PR_6360_6521_6609_bonus.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4--1lKbohsjh"
      },
      "outputs": [],
      "source": [
        "import os\n",
        "import cv2\n",
        "from google.colab.patches import cv2_imshow\n",
        "import numpy as np\n",
        "from numpy import linalg as LA\n",
        "from sklearn.neighbors import KNeighborsClassifier\n",
        "from sklearn import metrics\n",
        "from sklearn.metrics import classification_report, confusion_matrix\n",
        "import matplotlib.pyplot as plt\n",
        "from random import sample\n",
        "import random\n",
        "from sklearn.model_selection import train_test_split\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c1eSdO_NCdZS"
      },
      "source": [
        "## 1. Download the Dataset and Understand the Format"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 74,
          "resources": {
            "http://localhost:8080/nbextensions/google.colab/files.js": {
              "data": 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              "headers": [
                [
                  "content-type",
                  "application/javascript"
                ]
              ],
              "ok": true,
              "status": 200,
              "status_text": ""
            }
          }
        },
        "id": "yac6NfsqgWiZ",
        "outputId": "ee29ec0d-c058-498d-84cc-62f31c358748"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "     <input type=\"file\" id=\"files-fe4621f8-8341-4f8b-8ef9-ad7bbddf47ff\" name=\"files[]\" multiple disabled\n",
              "        style=\"border:none\" />\n",
              "     <output id=\"result-fe4621f8-8341-4f8b-8ef9-ad7bbddf47ff\">\n",
              "      Upload widget is only available when the cell has been executed in the\n",
              "      current browser session. Please rerun this cell to enable.\n",
              "      </output>\n",
              "      <script src=\"/nbextensions/google.colab/files.js\"></script> "
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Saving archive.zip to archive.zip\n"
          ]
        }
      ],
      "source": [
        "from google.colab import files\n",
        "uploaded = files.upload()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "UmdC_bmwgmhp",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f7976c4c-f01a-4ec1-ed1f-59b1ee5251da"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Archive:  archive.zip\n",
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          ]
        }
      ],
      "source": [
        "!unzip archive.zip -d images/\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ExdcGm4ag2Ba",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "012df145-c0fc-4026-9aa5-7629a630905d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "10.pgm\t1.pgm  2.pgm  3.pgm  4.pgm  5.pgm  6.pgm  7.pgm  8.pgm\t9.pgm\n"
          ]
        }
      ],
      "source": [
        "!ls images/s1\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HxZwIPTCE4YE"
      },
      "source": [
        "##2. Generate the Data Matrix and the Label vector"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "APljhegDiH4k",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f1581102-a877-4606-b280-7fb0bb0597c1"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(400, 10304)"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "directory = 'images/'\n",
        "image_vectors = []\n",
        "\n",
        "for folder in os.listdir(directory):\n",
        "  path = os.path.join(directory, folder)\n",
        "  if os.path.isdir(path):\n",
        "    sub_directory = path\n",
        "    for image in os.listdir(sub_directory):\n",
        "            f = os.path.join(sub_directory, image)\n",
        "            # The function imread loads an image from the specified file and returns it\n",
        "            img = cv2.imread(f, cv2.IMREAD_GRAYSCALE)\n",
        "            vector = np.array(img)\n",
        "            result = vector.flatten()\n",
        "            image_vectors.append(result)\n",
        "image_vectors = np.array(image_vectors)\n",
        "image_vectors.shape       "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5pNI-3skPmUx",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 129
        },
        "outputId": "d818090f-5100-4614-f32c-af9bdb244a62"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<PIL.Image.Image image mode=L size=92x112 at 0x7F3A41FA0BD0>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "cv2_imshow(img)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bHuvrB4WvLjf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e521bec5-6dbf-4673-bce9-6d92993027ed"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  2,  2,  2,  2,  2,  2,  2,\n",
              "        2,  2,  2,  3,  3,  3,  3,  3,  3,  3,  3,  3,  3,  4,  4,  4,  4,\n",
              "        4,  4,  4,  4,  4,  4,  5,  5,  5,  5,  5,  5,  5,  5,  5,  5,  6,\n",
              "        6,  6,  6,  6,  6,  6,  6,  6,  6,  7,  7,  7,  7,  7,  7,  7,  7,\n",
              "        7,  7,  8,  8,  8,  8,  8,  8,  8,  8,  8,  8,  9,  9,  9,  9,  9,\n",
              "        9,  9,  9,  9,  9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11,\n",
              "       11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12,\n",
              "       12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14,\n",
              "       14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16,\n",
              "       16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17,\n",
              "       18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19,\n",
              "       19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21,\n",
              "       21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 23,\n",
              "       23, 23, 23, 23, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 24, 24,\n",
              "       24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26,\n",
              "       26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 28, 28,\n",
              "       28, 28, 28, 28, 28, 28, 28, 28, 29, 29, 29, 29, 29, 29, 29, 29, 29,\n",
              "       29, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 31, 31, 31, 31, 31,\n",
              "       31, 31, 31, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 33, 33, 33,\n",
              "       33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34,\n",
              "       35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 36, 36, 36, 36, 36, 36, 36,\n",
              "       36, 36, 36, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 38, 38, 38, 38,\n",
              "       38, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 40,\n",
              "       40, 40, 40, 40, 40, 40, 40, 40, 40])"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "labels = []\n",
        "\n",
        "for i in range (1,41):\n",
        "    for j in range (0,10):\n",
        "        labels.append(i)\n",
        "\n",
        "labels = np.array(labels)\n",
        "labels    "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WA4CGZJNQO9E"
      },
      "source": [
        "## 3. Split the Dataset into Training and Test sets"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We used a random number generator with a set seed so we can always have the same split."
      ],
      "metadata": {
        "id": "QL0iCg2tWUH1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def split_train_test(train_percentage, data, labels):\n",
        "  test_percentage = 100-train_percentage\n",
        "  number_of_data = data.shape[0]  \n",
        "  random.seed(2)\n",
        "\n",
        "  train_split_size = (number_of_data * train_percentage) // 100 \n",
        "  test_split_size = number_of_data - train_split_size\n",
        "\n",
        "\n",
        "  list1 = range(number_of_data)\n",
        "  list11 = np.arange(number_of_data)\n",
        "\n",
        "  train_indices = random.sample(list1, train_split_size)\n",
        "  test_indices = np.delete(list11, train_indices)\n",
        "\n",
        "\n",
        "  train_data = np.zeros( (train_split_size, data.shape[1]) )\n",
        "  test_data = np.zeros( (test_split_size, data.shape[1] ) ) \n",
        "  train_labels = np.zeros( (train_split_size, ) )\n",
        "  test_labels = np.zeros( (test_split_size, ) )\n",
        "\n",
        "  for index1, index2 in enumerate(train_indices) :\n",
        "    train_data[index1] = data[index2]\n",
        "    train_labels[index1] = int(labels[index2])\n",
        "                \n",
        "  for index1, index2 in enumerate(test_indices):\n",
        "    test_data[index1] = data[index2]\n",
        "    test_labels[index1] = int(labels[index2])\n",
        "\n",
        "\n",
        "  return train_data, test_data, train_labels, test_labels \n",
        "\n",
        "\n",
        "  \n",
        "\n",
        "\n",
        "    \n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "A9Y0iLb8VZDH"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "train_data, test_data, train_labels, test_labels = split_train_test(70, image_vectors,labels)\n",
        "print(train_labels)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qyFyggtejoWs",
        "outputId": "29f86f00-ce05-4865-b51f-0ecf1b1b2075"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 3.  5.  5. 19.  9. 38. 35. 16. 13. 32. 11. 40.  2. 30. 35.  9. 23. 33.\n",
            " 21. 38. 27. 20. 28. 23. 26. 14. 39.  2. 19. 24. 17. 20. 22. 27.  9. 29.\n",
            " 10. 13. 12.  2. 37. 17.  9.  7. 27. 36. 40. 27. 35. 37. 10. 23. 22. 27.\n",
            " 38. 31. 19. 19. 39.  9. 21. 24. 34. 28. 13. 26. 15. 26. 26. 36. 35. 24.\n",
            " 34. 18. 30. 29. 24. 25. 12. 36.  9. 32. 38. 25. 16. 16. 26. 29. 27. 26.\n",
            " 31. 21. 16. 11. 34. 27. 19.  4. 18.  1. 10.  6.  4. 30.  3. 14. 12. 30.\n",
            " 27. 36. 14. 13. 11. 39. 37.  2.  3. 40. 36. 36. 34. 37.  5.  6.  4. 38.\n",
            "  3.  2. 20. 14.  7.  9. 10.  1. 20.  3. 13.  8. 38.  1. 18.  6. 15. 18.\n",
            " 31.  1.  8. 12. 15. 20. 16. 19.  2. 24.  7. 20. 11. 39. 31. 19.  4. 13.\n",
            " 32.  3. 17. 18. 35. 22.  3.  1. 26. 39. 23.  4. 14. 15. 20. 11. 13. 14.\n",
            "  9.  4.  9.  7. 32. 32. 32. 17. 31. 39. 34.  4. 18. 38.  7.  1.  4.  5.\n",
            " 40.  3. 30. 17.  6. 28. 33. 34.  7. 32. 19. 33. 36. 21. 28. 16. 28. 25.\n",
            " 29. 20. 10. 37. 24. 39.  8. 14.  1. 31.  1. 10. 11. 21. 40. 25. 27.  7.\n",
            " 24. 30.  1. 40. 20. 17.  6. 25. 14. 37. 40.  8. 32. 30. 30.  6. 12. 18.\n",
            " 34. 37.  2. 22. 39. 20. 21. 13. 35. 22. 23. 36. 30.  8. 10. 26. 14. 11.\n",
            " 17. 17. 16. 13. 15. 10. 40. 15. 38. 11.]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HQloCPPVX3QI"
      },
      "source": [
        "## 4. Classification using PCA"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "jZ7q6myPSs2l"
      },
      "outputs": [],
      "source": [
        "alphaaa = np.array([0.8,0.85,0.9,0.95])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VR-O_Uv-Ro96"
      },
      "source": [
        "Compute mean"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "2cMEW5hvUU_F",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d6fc79ba-f9d9-4b60-d108-067803ffaf90"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[83.73571429 83.81071429 84.25       ... 75.57857143 74.80714286\n",
            " 73.62142857]\n"
          ]
        }
      ],
      "source": [
        "train_data_mean = np.mean(train_data,axis=0)\n",
        "print(train_data_mean)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "train_data_mean.shape"
      ],
      "metadata": {
        "id": "eJssPIPxlAZV",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cf1f9e88-9dd1-4c6c-f88d-f1aef90ccd99"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10304,)"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p-PC8OgDSvhR"
      },
      "source": [
        "Centering data matrix"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "SAjLsK3wVis1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "315b8c94-dd84-4450-b500-8f9cdb3c34ab"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ 35.26428571  36.18928571  35.75       ...  13.42142857  19.19285714\n",
            "   11.37857143]\n",
            " [ 13.26428571  10.18928571   7.75       ...  68.42142857  68.19285714\n",
            "   55.37857143]\n",
            " [ -0.73571429   2.18928571  -0.25       ...  60.42142857  63.19285714\n",
            "   60.37857143]\n",
            " ...\n",
            " [ 19.26428571  20.18928571  20.75       ...   0.42142857   1.19285714\n",
            "    1.37857143]\n",
            " [-11.73571429 -10.81071429  -7.25       ...  24.42142857  11.19285714\n",
            "    2.37857143]\n",
            " [-55.73571429 -58.81071429 -57.25       ... 111.42142857 112.19285714\n",
            "  116.37857143]]\n",
            "(280, 10304)\n"
          ]
        }
      ],
      "source": [
        "Centered_Train_Data_Matrix = train_data - np.transpose(train_data_mean)\n",
        "print(Centered_Train_Data_Matrix)\n",
        "print(Centered_Train_Data_Matrix.shape)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dS-a6RHPS8hk"
      },
      "source": [
        "Compute covariance matrix"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "a0pS0_d5YAII",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "78efad66-8154-4297-eacd-7e40ea3e1246"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1343.83729592 1331.48568878 1327.15535714 ... -187.43280612\n",
            "  -162.85096939  -79.55362245]\n",
            " [1331.48568878 1335.06774235 1324.27946429 ... -177.80834184\n",
            "  -154.6365051   -74.81451531]\n",
            " [1327.15535714 1324.27946429 1331.57321429 ... -175.16607143\n",
            "  -148.47321429  -71.50892857]\n",
            " ...\n",
            " [-187.43280612 -177.80834184 -175.16607143 ... 2271.85811224\n",
            "  2008.51515306 1765.74045918]\n",
            " [-162.85096939 -154.6365051  -148.47321429 ... 2008.51515306\n",
            "  2030.63423469 1841.75913265]\n",
            " [ -79.55362245  -74.81451531  -71.50892857 ... 1765.74045918\n",
            "  1841.75913265 1920.62811224]]\n"
          ]
        }
      ],
      "source": [
        "Train_Covariance_Matrix = np.dot(np.transpose(Centered_Train_Data_Matrix),Centered_Train_Data_Matrix)/Centered_Train_Data_Matrix.shape[0]\n",
        "print(Train_Covariance_Matrix)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LGkZ1rbBW-q2"
      },
      "source": [
        "Asserting that our calculation of the covariance matrix is correct"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "8B0wTJCdTHk_",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "42fe8d43-4904-4680-9efa-14adb8a6d18d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1343.83729592 1331.48568878 1327.15535714 ... -187.43280612\n",
            "  -162.85096939  -79.55362245]\n",
            " [1331.48568878 1335.06774235 1324.27946429 ... -177.80834184\n",
            "  -154.6365051   -74.81451531]\n",
            " [1327.15535714 1324.27946429 1331.57321429 ... -175.16607143\n",
            "  -148.47321429  -71.50892857]\n",
            " ...\n",
            " [-187.43280612 -177.80834184 -175.16607143 ... 2271.85811224\n",
            "  2008.51515306 1765.74045918]\n",
            " [-162.85096939 -154.6365051  -148.47321429 ... 2008.51515306\n",
            "  2030.63423469 1841.75913265]\n",
            " [ -79.55362245  -74.81451531  -71.50892857 ... 1765.74045918\n",
            "  1841.75913265 1920.62811224]]\n",
            "(10304, 10304)\n",
            "(10304, 10304)\n"
          ]
        }
      ],
      "source": [
        "cov_mat = np.cov(np.transpose(train_data), bias=True)\n",
        "print(cov_mat)\n",
        "print(cov_mat.shape)\n",
        "print(Train_Covariance_Matrix.shape)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "b10JHzyVXGQF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "45bc0f5c-f2cd-440d-e3b6-a4aad0f7bc5b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Arrays are not equal\n",
            "\n",
            "Mismatched elements: 21524996 / 106172416 (20.3%)\n",
            "Max absolute difference: 4.54747351e-13\n",
            "Max relative difference: 2.22044605e-16\n",
            " x: array([[1343.837296, 1331.485689, 1327.155357, ..., -187.432806,\n",
            "        -162.850969,  -79.553622],\n",
            "       [1331.485689, 1335.067742, 1324.279464, ..., -177.808342,...\n",
            " y: array([[1343.837296, 1331.485689, 1327.155357, ..., -187.432806,\n",
            "        -162.850969,  -79.553622],\n",
            "       [1331.485689, 1335.067742, 1324.279464, ..., -177.808342,...\n"
          ]
        }
      ],
      "source": [
        "try:\n",
        "  np.testing.assert_array_equal(cov_mat, Train_Covariance_Matrix)\n",
        "except AssertionError as e:\n",
        "  print(e)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aiIIZWpgYuLf"
      },
      "source": [
        "The difference is within acceptable range"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0kqcBgB2yS5f"
      },
      "source": [
        "Compute eigenvalues and eigenvectors"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "MTUZ1m0WZx5V",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "998443da-8774-4d5b-f5c8-3f37c281f2d2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 2.72286968e+06  2.20750326e+06  1.13898868e+06 ... -1.17174915e-09\n",
            " -1.72432382e-09 -1.75139081e-09]\n",
            "[[ 0.0037122  -0.01476915 -0.02046483 ...  0.          0.\n",
            "   0.        ]\n",
            " [ 0.00367362 -0.0147245  -0.0204496  ... -0.07383385  0.36807271\n",
            "   0.33130376]\n",
            " [ 0.00366895 -0.014701   -0.02050773 ... -0.33440161 -0.2813665\n",
            "  -0.20421921]\n",
            " ...\n",
            " [ 0.00638864  0.01048788 -0.01195504 ...  0.0153833   0.00037995\n",
            "  -0.01709879]\n",
            " [ 0.00651046  0.01003697 -0.01186481 ... -0.00707523 -0.00171888\n",
            "   0.02504252]\n",
            " [ 0.00717956  0.0085864  -0.01226095 ...  0.02767162  0.00308461\n",
            "  -0.00457921]]\n"
          ]
        }
      ],
      "source": [
        "train_eigen_vals, train_eigen_vecs = LA.eigh(Train_Covariance_Matrix)\n",
        "idx = train_eigen_vals.argsort()[::-1]   \n",
        "train_eigen_vals = train_eigen_vals[idx]\n",
        "train_eigen_vecs = train_eigen_vecs[:,idx]\n",
        "print(train_eigen_vals)\n",
        "print(train_eigen_vecs)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qr7k_dGYROGD"
      },
      "source": [
        "Covariance matrix is symmetric, so the eigenvalues should be real numbers. When using the function eig() instead of eigh(), by default the returned value is complex. The imaginary part is due to numeric error so we should discard it. But since the matrix is symmetric we simply used eigh() which is optimized for symmetric matrices specifically and thus faster."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "L3D9guRERNf8"
      },
      "outputs": [],
      "source": [
        "#train_eigen_vals = train_eigen_vals.real\n",
        "#train_eigen_vecs = train_eigen_vecs.real"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5arphaPPdX-q"
      },
      "source": [
        "Fraction of total variance"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KWQIvX3ZbbES",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b80eb6ec-260d-41f9-ab23-59c7ec1f439c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Sum of  Eigen Values=  16227364.03187499 \n",
            "\n",
            "Explained variance for alpha = 0.8 is 40.0 dimensions\n",
            "Explained variance for alpha = 0.85 is 59.0 dimensions\n",
            "Explained variance for alpha = 0.9 is 92.0 dimensions\n",
            "Explained variance for alpha = 0.95 is 149.0 dimensions\n"
          ]
        }
      ],
      "source": [
        "train_eigen_values_total = np.sum(train_eigen_vals)\n",
        "\"\"\"\n",
        "train_eigen_vals = np.flip(train_eigen_vals)\n",
        "train_eigen_vecs = np.flip(train_eigen_vecs,axis=1)\n",
        "print(train_eigen_vals)\n",
        "print(train_eigen_vecs)\n",
        "\"\"\"\n",
        "print(\"\\nSum of  Eigen Values= \",train_eigen_values_total,\"\\n\")\n",
        "num_of_dim = np.empty(len(alphaaa),)\n",
        "k = 0\n",
        "for alpha in alphaaa:\n",
        "  sum = 0\n",
        "  r = 0\n",
        "  while sum < alpha * train_eigen_values_total:\n",
        "        sum += train_eigen_vals[r]\n",
        "        r += 1\n",
        "  num_of_dim[k] = r\n",
        "  print(\"Explained variance for alpha = \" + str(alpha) + \" is \" + str(num_of_dim[k]) + \" dimensions\")\n",
        "  k += 1\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DScLTVucgF1a"
      },
      "source": [
        "Getting Reduced Dimentionality Matrix"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_8TQBmivfNSx"
      },
      "outputs": [],
      "source": [
        "def get_reduced_dim_mat(dimensions, matrix):\n",
        "  projection_matrix_r = np.delete(train_eigen_vecs, np.s_[int(dimensions) : train_eigen_vecs.shape[1]], axis=1)\n",
        "  reduced_dim_mat = np.dot(np.transpose(projection_matrix_r),np.transpose(matrix)) \n",
        "  reduced_dim_mat = np.transpose(reduced_dim_mat)\n",
        "\n",
        "  return reduced_dim_mat"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "iosdVZvCMj3K"
      },
      "outputs": [],
      "source": [
        "def KNNclf(neighbours, X_train, y_train, X_test, y_test):\n",
        "  clf = KNeighborsClassifier(n_neighbors=neighbours)\n",
        "  clf.fit(X_train, y_train)\n",
        "  y_pred = clf.predict(X_test)\n",
        "  accuracy = metrics.accuracy_score(y_test, y_pred)\n",
        "  print(\"Accuracy: \", accuracy)\n",
        "  #print(confusion_matrix(y_test, y_pred))\n",
        "  #print(classification_report(y_test, y_pred))\n",
        "  return accuracy"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "kb7PI3MZONUy",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c5851fb5-2ad1-4864-ed50-bd64f2f1413d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(4, 4)\n",
            "40 dimensions with 1 nearest neighbours\n",
            "Accuracy:  0.8916666666666667\n",
            "40 dimensions with 3 nearest neighbours\n",
            "Accuracy:  0.8666666666666667\n",
            "40 dimensions with 5 nearest neighbours\n",
            "Accuracy:  0.8083333333333333\n",
            "40 dimensions with 7 nearest neighbours\n",
            "Accuracy:  0.7333333333333333\n",
            "59 dimensions with 1 nearest neighbours\n",
            "Accuracy:  0.9083333333333333\n",
            "59 dimensions with 3 nearest neighbours\n",
            "Accuracy:  0.8666666666666667\n",
            "59 dimensions with 5 nearest neighbours\n",
            "Accuracy:  0.8166666666666667\n",
            "59 dimensions with 7 nearest neighbours\n",
            "Accuracy:  0.7083333333333334\n",
            "92 dimensions with 1 nearest neighbours\n",
            "Accuracy:  0.9083333333333333\n",
            "92 dimensions with 3 nearest neighbours\n",
            "Accuracy:  0.875\n",
            "92 dimensions with 5 nearest neighbours\n",
            "Accuracy:  0.7916666666666666\n",
            "92 dimensions with 7 nearest neighbours\n",
            "Accuracy:  0.7083333333333334\n",
            "149 dimensions with 1 nearest neighbours\n",
            "Accuracy:  0.9083333333333333\n",
            "149 dimensions with 3 nearest neighbours\n",
            "Accuracy:  0.875\n",
            "149 dimensions with 5 nearest neighbours\n",
            "Accuracy:  0.7833333333333333\n",
            "149 dimensions with 7 nearest neighbours\n",
            "Accuracy:  0.6916666666666667\n"
          ]
        }
      ],
      "source": [
        "k_neighbours = [1, 3, 5, 7]\n",
        "accuracies = np.empty((len(alphaaa), len(k_neighbours)))\n",
        "print(accuracies.shape)\n",
        "for i, dim in enumerate(num_of_dim):\n",
        "  X_train = get_reduced_dim_mat(dim, train_data - np.transpose(train_data_mean))\n",
        "  X_test = get_reduced_dim_mat(dim, test_data - np.transpose(train_data_mean))\n",
        "  y_train = train_labels\n",
        "  y_test = test_labels\n",
        "  for j, k in enumerate(k_neighbours):\n",
        "    print(str(int(dim)) + \" dimensions with \" + str(k) + \" nearest neighbours\")\n",
        "    accuracy = KNNclf(k, X_train, y_train, X_test, y_test)\n",
        "    accuracies[i][j] = accuracy\n",
        "accuracies = np.transpose(accuracies)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We tried to project with the data before centering and after centering. As long as we centered both the train data and test data, we got the same results."
      ],
      "metadata": {
        "id": "lkWHECqDhlqO"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6ITbRunKcBbn"
      },
      "source": [
        "plotting different alpha values against accuracy for different k values for the KNN classifier"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(10, 10))\n",
        "\n",
        "for i in range(len(alphaaa)):\n",
        "  plt.subplot(2, 2, i+1)\n",
        "  plt.title(\"alpha=\" + str(alphaaa[i]))\n",
        "  plt.plot(k_neighbours, accuracies.T[i])"
      ],
      "metadata": {
        "id": "P61cIWFQ7-Ve",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 607
        },
        "outputId": "b6bf812f-5774-4b45-df2c-bcaa7b6ab5bb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x720 with 4 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "RuuzOkKtUx4d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 694
        },
        "outputId": "58671390-a511-4f21-9ecf-d30a981416ff"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0.8  0.85 0.9  0.95]\n",
            "[[0.89166667 0.90833333 0.90833333 0.90833333]\n",
            " [0.86666667 0.86666667 0.875      0.875     ]\n",
            " [0.80833333 0.81666667 0.79166667 0.78333333]\n",
            " [0.73333333 0.70833333 0.70833333 0.69166667]]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x720 with 4 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "print(alphaaa)\n",
        "print(accuracies)\n",
        "plt.figure(figsize=(10, 10))\n",
        "\n",
        "for i in range(len(k_neighbours)):\n",
        "  plt.subplot(2, 2, i+1)\n",
        "  plt.title(str(k_neighbours[i]) + \" neighbour(s)\")\n",
        "  plt.plot(alphaaa, accuracies[i])\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OvAWydf9fCXo"
      },
      "source": [
        "## 5. Classification Using LDA"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GIeNPfQkjN3e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "58a9cb33-f489-47de-de49-57c367e19627"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ 60298.73228363  59686.56795933  59452.07509752 ... -26666.32218279\n",
            "  -22440.40777525 -17666.29282044]\n",
            " [ 59686.54951656  59517.52456121  59053.80672757 ... -25529.61094069\n",
            "  -21777.78282017 -17444.05569932]\n",
            " [ 59452.05096375  59053.80097897  59246.47949227 ... -25977.36909789\n",
            "  -20858.65472196 -15871.79797524]\n",
            " ...\n",
            " [-26666.34567022 -25529.62104862 -25977.34175956 ...  74991.11661639\n",
            "   61415.25334503  44943.90638864]\n",
            " [-22440.38924319 -21777.79457602 -20858.64993237 ...  61415.23099233\n",
            "   60542.16717983  48811.70651046]\n",
            " [-17666.30457921 -17444.06120111 -15871.75804267 ...  44943.88773905\n",
            "   48811.7085864   51592.4500367 ]]\n"
          ]
        }
      ],
      "source": [
        "n = 7\n",
        "m = 3\n",
        "LDA_mean = np.zeros((40,train_data.shape[1]))\n",
        "for i in range(0,train_data.shape[0], n):\n",
        "    #print(i//5,\"\\t\",i,\"\\t\",i+5)\n",
        "    LDA_mean[i//n] = np.mean(train_data[i:i+n,:], axis=0)\n",
        "#print(LDA_mean)\n",
        "#print(\"\\n Dimensions:\",LDA_mean.shape)\n",
        "B = np.empty((10304,10304))\n",
        "data_mean = train_data_mean.reshape(1, train_data.shape[1])\n",
        "for i, mean_vec in enumerate(LDA_mean):\n",
        "\n",
        "  mean_vec = mean_vec.reshape(1, train_data.shape[1])\n",
        "  mu1_mu2 = mean_vec - data_mean\n",
        "  B += n * np.dot(mu1_mu2.T, mu1_mu2)\n",
        "print(B)\n",
        "#print(\"\\n Dimensions:\", B.shape)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Fm8AobU_kxCE",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6ec775e7-f8fd-4877-e7eb-5c564935d955"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ 45.71428571  46.28571429  46.         ...   0.57142857   4.85714286\n",
            "    5.14285714]\n",
            " [ 23.71428571  20.28571429  18.         ...  55.57142857  53.85714286\n",
            "   49.14285714]\n",
            " [  9.71428571  12.28571429  10.         ...  47.57142857  48.85714286\n",
            "   54.14285714]\n",
            " ...\n",
            " [ 41.28571429  42.57142857  42.71428571 ...   1.85714286   2.57142857\n",
            "    3.85714286]\n",
            " [ 10.28571429  11.57142857  14.71428571 ...  25.85714286  12.57142857\n",
            "    4.85714286]\n",
            " [-33.71428571 -36.42857143 -35.28571429 ... 112.85714286 113.57142857\n",
            "  118.85714286]]\n",
            "(280, 10304)\n",
            "0 \t 0 \t 7\n",
            "1 \t 7 \t 14\n",
            "2 \t 14 \t 21\n",
            "3 \t 21 \t 28\n",
            "4 \t 28 \t 35\n",
            "5 \t 35 \t 42\n",
            "6 \t 42 \t 49\n",
            "7 \t 49 \t 56\n",
            "8 \t 56 \t 63\n",
            "9 \t 63 \t 70\n",
            "10 \t 70 \t 77\n",
            "11 \t 77 \t 84\n",
            "12 \t 84 \t 91\n",
            "13 \t 91 \t 98\n",
            "14 \t 98 \t 105\n",
            "15 \t 105 \t 112\n",
            "16 \t 112 \t 119\n",
            "17 \t 119 \t 126\n",
            "18 \t 126 \t 133\n",
            "19 \t 133 \t 140\n",
            "20 \t 140 \t 147\n",
            "21 \t 147 \t 154\n",
            "22 \t 154 \t 161\n",
            "23 \t 161 \t 168\n",
            "24 \t 168 \t 175\n",
            "25 \t 175 \t 182\n",
            "26 \t 182 \t 189\n",
            "27 \t 189 \t 196\n",
            "28 \t 196 \t 203\n",
            "29 \t 203 \t 210\n",
            "30 \t 210 \t 217\n",
            "31 \t 217 \t 224\n",
            "32 \t 224 \t 231\n",
            "33 \t 231 \t 238\n",
            "34 \t 238 \t 245\n",
            "35 \t 245 \t 252\n",
            "36 \t 252 \t 259\n",
            "37 \t 259 \t 266\n",
            "38 \t 266 \t 273\n",
            "39 \t 273 \t 280\n",
            "Center Class matrices: \n",
            " [[[ 45.71428571  46.28571429  46.         ...   0.57142857   4.85714286\n",
            "     5.14285714]\n",
            "  [ 23.71428571  20.28571429  18.         ...  55.57142857  53.85714286\n",
            "    49.14285714]\n",
            "  [  9.71428571  12.28571429  10.         ...  47.57142857  48.85714286\n",
            "    54.14285714]\n",
            "  ...\n",
            "  [-33.28571429 -38.71428571 -37.         ... -55.42857143 -58.14285714\n",
            "   -50.85714286]\n",
            "  [-27.28571429 -28.71428571 -25.         ... -32.42857143 -29.14285714\n",
            "   -21.85714286]\n",
            "  [ 12.71428571  15.28571429  16.         ...  35.57142857  26.85714286\n",
            "     3.14285714]]\n",
            "\n",
            " [[ 36.42857143  39.42857143  39.28571429 ...   0.71428571   4.42857143\n",
            "     6.        ]\n",
            "  [-32.57142857 -35.57142857 -33.71428571 ... -45.28571429 -42.57142857\n",
            "   -35.        ]\n",
            "  [ 26.42857143  29.42857143  25.28571429 ... -26.28571429 -20.57142857\n",
            "   -28.        ]\n",
            "  ...\n",
            "  [-30.57142857 -40.57142857 -34.71428571 ... -34.28571429 -32.57142857\n",
            "   -30.        ]\n",
            "  [ 37.42857143  37.42857143  38.28571429 ...  -4.28571429  -1.57142857\n",
            "     4.        ]\n",
            "  [ 22.42857143  27.42857143  22.28571429 ...   2.71428571 -18.57142857\n",
            "   -27.        ]]\n",
            "\n",
            " [[-15.         -19.71428571   2.28571429 ...  92.71428571  77.85714286\n",
            "    50.28571429]\n",
            "  [-44.         -48.71428571 -42.71428571 ... -48.28571429 -51.14285714\n",
            "   -71.71428571]\n",
            "  [ 52.          56.28571429  50.28571429 ... -19.28571429  -0.14285714\n",
            "   -13.71428571]\n",
            "  ...\n",
            "  [ 15.          23.28571429  21.28571429 ...   1.71428571 -12.14285714\n",
            "   -20.71428571]\n",
            "  [-21.         -23.71428571 -26.71428571 ... -15.28571429 -15.14285714\n",
            "   -33.71428571]\n",
            "  [-26.         -23.71428571 -35.71428571 ... -11.28571429  -4.14285714\n",
            "    94.28571429]]\n",
            "\n",
            " ...\n",
            "\n",
            " [[-50.14285714 -48.42857143 -51.42857143 ... -48.         -44.\n",
            "   -33.14285714]\n",
            "  [-10.14285714  -0.42857143   4.57142857 ... -45.         -23.\n",
            "   -15.14285714]\n",
            "  [ 23.85714286  23.57142857  21.57142857 ...  50.          33.\n",
            "    31.85714286]\n",
            "  ...\n",
            "  [-50.14285714 -52.42857143 -49.42857143 ... 107.          85.\n",
            "    35.85714286]\n",
            "  [ 19.85714286  15.57142857  13.57142857 ... -14.         -10.\n",
            "    -2.14285714]\n",
            "  [ 25.85714286  25.57142857  21.57142857 ...  13.          18.\n",
            "    28.85714286]]\n",
            "\n",
            " [[-25.85714286 -20.57142857 -25.57142857 ...  51.57142857  49.71428571\n",
            "    56.        ]\n",
            "  [ 44.14285714  41.42857143  44.42857143 ... -34.42857143 -45.28571429\n",
            "   -56.        ]\n",
            "  [-11.85714286  -9.57142857  -9.57142857 ...   3.57142857   1.71428571\n",
            "     7.        ]\n",
            "  ...\n",
            "  [-12.85714286 -17.57142857  -7.57142857 ... -47.42857143 -18.28571429\n",
            "   -10.        ]\n",
            "  [-13.85714286 -11.57142857 -19.57142857 ... -48.42857143 -52.28571429\n",
            "   -55.        ]\n",
            "  [ 55.14285714  53.42857143  52.42857143 ... -27.42857143 -36.28571429\n",
            "   -37.        ]]\n",
            "\n",
            " [[-13.71428571 -16.42857143 -17.28571429 ... -46.14285714 -36.42857143\n",
            "   -42.14285714]\n",
            "  [ 37.28571429  40.57142857  34.71428571 ... -24.14285714 -20.42857143\n",
            "   -21.14285714]\n",
            "  [-27.71428571 -25.42857143 -27.28571429 ... -42.14285714 -48.42857143\n",
            "   -46.14285714]\n",
            "  ...\n",
            "  [ 41.28571429  42.57142857  42.71428571 ...   1.85714286   2.57142857\n",
            "     3.85714286]\n",
            "  [ 10.28571429  11.57142857  14.71428571 ...  25.85714286  12.57142857\n",
            "     4.85714286]\n",
            "  [-33.71428571 -36.42857143 -35.28571429 ... 112.85714286 113.57142857\n",
            "   118.85714286]]] \n",
            "\n",
            "[[ 3.19466154e+05  3.15036604e+05  3.15149809e+05 ... -2.14019889e+04\n",
            "  -1.87752926e+04  1.87366071e+01]\n",
            " [ 3.16359635e+05  3.16066412e+05  3.14519261e+05 ... -1.97514804e+04\n",
            "  -1.70461326e+04  1.22030804e+03]\n",
            " [ 3.15449246e+05  3.13546355e+05  3.16426912e+05 ... -1.89877329e+04\n",
            "  -1.66604746e+04  1.29160714e+02]\n",
            " ...\n",
            " [-2.58148571e+04 -2.42567143e+04 -2.30691429e+04 ...  5.61129143e+05\n",
            "   5.00969000e+05  4.49463429e+05]\n",
            " [-2.31578571e+04 -2.15204286e+04 -2.07138571e+04 ...  5.00969000e+05\n",
            "   5.08035429e+05  4.66880857e+05]\n",
            " [-4.60871429e+03 -3.50400000e+03 -4.15071429e+03 ...  4.49463429e+05\n",
            "   4.66880857e+05  4.86183429e+05]]\n",
            "\n",
            "S dims: (10304, 10304)\n"
          ]
        }
      ],
      "source": [
        "LDA_Centered_Data_Matrix = np.zeros((train_data.shape[0],train_data.shape[1]))\n",
        "\n",
        "for i in range(0,train_data.shape[0],1):\n",
        "  LDA_Centered_Data_Matrix[i,:] = train_data[i,:] - LDA_mean[i//n,:]\n",
        "  \n",
        "print(LDA_Centered_Data_Matrix)   \n",
        "print(LDA_Centered_Data_Matrix.shape)\n",
        "\n",
        "LDA_Centered_Data_Matrix40 = np.empty((40, n, 10304))\n",
        "for i in range(0, train_data.shape[0], n):\n",
        "   print(i//n,\"\\t\",i,\"\\t\",i+n)\n",
        "   LDA_Centered_Data_Matrix40[i//n] = LDA_Centered_Data_Matrix[i:i+n,:]\n",
        "\n",
        "print(\"Center Class matrices: \\n\",LDA_Centered_Data_Matrix40,\"\\n\") \n",
        "S = np.empty((10304,10304))\n",
        "for i in range(0,40,1):\n",
        "  S += np.dot(np.transpose(LDA_Centered_Data_Matrix40[i]),LDA_Centered_Data_Matrix40[i])\n",
        "\n",
        "print(S)\n",
        "print(\"\\nS dims:\",S.shape)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "AU4vwi21oMH-",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5a02f1d8-6b18-4308-a76b-a5a96744f0c9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(10304, 10304)\n",
            "\n",
            " [[-1.60056798e+08  7.85304176e+08 -5.76323567e+08 ... -5.26535239e+00\n",
            "   1.08119864e+00  3.90939650e+00]\n",
            " [ 1.31332768e+09  4.65377475e+08  6.75851330e+08 ... -9.49390840e+00\n",
            "   1.24553542e+01  5.15243299e+00]\n",
            " [ 8.22152974e+08  9.42141892e+08 -2.01404584e+08 ...  6.36782876e+00\n",
            "  -8.24456824e+00 -6.63835462e+00]\n",
            " ...\n",
            " [ 1.83165601e+08 -6.36586749e+06 -1.12450909e+08 ...  8.13028775e-01\n",
            "  -3.83845739e-01 -4.11892660e-01]\n",
            " [-1.11078356e+08 -2.43386383e+07  5.40901826e+07 ... -7.46492288e-01\n",
            "   1.36289361e-01  4.43986327e-01]\n",
            " [ 2.98384256e+08  1.30765043e+08 -9.06900204e+06 ... -5.33202395e-01\n",
            "   6.99215365e-01  1.51329147e+00]]\n"
          ]
        }
      ],
      "source": [
        "S_inv=np.linalg.inv(S)\n",
        "print(S_inv.shape)\n",
        "print(\"\\n\",S_inv)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "l8Ag4-qUpPNw"
      },
      "outputs": [],
      "source": [
        "SB = np.dot(S_inv,B)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "RCQJIHwtpTRF"
      },
      "outputs": [],
      "source": [
        "S_eigenvals, S_eigenvecs = LA.eigh(SB)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "idx = S_eigenvals.argsort()[::-1]   \n",
        "S_eigenvals = S_eigenvals[idx].real\n",
        "S_eigenvecs = S_eigenvecs[:,idx].real\n",
        "print(S_eigenvals)\n",
        "print(S_eigenvals.shape)\n",
        "print(S_eigenvecs)\n",
        "print(S_eigenvecs.shape)\n"
      ],
      "metadata": {
        "id": "eVA6l9aRF_d3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5fdfe9a0-2e60-4668-fbb4-f34dd63d7b3b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 1.23814829e+18  8.39587636e+17  5.09143536e+17 ... -5.12664070e+17\n",
            " -8.40100939e+17 -1.22846209e+18]\n",
            "(10304,)\n",
            "[[ 0.01546645 -0.01532329  0.00107502 ... -0.00067285  0.01542198\n",
            "  -0.01566157]\n",
            " [ 0.01519905 -0.01490355  0.00154007 ... -0.00113982  0.01500154\n",
            "  -0.01539516]\n",
            " [ 0.01507211 -0.01536317  0.00160428 ... -0.00119117  0.01561984\n",
            "  -0.01536788]\n",
            " ...\n",
            " [-0.0008092   0.00159349  0.00136606 ...  0.00135391  0.00165004\n",
            "  -0.00080553]\n",
            " [ 0.00120944 -0.00237716 -0.00254821 ... -0.00254566 -0.00241795\n",
            "   0.00119298]\n",
            " [ 0.00061009 -0.00075608 -0.00087022 ... -0.00087038 -0.00079486\n",
            "   0.00061657]]\n",
            "(10304, 10304)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "projection_matrix = S_eigenvecs[:,0:39]\n",
        "print(projection_matrix)\n",
        "print(projection_matrix.shape)"
      ],
      "metadata": {
        "id": "IhQ4gEufSYid",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "73d593c9-7d02-405a-c0d4-894bfce43528"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ 0.01546645 -0.01532329  0.00107502 ... -0.00527558  0.0084604\n",
            "  -0.00235456]\n",
            " [ 0.01519905 -0.01490355  0.00154007 ... -0.00439124  0.00998622\n",
            "  -0.0027463 ]\n",
            " [ 0.01507211 -0.01536317  0.00160428 ... -0.00578172  0.00860771\n",
            "  -0.00264924]\n",
            " ...\n",
            " [-0.0008092   0.00159349  0.00136606 ...  0.00118761  0.0001376\n",
            "  -0.00040163]\n",
            " [ 0.00120944 -0.00237716 -0.00254821 ...  0.00248414  0.00146296\n",
            "  -0.00190362]\n",
            " [ 0.00061009 -0.00075608 -0.00087022 ... -0.00225601 -0.00045022\n",
            "  -0.00082102]]\n",
            "(10304, 39)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "j7Be_w09p57I",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e5d87958-8027-4b6d-f8bb-28500375d5d9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Reduced Data Matrix\n",
            " [[4767.11445797 2835.86680959 2691.44538574 ...   95.05042948\n",
            "    80.42716632 -684.47535461]\n",
            " [3839.84953207 2186.32312804 1991.38530969 ...  234.1959398\n",
            "  -146.57990062 -345.60858354]\n",
            " [4780.00560332 1397.03003451 1893.91715944 ...   77.15769502\n",
            "  -168.08065498 -550.63019572]\n",
            " ...\n",
            " [4243.26434218  783.19235934 2211.19019321 ...  243.96283753\n",
            "   116.87092469 -659.40389265]\n",
            " [4325.8172513  1543.64251529 2949.74299173 ...   50.52993494\n",
            "  -264.90308997 -390.64038372]\n",
            " [4577.31379607 2090.44739121 2885.29474397 ...  209.66731442\n",
            "    43.75087214 -385.91458901]]\n",
            "Reduced Data Matrix Dimensions\n",
            " (120, 39)\n"
          ]
        }
      ],
      "source": [
        "test_LDA =np.dot(np.transpose(projection_matrix),np.transpose(test_data))\n",
        "test_LDA = np.transpose(test_LDA)\n",
        "print(\"Reduced Data Matrix\\n\",test_LDA)\n",
        "print(\"Reduced Data Matrix Dimensions\\n\",test_LDA.shape)\n",
        "train_LDA=np.dot(np.transpose(projection_matrix),np.transpose(train_data))\n",
        "train_LDA = np.transpose(train_LDA)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "sqNcjXbWrQk4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "183cd4d4-b2f8-4962-ccde-4b81da578fb9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Train Data Dimensions: (280, 39)\n",
            "Test Data Dimensions: (120, 39)\n"
          ]
        }
      ],
      "source": [
        "X_train = train_LDA\n",
        "X_test = test_LDA\n",
        "y_train=train_labels\n",
        "y_test=test_labels\n",
        "print(\"Train Data Dimensions:\",train_LDA.shape)\n",
        "print(\"Test Data Dimensions:\",test_LDA.shape)\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "k_neighbours = [1, 3, 5, 7]\n",
        "accuracies_LDA = np.empty( (len(k_neighbours),))\n",
        "\n",
        "\n",
        "\n",
        "for i, k in enumerate(k_neighbours):\n",
        "  print(str(k) + \" nearest neighbours\")\n",
        "  accuracy = KNNclf(k, X_train, y_train, X_test, y_test)\n",
        "  accuracies_LDA[i] = accuracy\n",
        "\n",
        "\n",
        "accuracies_LDA = np.transpose(accuracies_LDA)\n",
        "accuracies_LDA"
      ],
      "metadata": {
        "id": "avDp8DTNSx4l",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7ed9bb9b-c41a-4f5a-de7e-0c1cfaf19799"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1 nearest neighbours\n",
            "Accuracy:  0.825\n",
            "3 nearest neighbours\n",
            "Accuracy:  0.8\n",
            "5 nearest neighbours\n",
            "Accuracy:  0.7583333333333333\n",
            "7 nearest neighbours\n",
            "Accuracy:  0.675\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.825     , 0.8       , 0.75833333, 0.675     ])"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(7, 7))\n",
        "\n",
        "plt.plot(k_neighbours, accuracies_LDA)\n",
        "\n"
      ],
      "metadata": {
        "id": "NM8xtDnqT8TV",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 72
        },
        "outputId": "7ef6e4f1-c099-462e-8aa2-00111c8e1233"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f3a3f049dd0>]"
            ]
          },
          "metadata": {},
          "execution_count": 35
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 504x504 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "PR_6360_6521_6609_bonus.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}