel == predlabel\n",
        "    ).sum()  # count the number of times the groundtruth label is equal to the predicted label.\n",
        "    return correct / len(gtlabel)\n",
        "\n",
        "\n",
        "def cumArray(img):\n",
        "    img2 = img.copy()\n",
        "    for ii in range(1, img2.shape[1]):\n",
        "        # for every row, add up all the rows above it.\n",
        "        img2[ii, :] = img2[ii, :] + img2[ii - 1, :]\n",
        "    img2 = img2 > 0\n",
        "    return img2\n",
        "\n",
        "\n",
        "def getHolePixels(img):\n",
        "    \"\"\"\n",
        "    This function takes in a binary image and returns the pixels that are holes in the image\n",
        "\n",
        "    img: numpy array of shape (n,m) where n is the height of the image and m is the width of the image\n",
        "\n",
        "    returns: a binary image of the same shape as the input image where the holes are filled in\n",
        "    \"\"\"\n",
        "    im1 = cumArray(img)\n",
        "    # rotate and cumulate it again for differnt direction\n",
        "    im2 = np.rot90(cumArray(np.rot90(img)), 3)\n",
        "    im3 = np.rot90(cumArray(np.rot90(img, 2)), 2)\n",
        "    im4 = np.rot90(cumArray(np.rot90(img, 3)), 1)\n",
        "    # this will create a binary image with all the holes filled in.\n",
        "    hull = im1 & im2 & im3 & im4\n",
        "    # remove the original digit to leave behind the holes\n",
        "    hole = hull & ~(img > 0)\n",
        "    return hole\n",
        "\n",
        "\n",
        "def getHullPixels(img):\n",
        "    \"\"\"\n",
        "    This function takes in a binary image and returns the pixels that are the convex hull of the image\n",
        "\n",
        "    img: numpy array of shape (n,m) where n is the height of the image and m is the width of the image\n",
        "\n",
        "    returns: a binary image of the same shape as the input image where the convex hull is filled in\n",
        "    \"\"\"\n",
        "    im1 = cumArray(img)\n",
        "    # rotate and cumulate it again for differnt direction\n",
        "    im2 = np.rot90(cumArray(np.rot90(img)), 3)\n",
        "    im3 = np.rot90(cumArray(np.rot90(img, 2)), 2)\n",
        "    im4 = np.rot90(cumArray(np.rot90(img, 3)), 1)\n",
        "    # this will create a binary image with all the holes filled in.\n",
        "    hull = im1 & im2 & im3 & im4\n",
        "    return hull\n",
        "\n",
        "\n",
        "def minus(a, b):\n",
        "    \"\"\"\n",
        "    This function takes in two binary images and returns the difference between the two images\n",
        "    \"\"\"\n",
        "    return a & ~b\n",
        "\n",
        "\n",
        "def getBoundaryPixels(img):\n",
        "    \"\"\"\n",
        "    This function takes in a binary image and returns the pixels that are the boundary of the image\n",
        "\n",
        "    img: numpy array of shape (n,m) where n is the height of the image and m is the width of the image\n",
        "\n",
        "    returns: a binary image of the same shape as the input image where the boundary is filled in\n",
        "    \"\"\"\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 = (\n",
        "        minus(img, rshift)\n",
        "        | minus(img, lshift)\n",
        "        | minus(img, ushift)\n",
        "        | minus(img, dshift)\n",
        "    )\n",
        "    return boundary"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bHz5BVmLUjzb",
        "outputId": "a183885d-1bd9-4cb9-c80c-c5c381d009ca"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n",
            "11490434/11490434 [==============================] - 0s 0us/step\n"
          ]
        }
      ],
      "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",
        "# We are only taking a subset of the training set\n",
        "train_X = train_X[::100].copy()\n",
        "train_y = train_y[::100].copy()  # do the same to the labels\n",
        "\n",
        "# taking a subset of the test set. This code takes every 500th sample\n",
        "test_X = test_X[::100].copy()\n",
        "test_y = test_y[::100].copy()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "uvavjmfvH515"
      },
      "outputs": [],
      "source": [
        "# feature extraction\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(\n",
        "    (train_hole, train_bound)).transpose()\n",
        "test_feats = np.vstack(\n",
        "    (test_hole, test_bound)).transpose()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I7qGVrlnQCUy"
      },
      "source": [
        "Let us plot the samples and see what they look like:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 240
        },
        "id": "saRzHfi9QAGd",
        "outputId": "cbc947fb-f768-41c5-e03a-3ff4fc956c24"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "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)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hCb4DikQP1ck"
      },
      "source": [
        "Check the baseline accuracy on the test set:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rxVr6bd9PzlI",
        "outputId": "0c4f6d8d-4adb-4516-9231-e49cb578d4e0"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Baseline accuracy: 76.19047619047619 % for 4 classes\n"
          ]
        }
      ],
      "source": [
        "test_pred = NN(train_feats, train_y, test_feats)\n",
        "acc = Accuracy(test_y, test_pred)\n",
        "print(\"Baseline accuracy:\", acc*100, \"%\", \"for\", nclasses, \"classes\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nl8Noo8pZRek"
      },
      "source": [
        "Let us try transforming the features and checking their accuracy. The intuition to using the transformation matrix is to find the basis vectors of the dataset and transform the data to a new coordinate system where the basis vectors are orthogonal. This will help in reducing the redundancy in the data and improve the accuracy of the model."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "8dUPWRsEZKwo",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a8fe22b4-5d0c-40cc-bd2c-9f01b4eae4ed"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ 0.5 -0.5]\n",
            " [ 0.   2.5]]\n"
          ]
        }
      ],
      "source": [
        "transform = np.array([[0.5, -0.5], [0, 2.5]])\n",
        "print(transform)\n",
        "\n",
        "train_feats_t = np.matmul(train_feats, transform)\n",
        "# whatever transform we are applying to the training set should be applied to the test set also\n",
        "test_feats_t = np.matmul(test_feats, transform)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 240
        },
        "id": "iRH4VckHZaWv",
        "outputId": "a37a6dc7-b85a-49c3-dbd1-3d6f7b0b2b96"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "fig, ax = plotData(train_feats_t, train_y)\n",
        "ax.set_xlim(xlim)\n",
        "ax.set_ylim(ylim)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "l9fknczfZdYF",
        "outputId": "5b477c0a-2f3f-43fd-bdec-b4b39fe2b527"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Baseline accuracy: 80.95238095238095 % for 4 classes\n"
          ]
        }
      ],
      "source": [
        "test_pred = NN(train_feats_t, train_y, test_feats_t)\n",
        "acc = Accuracy(test_y, test_pred)\n",
        "print(\"Baseline accuracy:\", acc*100, \"%\", \"for\", nclasses, \"classes\")"
      ]
    },
    {
      "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": "wXCnbDsVH516"
      },
      "source": [
        "> Exercise: Is it possible that adding all 4 features at a time is not the best strategy? Can you think of a better combination of features that can help in improving the accuracy of the model? Maybe you can try adding 2 features at a time and see if that helps."
      ]
    },
    {
      "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",
      "execution_count": 16,
      "metadata": {
        "id": "ni19QKDLZzeo"
      },
      "outputs": [],
      "source": [
        "def rescale(data):\n",
        "    return (data - data.min()) / (data.max() - data.min())"
      ]
    },
    {
      "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",
      "execution_count": 18,
      "metadata": {
        "id": "1JLOPwhvehpR"
      },
      "outputs": [],
      "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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RaZVy9vxfKwX"
      },
      "source": [
        "Let us plot the rescaled features:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 249
        },
        "id": "LXyatpwZevOH",
        "outputId": "87360810-168a-4344-d8a2-99020e393d42"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "fig, ax = plotData(train_feats_rescaled, train_y)"
      ]
    },
    {
      "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",
      "execution_count": 20,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hKQnsj-KgNZc",
        "outputId": "90af60ee-3215-4ed4-9701-7098081bbd00"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy after transform: 80.95238095238095 %\n"
          ]
        }
      ],
      "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*100, \"%\")"
      ]
    },
    {
      "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"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
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