{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ctxfpXLwzIFf"
      },
      "source": [
        "## HW1 - Basics of ML\n",
        "Include your code in the relevant cells below.\n",
        "Subparts labeled as questions (Q1.1, Q1.2, etc.) should have their answers filled in or plots placed prominently, as appropriate."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y3JkhtmuzIFh"
      },
      "source": [
        "#### Important notes: \n",
        "\n",
        "1. On this and future homeworks, depending on the data size and your hardware configuration, experiments may take too long if you use the complete dataset. This may be challenging, as you may need to run multiple experiments. So, if an experiment takes too much time, start first with a smaller sample that will allow you to run your code within a reasonable time. Once you complete all tasks, before the final submission, you can allow longer run times and run your code with the complete set. However, if this is still taking too much time or causing your computer to freeze, it will be OK to submit experiments using a sample size that is feasible for your setting (indicate it clearly in your submission). Grading of the homework will not be affected from this type of variations in the design of your experiments.\n",
        "\n",
        "\n",
        "2. You can switch between 2D image data and 1D vector data using the numpy functions flatten() and resize()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DASCSh47zIFi"
      },
      "source": [
        "### S1: Understanding the data\n",
        "- Load MNIST dataset (hint it's available as part of https://keras.io/api/datasets)\n",
        "\n",
        "Q1.1: What is the number of features in the training dataset:   ___\n",
        "\n",
        "Q1.2: What is the number of samples in the training dataset:   ___\n",
        "\n",
        "Q1.1: What is the number of features in the testing dataset:   ___\n",
        "\n",
        "Q1.4: What is the number of samples in the testing dataset:   ___\n",
        "\n",
        "Q1.3: What is the dimensionality of each data sample: ___"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GtK6dcBdzIFi"
      },
      "outputs": [],
      "source": [
        "import keras\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from keras.datasets import mnist"
      ],
      "metadata": {
        "id": "ynjUJ-I9z89o"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "(X_tr, Y_tr), (X_te, Y_te) = mnist.load_data()"
      ],
      "metadata": {
        "id": "lhk5c9VGzXM0"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print('X_tr: ' + str(X_tr.shape))\n",
        "print('Y_tr: ' + str(Y_tr.shape))\n",
        "print('X_te:  '  + str(X_te.shape))\n",
        "print('Y_te:  '  + str(Y_te.shape))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tolr-fSezaQ0",
        "outputId": "754cf4d0-c536-4e04-ff73-9443d3c0cb36"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "X_tr: (60000, 28, 28)\n",
            "Y_tr: (60000,)\n",
            "X_te:  (10000, 28, 28)\n",
            "Y_te:  (10000,)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print('Unique labels: ' + str(np.unique(Y_tr, return_counts=True)))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Vsxkiek5zxOK",
        "outputId": "a76fccd2-bdf3-484b-efe7-8ac1d1ffbee0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Unique labels: (array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([5923, 6742, 5958, 6131, 5842, 5421, 5918, 6265, 5851, 5949]))\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mKCD1xmkzIFj"
      },
      "source": [
        "### S2: Viewing the data\n",
        "- Select one random example from each category from the training set. Display the 2D image with the name of the category\n",
        "\n",
        "Q2.1: Visualize the example image:   ___"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Read categories\n",
        "labels = np.unique(Y_tr)\n",
        "\n",
        "## Create 2x5 subplot\n",
        "fig, ax = plt.subplots(nrows = 2, ncols = 5)\n",
        "\n",
        "## Loop to plot each category\n",
        "for i, tmpl in enumerate(labels):\n",
        "\n",
        "  ## Select a random image with the current label\n",
        "  indAll = np.where(Y_tr == tmpl)[0]\n",
        "  indSel = indAll[np.random.randint(indAll.shape)]\n",
        "  selImg = X_tr[indSel,:,:].squeeze()\n",
        "\n",
        "  ## Convert loop index to 2D index for the 2x5 plot\n",
        "  a1, a2 = np.unravel_index(i, [2,5])      \n",
        "  \n",
        "  ## Plot image\n",
        "  ax[a1, a2].imshow(selImg)\n",
        "  ax[a1, a2].set_title('Label ' + str(tmpl))\n",
        "\n",
        "## Show image\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 240
        },
        "id": "cDnEoqPvzqfA",
        "outputId": "66ef9396-7141-4924-f3bf-b9517e991b1f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 10 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6V9p1no0zIFk"
      },
      "source": [
        "### S3: Sub-sampling the data\n",
        "- Reduce training and testing sample sizes by **randomly selecting** %10 of the initial samples\n",
        "\n",
        "Q3.1: What is the distribution of each label in the initial train data (i.e. percentage of each label):   ___\n",
        "\n",
        "Q3.2: What is the distribution of each label in the reduced train data:   ___"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Randomly sample data\n",
        "def sample_data(X, Y, p):\n",
        "  ## Shuffle array indices\n",
        "  num_sample = X.shape[0]\n",
        "  ind_shuf = np.random.permutation(num_sample)\n",
        "\n",
        "  ## Select p percent of the shuffled indices\n",
        "  num_sel = int(num_sample / 100 * p )\n",
        "  ind_sel = ind_shuf[0:num_sel]\n",
        "  \n",
        "  ## Select data\n",
        "  X_out = X[ind_sel, :]\n",
        "  Y_out = Y[ind_sel]\n",
        "\n",
        "  return X_out, Y_out\n",
        "\n",
        "X_tr_sel1, Y_tr_sel1 = sample_data(X_tr, Y_tr, 1)\n",
        "X_te_sel1, Y_te_sel1 = sample_data(X_te, Y_te, 1)"
      ],
      "metadata": {
        "id": "MFCK2uoo55rP"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "## Find number of samples for each label\n",
        "_, c1 = np.unique(Y_tr, return_counts=True)\n",
        "_, c2 = np.unique(Y_tr_sel1, return_counts=True)\n",
        "\n",
        "## Find percentage of samples for each label\n",
        "p1 = (100*c1 / Y_tr.shape[0]).reshape(1,-1)\n",
        "p2 = (100*c2 / Y_tr_sel1.shape[0]).reshape(1,-1)\n",
        "\n",
        "print(p1)\n",
        "print(p2)\n",
        "\n",
        "## or\n",
        "p12 = np.concatenate((p1, p2), axis=0)\n",
        "df = pd.DataFrame(data = p12, columns = labels, index = ['X_tr','X_tr_sel1'])\n",
        "\n",
        "df.plot.bar()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 370
        },
        "id": "t-fww7GJ8LDg",
        "outputId": "cf1acfdc-1108-46b5-8f09-473371278edd"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ 9.87166667 11.23666667  9.93       10.21833333  9.73666667  9.035\n",
            "   9.86333333 10.44166667  9.75166667  9.915     ]]\n",
            "[[ 9.         11.33333333 10.66666667 12.          9.66666667  9.83333333\n",
            "   9.          8.83333333  8.         11.66666667]]\n"
          ]
        },
        {
          "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": "ZMS7ZMKwzIFk"
      },
      "source": [
        "### S4: Sub-sampling the data (again)\n",
        "- Reduce training and testing sample sizes by selecting **the first** %10 of the initial samples\n",
        "\n",
        "Q4.1: What is the distribution of each label in the initial train data (i.e. percentage of each label):   ___\n",
        "\n",
        "Q4.2: What is the distribution of each label in the reduced train data:   ___\n",
        "\n",
        "Q4.3: What are your comments/interpretation on comparison of the results for S3 and S4"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rF80JiB_zIFk"
      },
      "source": [
        "#### ! For the rest of the HW, please discard sub-sampled data from S3 and use subsampled data from S4"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Randomly sample data\n",
        "def sample_data(X, Y, p, is_shuffle = False):\n",
        "  ## Shuffle array indices\n",
        "  num_sample = X.shape[0]\n",
        "\n",
        "  if is_shuffle == True:\n",
        "    ind_shuf = np.random.permutation(num_sample)\n",
        "  else:\n",
        "    ind_shuf = np.arange(0,num_sample)\n",
        "\n",
        "  ## Select p percent of the shuffled indices\n",
        "  num_sel = int(num_sample / 100 * p )\n",
        "  ind_sel = ind_shuf[0:num_sel]\n",
        "  \n",
        "  ## Select data\n",
        "  X_out = X[ind_sel, :]\n",
        "  Y_out = Y[ind_sel]\n",
        "\n",
        "  return X_out, Y_out\n",
        "\n",
        "X_tr_sel2, Y_tr_sel2 = sample_data(X_tr, Y_tr, 1)\n",
        "X_te_sel2, Y_te_sel2 = sample_data(X_te, Y_te, 1)"
      ],
      "metadata": {
        "id": "TOcO5elMBGLE"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "## Find number of samples for each label\n",
        "_, c1 = np.unique(Y_tr, return_counts=True)\n",
        "_, c2 = np.unique(Y_tr_sel2, return_counts=True)\n",
        "\n",
        "## Find percentage of samples for each label\n",
        "p1 = (100*c1 / Y_tr.shape[0]).reshape(1,-1)\n",
        "p2 = (100*c2 / Y_tr_sel2.shape[0]).reshape(1,-1)\n",
        "\n",
        "print(p1)\n",
        "print(p2)\n",
        "\n",
        "## or\n",
        "p12 = np.concatenate((p1, p2), axis=0)\n",
        "df = pd.DataFrame(data = p12, columns = labels, index = ['X_tr','X_tr_sel1'])\n",
        "\n",
        "df.plot.bar()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 370
        },
        "id": "VmJT8htKBijj",
        "outputId": "8f8ecb04-adb2-4602-a4aa-ea353c40fb4d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ 9.87166667 11.23666667  9.93       10.21833333  9.73666667  9.035\n",
            "   9.86333333 10.44166667  9.75166667  9.915     ]]\n",
            "[[ 9.66666667 13.16666667 10.66666667  9.83333333  9.83333333  8.5\n",
            "   9.         10.33333333  8.16666667 10.83333333]]\n"
          ]
        },
        {
          "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": "-CKsJFe3zIFl"
      },
      "source": [
        "### S5: Exploring the dataset\n",
        "- Select all **train** images in category \"3\". Create and display a single pixel-wise \"average image\" for this category.\n",
        "- Create and display a single pixel-wise \"standard deviation image\" for this category?\n",
        "- Repeat the items above for category \"3\" images in the **test** set. Compare the average and standard deviation images.\n",
        "- Repeat the items above for a different category you select.\n",
        "\n",
        "Q5.1: Plot the 2D mean and std images for category 3 in training and testing sets:   ___\n",
        "\n",
        "Q5.2: Plot the 2D mean and std images for the category you selected in training and testing sets:   ___\n",
        "\n",
        "Q5.3: Comment on differences between the mean and std images from training and testing datasets? ___"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Select images\n",
        "X = X_tr_sel2\n",
        "Y = Y_tr_sel2\n",
        "indAll = np.where(Y == 7)[0]\n",
        "imgAll = X[indAll, :, :]\n",
        "print('Num sel: ' + str(indAll.shape))\n",
        "print('Num img mat: ' + str(imgAll.shape))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "crbHYaCnBuP4",
        "outputId": "1bd06eea-f136-4289-b003-464bb5b84382"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Num sel: (62,)\n",
            "Num img mat: (62, 28, 28)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Calculate avg img\n",
        "img_mean = np.mean(imgAll, axis = 0)\n",
        "img_mean.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KfVBn77mCTPm",
        "outputId": "cdf597e0-af56-4862-bdd9-f8f3e57d87b8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 209
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Show mean img\n",
        "plt.imshow(img_mean)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "OTcv9rBZCvLD",
        "outputId": "54ec0e0f-48bc-405d-aa44-fe8df1454a96"
      },
      "execution_count": null,
      "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": "-I1-bxGZzIFl"
      },
      "source": [
        "### S6: Image distances\n",
        "- In the training set, find the image in category 3 that is most dissimilar to the mean image of category 3. Show it as a 2D image\n",
        "- In the training set, find the image in category 3 that is most similar to mean image of category 3. Show it as a 2D image\n",
        "- In the training set, find the image in category 9 that is most similar to mean image of category 3. Show it as a 2D image\n",
        "\n",
        "**Hint:** You can use the \"euclidean distance\" as your similarity metric. Given that an image i is represented with a flattened feature vector v_i , and the second image j with v_m, the distance between these two images can be calculated using the vector norm of their differences ( | v_i - v_j | ) \n",
        "\n",
        "Q6.1: What is the index of most dissimilar image in category 3:   ___\n",
        "\n",
        "Q6.2: Plot the most dissimilar category 3 image in 2D:   ___\n",
        "\n",
        "Q6.3: Plot the most similar category 3 image in 2D:   ___"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Find pixelwise \"distance\" of each image to the mean image\n",
        "vec_mean = img_mean.flatten() \n",
        "arr_d = np.zeros(indAll.shape[0])\n",
        "for i, ind_sel in enumerate(indAll):\n",
        "  img_sel = X[ind_sel, :, :].flatten()\n",
        "\n",
        "  d_sel = np.sqrt(np.dot(vec_mean - img_sel, vec_mean - img_sel))\n",
        "  #d_sel = np.linalg.norm(img_sel - vec_mean)\n",
        "  #d_sel = np.sqrt(np.square(img_sel - vec_mean).sum())\n",
        "\n",
        "  arr_d[i] = d_sel"
      ],
      "metadata": {
        "id": "1q3AwdDOC82X"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "ind_similar = indAll[arr_d.argmin()]\n",
        "ind_dissimilar = indAll[arr_d.argmax()]"
      ],
      "metadata": {
        "id": "Rhc6Ejx5D5iw"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "## Show similar / dissimilar images\n",
        "fig, ax = plt.subplots(nrows = 1, ncols = 3)\n",
        "ax[0].imshow(img_mean)\n",
        "ax[1].imshow(X[ind_similar,:,:])\n",
        "ax[2].imshow(X[ind_dissimilar,:,:])\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 149
        },
        "id": "6inqNhb-EIkt",
        "outputId": "4248a336-3cdd-4ada-dbb1-929c6e56b7ea"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 3 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4B63sTNnzIFm"
      },
      "source": [
        "### S7: Image distances, part 2\n",
        "- Repeat questions S5 and S6 after binarizing the images first\n",
        "\n",
        "Q7.1: What is the index of most dis-similar category 3 image:   ___\n",
        "\n",
        "Q7.2: What is the index of most similar category 3 image:   ___\n",
        "\n",
        "Q7.3: Did the answer change after binarization? How do you interprete this finding?:   ___"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Select images\n",
        "X = X_tr_sel2\n",
        "Y = Y_tr_sel2\n",
        "\n",
        "## Binarize images\n",
        "X = (X>128).astype(int)\n",
        "\n",
        "indAll = np.where(Y == 7)[0]\n",
        "imgAll = X[indAll, :, :]\n",
        "print('Num sel: ' + str(indAll.shape))\n",
        "print('Num img mat: ' + str(imgAll.shape))\n",
        "\n",
        "## Calculate avg img\n",
        "img_mean = np.mean(imgAll, axis = 0)\n",
        "img_mean.shape\n",
        "\n",
        "## Find pixelwise \"distance\" of each image to the mean image\n",
        "vec_mean = img_mean.flatten() \n",
        "arr_d = np.zeros(indAll.shape[0])\n",
        "for i, ind_sel in enumerate(indAll):\n",
        "  img_sel = X[ind_sel, :, :].flatten()\n",
        "\n",
        "  d_sel = np.sqrt(np.dot(vec_mean - img_sel, vec_mean - img_sel))\n",
        "  #d_sel = np.linalg.norm(img_sel - vec_mean)\n",
        "  #d_sel = np.sqrt(np.square(img_sel - vec_mean).sum())\n",
        "\n",
        "  arr_d[i] = d_sel\n",
        "  \n",
        "ind_similar = indAll[arr_d.argmin()]\n",
        "ind_dissimilar = indAll[arr_d.argmax()]\n",
        "\n",
        "## Show similar / dissimilar images\n",
        "fig, ax = plt.subplots(nrows = 1, ncols = 3)\n",
        "ax[0].imshow(img_mean)\n",
        "ax[1].imshow(X[ind_similar,:,:])\n",
        "ax[2].imshow(X[ind_dissimilar,:,:])\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 184
        },
        "id": "AEhkUFKrGdzJ",
        "outputId": "61dd7ab0-f176-4d7f-f011-dae62486f13a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Num sel: (62,)\n",
            "Num img mat: (62, 28, 28)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 3 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mNWILCmDzIFm"
      },
      "source": [
        "### S8: Binary classification between category 3 and 9  (split train data)\n",
        "- Select images from these two categories in the training dataset\n",
        "- Split them into two sets (Set1, Set2) with a %60 and %40 random split\n",
        "- Replace category labels as 0 (for 3) and 1 (for 9)\n",
        "- Use Set1 to train a linear SVM classifier with default parameters and predict the class labels for Set2 \n",
        "- Use Set2 to train a linear SVM classifier with default parameters and predict the class labels for Set1 \n",
        "\n",
        "Q8.1: What is the prediction accuracy using the model trained on Set1:   ___\n",
        "\n",
        "Q8.2: What is the prediction accuracy using the model trained on Set2:   ___"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "## Select data\n",
        "X = X_tr_sel2\n",
        "Y = Y_tr_sel2\n",
        "\n",
        "indSel = np.where((Y == 3) | (Y == 9))[0]\n",
        "X = X[indSel, :, :]\n",
        "Y = Y[indSel]\n",
        "\n",
        "## Replace labels\n",
        "Y[Y == 3] = 0\n",
        "Y[Y == 9] = 1\n",
        "\n",
        "## Flatten images\n",
        "X = X.reshape(X.shape[0], -1)\n",
        "\n",
        "## Create train test data\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=0.4, random_state=42)"
      ],
      "metadata": {
        "id": "9nVa2eMaHsYt"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn import svm\n",
        "\n",
        "# Create the svm classifier\n",
        "clf = svm.SVC(kernel='linear') # Linear Kernel\n",
        "\n",
        "# Train the model\n",
        "clf.fit(X_train, y_train)\n",
        "\n",
        "# Predict the label\n",
        "y_pred = clf.predict(X_test)"
      ],
      "metadata": {
        "id": "bFKBS872Ipmc"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn import metrics\n",
        "print('Accuracy: ', metrics.accuracy_score(y_test, y_pred))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pKJFZmRFKGzI",
        "outputId": "cb1db9f0-973d-45d8-da85-a16e15575305"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy:  0.86\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Train the model\n",
        "clf.fit(X_test, y_test)\n",
        "\n",
        "# Predict the label\n",
        "y_pred = clf.predict(X_train)\n",
        "\n",
        "print('Accuracy: ', metrics.accuracy_score(y_train, y_pred))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "t3lEXRs8MkF4",
        "outputId": "10cb42f2-8677-4c3a-c4ff-edb4a4814413"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy:  0.9459459459459459\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N_t7LEpezIFn"
      },
      "source": [
        "### S9: Binary classification between category 3 and 9 (train + test sets)\n",
        "- Select images from these two categories in the training and testing datasets\n",
        "- Replace category labels as 0 (for 3) and 1 (for 9)\n",
        "- Use training set to train a linear SVM classifier with default parameters and predict the class labels for the testing set\n",
        "- Use testing set to train a linear SVM classifier with default parameters and predict the class labels for the training set\n",
        "\n",
        "Q9.1: What is the prediction accuracy using the model trained on the training set:   ___\n",
        "\n",
        "Q9.2: What is the prediction accuracy using the model trained on the testing set:   ___"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5cbcdf2_zIFn"
      },
      "source": [
        "### S10: k-NN Error Analysis\n",
        "- In training and testing datasets select the images in categories: 1, 3, 5, 7 or 9\n",
        "- Train k-NN classifiers using 4 to 40 nearest neighbors with a step size of 4\n",
        "- Calculate and plot overall testing accuracy for each experiment\n",
        "\n",
        "Q10.1: For k=4 what is the label that was predicted with lowest accuracy:   ___\n",
        "\n",
        "Q10.2: For k=20 what is the label that was predicted with lowest accuracy:   ___\n",
        "\n",
        "Q10.3: What is the label pair that was confused most often (i.e. class A is labeled as B, and vice versa):   ___\n",
        "\n",
        "Q10.4: Visualize 5 mislabeled samples with their actual and predicted labels"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "## Select data\n",
        "X = X_tr_sel2\n",
        "Y = Y_tr_sel2\n",
        "\n",
        "indSel = np.where(np.isin(Y,[1, 3, 5, 7, 9]) == True)[0]\n",
        "X = X[indSel, :, :]\n",
        "Y = Y[indSel]\n",
        "\n",
        "## Flatten images\n",
        "X = X.reshape(X.shape[0], -1)\n",
        "\n",
        "## Create train test data\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=0.4, random_state=42)"
      ],
      "metadata": {
        "id": "2HlrAMwFM1ba"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.neighbors import KNeighborsClassifier\n",
        "from sklearn.metrics import classification_report, confusion_matrix, accuracy_score\n",
        "\n",
        "arr_k = np.arange(4, 40, 4)\n",
        "mat_pred = np.zeros([arr_k.shape[0], y_test.shape[0]])     ## Matrix to keep predictions from each experiment\n",
        "acc_pred = np.zeros([arr_k.shape[0], 1])     ## Array to keep accuracy from each experiment\n",
        "for i, k in enumerate(arr_k):\n",
        "  classifier = KNeighborsClassifier(n_neighbors = k)\n",
        "  classifier.fit(X_train, y_train)\n",
        "  y_pred = classifier.predict(X_test)\n",
        " mat_pred [i, :] = y_pred\n",
        "  acc_pred[i] = metrics.accuracy_score(y_test, y_pred)\n"
      ],
      "metadata": {
        "id": "jRCTprrENl08"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(acc_pred)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yee88Y33PtEe",
        "outputId": "383aae80-2e46-45fe-ea5e-d6b09a118161"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.79527559]\n",
            " [0.77952756]\n",
            " [0.73228346]\n",
            " [0.7480315 ]\n",
            " [0.71653543]\n",
            " [0.71653543]\n",
            " [0.70866142]\n",
            " [0.69291339]\n",
            " [0.68503937]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "result = confusion_matrix(y_test, mat_pred[0])\n",
        "print(\"Confusion Matrix:\")\n",
        "print(result)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cEePL7yiQASf",
        "outputId": "3e09cd8e-2d92-461d-a8f5-2ddbf7e890fd"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Confusion Matrix:\n",
            "[[30  0  0  1  1]\n",
            " [ 4 17  0  2  1]\n",
            " [ 1  5 15  0  0]\n",
            " [ 5  0  0 14  3]\n",
            " [ 0  0  0  3 25]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "mat_pred_bin = mat_pred.copy()\n",
        "for i in np.arange(0, mat_pred.shape[0]):\n",
        "  mat_pred_bin[i,:] = (mat_pred[i,:] == y_test).astype(int)\n",
        "mat_pred_sum = mat_pred_bin.sum(axis=0) "
      ],
      "metadata": {
        "id": "9igxjQEFQNok"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "indsel = mat_pred_sum.argmin()"
      ],
      "metadata": {
        "id": "7a0GEnRVQ_lj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print('Label / Pred : ' + str(y_test[indsel]) + '    ' + str(mat_pred[:, indsel]))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KTabHhbhRY9y",
        "outputId": "af249cfb-59a5-4086-a2ff-6a51842b8370"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Label / Pred : 3    [7. 7. 7. 7. 7. 7. 7. 7. 7.]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.imshow(X_test[indsel,:].reshape([28,28]))\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "kM3U_OovR3AU",
        "outputId": "c363c353-c65b-4478-9bf7-d3716b427ea2"
      },
      "execution_count": null,
      "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": "_BMC-ZGLzIFo"
      },
      "source": [
        "### S11: Feature extraction\n",
        "\n",
        "- We describe each image by using a reduced set of features (compared to n=784 initial features for each pixel value) as follows:\n",
        "  \n",
        "  1. Binarize the image (background=0, foreground=1)\n",
        "\n",
        "  2. For each image row i, find n_i, the sum of 1's in the row (28 features) \n",
        "  \n",
        "  3. For each image column j, find n_j, the sum of 1's in the column (28 features)\n",
        "  \n",
        "  4. Concatenate these features into a feature vector of 56 features\n",
        "  \n",
        "Repeat classification experiments in S9 using this reduced feature set.\n",
        "\n",
        "Q11.1: What is the prediction accuracy using the model trained using the train data:   ___\n",
        "\n",
        "Q11.2: What is the prediction accuracy using the model trained using the test data:   ___\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X = X_tr_sel2\n",
        "X = (X > 0).astype(int)\n",
        "\n",
        "X.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "10j5HnL-SdKp",
        "outputId": "257bd86b-b952-4542-bac7-f663149c22aa"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(600, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 269
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X0 = X[0,:,:]\n",
        "plt.imshow(X0)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "WK-fWUrgSzRE",
        "outputId": "85199abb-f608-4dd2-b104-77d4b1ff0953"
      },
      "execution_count": null,
      "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": "code",
      "source": [
        "f1 = X0.sum(axis=0)\n",
        "print(f1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BzyP4JV2TAsd",
        "outputId": "bc1d6036-0c01-46e9-c810-9eea4a9187eb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 0  0  0  0  2  2  3  5  8  9 10 12 14 15 15 13 13 14 10  8  5  3  3  2\n",
            "  0  0  0  0]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "f2 = X0.sum(axis=1)\n",
        "print(f2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "U-3jc9-0TWEU",
        "outputId": "f10f3311-7ba0-49cb-81e8-c19b4eb99eda"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 0  0  0  0  0 12 16 16 11  9  5  4  4  6  6  6  5  4  7  8  9 10 10 10\n",
            "  8  0  0  0]\n"
          ]
        }
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      "source": [
        "f12 = np.concatenate((f1,f2))\n",
        "f12.shape"
      ],
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            "text/plain": [
              "(56,)"
            ]
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          "execution_count": 279
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      "source": [
        "### Bonus:\n",
        "\n",
        "- This time we describe each 28 x 28 image by using a different feature set (n = 28 x 4 features). This feature set encodes \"index of the first non-zero pixel in image columns or rows\" from each direction (from left, right, top, bottom)\n",
        "\n",
        "Example for a 6 x 6 image:\n",
        "\n",
        "Img:\n",
        " 0 0 0 0 0 0\n",
        " 0 0 0 1 0 0\n",
        " 0 0 0 1 0 0\n",
        " 0 0 0 1 0 0\n",
        " 0 0 0 1 0 0\n",
        " 0 0 0 0 0 0\n",
        " \n",
        "Extracted features:\n",
        " 0 3 3 3 3 0  0 2 2 2 2 0  0 0 0 1 0 0  0 0 0 1 0 0   (left, right, top, bottom)\n",
        "  \n",
        "Repeat classification experiments in S9 using this reduced feature set.\n",
        "\n",
        "Q11.1: What is the prediction accuracy using the model trained using the train data:   ___\n",
        "\n",
        "Q11.2: What is the prediction accuracy using the model trained using the test data:   ___\n"
      ]
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