MiniProject_3.ipynb

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  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8.5"
    },
    "colab": {
      "name": "MiniProject_3.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/du-hr/MNIST-CNN/blob/Teresa/MiniProject_3.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TwdLP40A4X-A"
      },
      "source": [
        "# MiniProject 3: Multi-label Classification of Image Data\n",
        "\n",
        "\n",
        "> MiniProject 3 of COMP 551 (Fall 2020) at McGill University\n",
        "\n",
        "\n",
        "> Authors (G17): Haoran Du (260776911), Robin Cho (260806783), Teresa Lee (260715070)\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CGhQKetcGX8y",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ba5d162e-45ca-42df-fd91-51d649199a90"
      },
      "source": [
        "import numpy as np\n",
        "import scipy as sci\n",
        "import pandas as pd\n",
        "import h5py\n",
        "import torch\n",
        "from google.colab import drive\n",
        "# ignore the follwoing line if running locally\n",
        "drive.mount('/content/drive')\n",
        "# make path = './' if running locally\n",
        "path = '/content/drive/My Drive/'\n",
        "\n",
        "#%matplotlib notebook\n",
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Mounted at /content/drive\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "P5VYQqenQbc4"
      },
      "source": [
        "## **1. Datasets**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WcWAWxDGWb5N"
      },
      "source": [
        "### **1.1 Import Data**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "F3U3KGvMOWxI",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "outputId": "ac0a3cda-54f5-4748-fc0a-8c842e33b119"
      },
      "source": [
        "# load the datasets\n",
        "with h5py.File(path+'MNIST_synthetic.h5', 'r') as hdfid:\n",
        "     print(hdfid.keys())\n",
        "     test_images = hdfid['test_dataset'][()]\n",
        "     train_images = hdfid['train_dataset'][()]\n",
        "     train_labels = hdfid['train_labels'][()]\n",
        "\n",
        "# display train_images properties\n",
        "print(train_images.shape)\n",
        "# print(train_iamges[10][30])\n",
        "\n",
        "# plot first 3 images in train_images\n",
        "images=[]\n",
        "titles=[]\n",
        "images.append(np.array(train_images[0], dtype='float').reshape(64,64))\n",
        "titles.append(\"img_1\")\n",
        "images.append(np.array(train_images[1], dtype='float').reshape(64,64))\n",
        "titles.append(\"img_2\")\n",
        "images.append(np.array(train_images[2], dtype='float').reshape(64,64))\n",
        "titles.append(\"img_3\")\n",
        "\n",
        "for i in range(3):\n",
        "    plt.subplot(1,3,i+1),plt.imshow(images[i])\n",
        "    plt.title(titles[i])\n",
        "    plt.xticks([]),plt.yticks([])\n",
        "\n",
        "plt.show()\n",
        "\n",
        "# display train_labels properties\n",
        "print(train_labels.shape)\n",
        "print(train_labels)"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "<KeysViewHDF5 ['test_dataset', 'train_dataset', 'train_labels']>\n",
            "(56000, 64, 64, 1)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "(56000, 5)\n",
            "[[ 8  5  0  3 10]\n",
            " [ 8  9  9  8  7]\n",
            " [ 1  7  9  1  8]\n",
            " ...\n",
            " [ 4  4 10 10 10]\n",
            " [ 7  9  8 10 10]\n",
            " [ 6 10 10 10 10]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_V7Rym-vWRc0"
      },
      "source": [
        "### **1.2 Data Preprocessing**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ELeEfetpnnuT"
      },
      "source": [
        "###**1.2.1 One Hot Encoding**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ihpulb94Wg5y"
      },
      "source": [
        "#First, perform OHE on training labels\n",
        "from keras.utils import to_categorical\n",
        "\n",
        "train_new_labels = to_categorical(train_labels)\n",
        "Y_train = torch.from_numpy(train_new_labels) #save the oneHotEncoded labels as tensor"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ApXhhzBjoGeX",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ea25d3d5-d1ea-412e-d2b5-64567da391cd"
      },
      "source": [
        "Y_train"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[[0., 0., 0.,  ..., 1., 0., 0.],\n",
              "         [0., 0., 0.,  ..., 0., 0., 0.],\n",
              "         [1., 0., 0.,  ..., 0., 0., 0.],\n",
              "         [0., 0., 0.,  ..., 0., 0., 0.],\n",
              "         [0., 0., 0.,  ..., 0., 0., 1.]],\n",
              "\n",
              "        [[0., 0., 0.,  ..., 1., 0., 0.],\n",
              "         [0., 0., 0.,  ..., 0., 1., 0.],\n",
              "         [0., 0., 0.,  ..., 0., 1., 0.],\n",
              "         [0., 0., 0.,  ..., 1., 0., 0.],\n",
              "         [0., 0., 0.,  ..., 0., 0., 0.]],\n",
              "\n",
              "        [[0., 1., 0.,  ..., 0., 0., 0.],\n",
              "         [0., 0., 0.,  ..., 0., 0., 0.],\n",
              "         [0., 0., 0.,  ..., 0., 1., 0.],\n",
              "         [0., 1., 0.,  ..., 0., 0., 0.],\n",
              "         [0., 0., 0.,  ..., 1., 0., 0.]],\n",
              "\n",
              "        ...,\n",
              "\n",
              "        [[0., 0., 0.,  ..., 0., 0., 0.],\n",
              "         [0., 0., 0.,  ..., 0., 0., 0.],\n",
              "         [0., 0., 0.,  ..., 0., 0., 1.],\n",
              "         [0., 0., 0.,  ..., 0., 0., 1.],\n",
              "         [0., 0., 0.,  ..., 0., 0., 1.]],\n",
              "\n",
              "        [[0., 0., 0.,  ..., 0., 0., 0.],\n",
              "         [0., 0., 0.,  ..., 0., 1., 0.],\n",
              "         [0., 0., 0.,  ..., 1., 0., 0.],\n",
              "         [0., 0., 0.,  ..., 0., 0., 1.],\n",
              "         [0., 0., 0.,  ..., 0., 0., 1.]],\n",
              "\n",
              "        [[0., 0., 0.,  ..., 0., 0., 0.],\n",
              "         [0., 0., 0.,  ..., 0., 0., 1.],\n",
              "         [0., 0., 0.,  ..., 0., 0., 1.],\n",
              "         [0., 0., 0.,  ..., 0., 0., 1.],\n",
              "         [0., 0., 0.,  ..., 0., 0., 1.]]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xLAJOrRgdpib",
        "outputId": "22cee308-8c66-49da-b77c-130c40e3ea22"
      },
      "source": [
        "Y_train.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([56000, 5, 11])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f7iV-2cYn4rn"
      },
      "source": [
        "### **1.2.2 Data Normalization**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t4fnW9LJwNLO"
      },
      "source": [
        "# normalize to range 0-1 with typecast to float\n",
        "def data_normalized(x):\n",
        "  scaled_x = x.astype('float32') / 255.0\n",
        "  return scaled_x\n",
        "\n",
        "scaled_train_images = data_normalized(train_images)\n",
        "X_train = torch.from_numpy(scaled_train_images)"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1oGTptaF2_x9"
      },
      "source": [
        "###**1.2.3 Detecting the number of digits**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0cY7Y3emwYOe"
      },
      "source": [
        "import cv2\n",
        "threshold = 1 #Hyperparameter?\n",
        "width = 12\n",
        "height = 12"
      ],
      "execution_count": 144,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r2dRRAe8wRIl"
      },
      "source": [
        "def findDigits(img):\n",
        "  #Note that a normalized image does not work\n",
        "  ret,thresh = cv2.threshold(img,threshold,255,0)\n",
        "  contours, hierarchy = cv2.findContours(thresh, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)\n",
        "\n",
        "  #print(len(contours))\n",
        "  def getKey(item):\n",
        "    return item[0]\n",
        "\n",
        "  digitsLoc = []\n",
        "  minArea = 15\n",
        "  for cnt in contours:\n",
        "    x, y, w, h = cv2.boundingRect(cnt)\n",
        "    if w == 1 and h > 4:\n",
        "      listTemp = [x, y, w, h]\n",
        "      digitsLoc.append(listTemp)\n",
        "    \n",
        "    elif w * h > minArea:\n",
        "      listTemp = [x, y, w, h]\n",
        "      digitsLoc.append(listTemp)\n",
        "  \n",
        "  return sorted(digitsLoc, key = lambda x: x[0])"
      ],
      "execution_count": 145,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ic8U8B8bzf_p",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "0b4465fb-be6a-4dcd-b7e3-cb0fe6894af2"
      },
      "source": [
        "images_scaled=[]\n",
        "images_scaled.append(np.array(train_images[4476], dtype='float').reshape(64,64))\n",
        "sample = plt.imshow(images_scaled[0])\n",
        "plt.show()\n",
        "\n",
        "#x = findDigits(train_images[3282])\n",
        "passed = 0\n",
        "total = 0\n",
        "\n",
        "for i in range(0, 56000):\n",
        "  x = len(findDigits(train_images[i]))\n",
        "  n = 0\n",
        "  for c in train_labels[i]:\n",
        "    if c != 10:\n",
        "      n = n + 1\n",
        "  \n",
        "  if n == x:\n",
        "    passed = passed + 1\n",
        "  else:\n",
        "    print(\"Case#: \",i, \"Detected: \" ,x, \" Expected: \", n)\n",
        "  total = total + 1\n",
        "\n",
        "print(passed/total)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Case#:  264 Detected:  3  Expected:  4\n",
            "Case#:  1530 Detected:  4  Expected:  5\n",
            "Case#:  3344 Detected:  1  Expected:  2\n",
            "Case#:  3709 Detected:  3  Expected:  4\n",
            "Case#:  4142 Detected:  4  Expected:  5\n",
            "Case#:  4155 Detected:  3  Expected:  4\n",
            "Case#:  4757 Detected:  3  Expected:  4\n",
            "Case#:  5245 Detected:  1  Expected:  2\n",
            "Case#:  7023 Detected:  4  Expected:  5\n",
            "Case#:  7348 Detected:  6  Expected:  5\n",
            "Case#:  7491 Detected:  4  Expected:  5\n",
            "Case#:  7958 Detected:  5  Expected:  4\n",
            "Case#:  9140 Detected:  3  Expected:  4\n",
            "Case#:  10223 Detected:  2  Expected:  3\n",
            "Case#:  11408 Detected:  2  Expected:  3\n",
            "Case#:  11739 Detected:  4  Expected:  5\n",
            "Case#:  12629 Detected:  2  Expected:  3\n",
            "Case#:  13291 Detected:  3  Expected:  4\n",
            "Case#:  13551 Detected:  4  Expected:  5\n",
            "Case#:  16801 Detected:  3  Expected:  4\n",
            "Case#:  17768 Detected:  6  Expected:  5\n",
            "Case#:  18127 Detected:  4  Expected:  5\n",
            "Case#:  20220 Detected:  3  Expected:  4\n",
            "Case#:  22505 Detected:  1  Expected:  2\n",
            "Case#:  22884 Detected:  5  Expected:  4\n",
            "Case#:  23959 Detected:  4  Expected:  5\n",
            "Case#:  26042 Detected:  3  Expected:  4\n",
            "Case#:  27399 Detected:  4  Expected:  5\n",
            "Case#:  28246 Detected:  5  Expected:  4\n",
            "Case#:  29910 Detected:  4  Expected:  5\n",
            "Case#:  31619 Detected:  3  Expected:  2\n",
            "Case#:  32954 Detected:  3  Expected:  4\n",
            "Case#:  33640 Detected:  6  Expected:  5\n",
            "Case#:  33935 Detected:  3  Expected:  4\n",
            "Case#:  35350 Detected:  4  Expected:  5\n",
            "Case#:  37873 Detected:  5  Expected:  4\n",
            "Case#:  39165 Detected:  3  Expected:  4\n",
            "Case#:  39721 Detected:  4  Expected:  5\n",
            "Case#:  41435 Detected:  4  Expected:  3\n",
            "Case#:  42162 Detected:  3  Expected:  4\n",
            "Case#:  42649 Detected:  5  Expected:  4\n",
            "Case#:  44362 Detected:  2  Expected:  3\n",
            "Case#:  46295 Detected:  4  Expected:  3\n",
            "Case#:  46373 Detected:  4  Expected:  5\n",
            "Case#:  48651 Detected:  3  Expected:  4\n",
            "Case#:  49483 Detected:  3  Expected:  2\n",
            "Case#:  50935 Detected:  3  Expected:  4\n",
            "Case#:  53330 Detected:  1  Expected:  2\n",
            "Case#:  54436 Detected:  2  Expected:  3\n",
            "Case#:  55359 Detected:  3  Expected:  4\n",
            "0.9991071428571429\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VtJy-sffpYok"
      },
      "source": [
        "### **1.2.4 Class Distribution**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5Vwee0UprjPB",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 280
        },
        "outputId": "b5e582b4-ba09-4345-c390-e49115f11cae"
      },
      "source": [
        "unique_y1, counts_y1 = np.unique(train_labels[:, 0], return_counts=True)\n",
        "plt.bar(unique_y1, counts_y1/sum(counts_y1))\n",
        "plt.xticks(unique_y1, unique_y1)\n",
        "plt.title(f\"Class Distribution of the first column\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dAJ4C4nbrtg2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 280
        },
        "outputId": "c062afd4-ea98-4ca5-8fc3-5562fdbf70f3"
      },
      "source": [
        "unique_y2, counts_y2 = np.unique(train_labels[:, 1], return_counts=True)\n",
        "plt.bar(unique_y2, counts_y2/sum(counts_y2))\n",
        "plt.xticks(unique_y2, unique_y2)\n",
        "plt.title(f\"Class Distribution of the second column\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DQln8QrArt3D",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 280
        },
        "outputId": "de2698e6-be4a-44bf-b916-46b6e26b4149"
      },
      "source": [
        "unique_y3, counts_y3 = np.unique(train_labels[:, 2], return_counts=True)\n",
        "plt.bar(unique_y3, counts_y3/sum(counts_y3))\n",
        "plt.xticks(unique_y3, unique_y3)\n",
        "plt.title(f\"Class Distribution of the third column\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEICAYAAABRSj9aAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAcKElEQVR4nO3de7hdZWHn8e/PQEAucjGnVnIhQaJj0BaYGOoo1EcuBvVJeFrQoDKgaEqHzGCxrWF0AKNWxI51ZgyjPBJlVIgItT2joVzkYh0L5ABRSDAlhEgSbpEEUUFI4Dd/rDd0Z7NPzkrO3iew8vs8z37Ourxrve/ae5/fXvtda68l20RERHO9bEc3ICIieitBHxHRcAn6iIiGS9BHRDRcgj4iouES9BERDZegf5GRdL6kb+3odrSSdLWkU7u0riMlLW8ZXyXpmG6su6xvqaS3dWt9NeuUpK9L2iDptprLfEPSZ3rYJks6eJB575d0bbfWt716sc7oLEG/A0h6n6QBSb+R9FAJ0rfuoLZY0m9LWx6T9ENJ720tY/t425fWXNdW/3Ft/7Pt1w233aW+F4Sl7UNs39SN9W+DtwLHAuNsT2ufKek0ST/uVeWSbpL04brlbX/b9nG9ak+8+CToR5iks4EvAX8DvAqYAFwEzNyBzfpD23sBrwO+AXxZ0nndrkTSLt1e54vEgcAq27/d0Q0Zrga/Rjs323mM0APYB/gNcNJWypwPfKtl/LvAw8CvgB8Bh7TMeyewDPg1sBb4yzJ9DPB94HFgPfDPwMsGqc/AwW3TTgR+B7yyjN8EfLgMHwzcXNrzS+A7ZfqPyrp+W7bxvcDbgDXAx8s2fHPztJa6VgHnlO3YAHwd2L3MOw34caf2ArOBjcAzpb7/27K+Y8rwblQfqg+Wx5eA3cq8zW37GPAo8BDwwa28LgcA/eX5XAF8pEw/vTxXz5Z2fKptude3zX+8TP8GMB/4QXn9bgVe07LcvwOuK/UtB94zSLs+W9b9u7L+L7c8T2cA95b3wXxAnZ7XUvbMUvb+Mu2vynPyIPAhOrxPWpbfv7xuD5bX8B9a5n2kPF/ry/N3QKf3Hi3vsa208T+VNv4a+DTwGuAnwBPAFcDo7Xltd4bHDm/AzvQApgObgF22UuZ8tgz6DwF7t4TWkpZ5DwFHluH9gMPL8OeArwC7lseRm//JO9TXKeh3Le08vow//08IXA58gurb4O7AWwdbV/mH2wR8vrT/5XQO+ruB8SUw/h/wmTJvi3/29jqowvIzbfNX8W9BPw+4Bfg9oK+Ewqfb2javbO87gSeB/QZ5nn5E9c1rd+BQYB3w9sHa2bZsp+34BvAYMA3YBfg2sLDM2xNYDXywzDuM6kN1yiDrf/71aXuevg/sS/WtcR0wvVN7StnryvP/cqr36SPAG0pbLuv0PmlZ/gfAd6jeg7sCf1ymv720+/Dy+v8v4EeDvJZbbMMgbfxH4BXAIcDTwA+Bg6h2oJYBp27Pa7szPNJ1M7JeCfzS9qa6C9heYPvXtp+m+hD4Q0n7lNkbgSmSXmF7g+07Wqa/GjjQ9kZX/eK1L2pkeyPVP+j+HWZvpOqqOMD272wP1ff8HHCe7adtPzVImS/bXm17PdUe6sl12zqE9wPzbD9qex3wKeCUlvkby/yNthdR7RG/4PiBpPHAW4CPl21eAnwN+I/DbN/3bN9W3g/fpvoAAXg3VVfQ121vsn0ncBVw0jau/wLbj9t+ALixZf2dfM72+vIavQf4uu27XXVHnT/YQpJeDRwPnFHegxtt31xmvx9YYPuO8v49B3izpInbuB2bXWj7CdtLqXYOrrW90vavgKupPhA3q/Xa7iwS9CPrMWBM3X5QSaMkXSDpPklPUO2tQtU1A/CnVHsrv5B0s6Q3l+lfoPq6fK2klZLmbksjJe1KtQe8vsPsvwYE3FbOcPnQEKtbZ/t3Q5RZ3TL8C6pukm44oKxvsHU/1vah+ySw1yDrWW/7123rGjvM9j08SN0HAkdIenzzgyo0f79L6++k9TU4gBe+JoMZT/XcbOgwb4vn3/ZvqP4Htvd5e6Rl+KkO463bV/e13Skk6EfWv1B95TyhZvn3UR2kPYbq6+nEMl0AthfbnknVNfEPVP2UlG8AH7N9EDADOFvS0dvQzplUX31fcKqg7Ydtf8T2AcCfARcNcaZNnW8S41uGJ1D19ULV37/H5hmS2oNuqHU/SBWanda9LR4E9pe0d9u61tZcflsvEbsauNn2vi2PvWz/eZfWP9Q6HuKFr8lgVlM9N/t2mLfF8y9pT6pvtZ2ety1ea7b9Qy22IkE/gspXzHOB+ZJOkLSHpF0lHS/pwg6L7E31wfAY1T/B32yeIWl0OR96n9LV8gRVNwmS3i3pYEmiOmj67OZ5WyNpf0nvpzpw93nbj3Uoc5KkcWV0A1VAbF73I1R9ptvqTEnjJO1P1f//nTL9p8Ahkg6VtDsv7EIYqr7LgU9K6pM0huq53+bfKNheTdW//zlJu0v6A6qDsHXX9QgwTtLomuW/D7xW0inl/bGrpDdJev1W1r89z/tgrgBOkzRF0h7AoGdg2X6IqtvkIkn7lbYeVWZfDnywvH67Ub1/b7W9qsOqlgB/Uv4nDqZ6fqNLEvQjzPZ/B84GPkl1gGw1MIdqj7zd/6H66ruW6mDTLW3zTwFWlW6dM6i+3gNMBq6n6pf8F+Ai2zdupVk/lfQbqu6eDwN/YfvcQcq+Cbi1lO8HzrK9ssw7H7i0dDe8Zyv1tbsMuBZYCdwHfAbA9r9SHVC7nupsi/bjAZdQHaN4XFKn5+8zwADwM+Au4I7N694OJ1N9o3oQ+B7VcYfray57A7AUeFjSL4cqXLqIjgNmlfoe5t8OaHfyP4ATyw+2/mfNNm2t/qupDvzfQPWeuGGIRU6h6hP/OdVZLh8t67ke+G9UxxceojpLZtYg6/g7qjOoHgEupTpmEV2y+XSriIhoqOzRR0Q0XII+IqLhEvQREQ2XoI+IaLgX3QWMxowZ44kTJ+7oZkREvKTcfvvtv7Td12neiy7oJ06cyMDAwI5uRkTES4qkQX/BnK6biIiGS9BHRDRcgj4iouES9BERDZegj4houAR9RETD1Qp6SdMlLZe0Yms3sZD0p5IsaWrLtHPKcsslvaMbjY6IiPqGPI9e0iiq65MfS3XD3cWS+m0vayu3N3AW1U2ON0+bQnVZ0kOo7jZzvaTX2n62e5sQERFbU2ePfhqwotyb8RlgIdUdiNp9muqa2a23jZtJdcPjp23fT3Vt62nDbHNERGyDOr+MHcuW949cAxzRWkDS4cB42z+Q9Fdty97StuwL7hcpaTYwG2DChK3dtSwiYseaOPcHPVv3qgve1ZP1DvtgrKSXAV8EPra967B9se2ptqf29XW8VENERGynOnv0a9nyRsHj2PLmvnsDbwBuqm5Ryu8D/ZJm1Fg2IiJ6rM4e/WJgsqRJ5ebGs6juFQpUN7y2Pcb2RNsTqbpqZtgeKOVmSdpN0iSqe5ne1vWtiIiIQQ25R297k6Q5wDXAKGCB7aWS5gEDtvu3suxSSVdQ3dh6E3BmzriJiBhZtS5TbHsRsKht2rmDlH1b2/hngc9uZ/siImKY8svYiIiGS9BHRDRcgj4iouES9BERDZegj4houAR9RETDJegjIhouQR8R0XAJ+oiIhkvQR0Q0XII+IqLhEvQREQ2XoI+IaLgEfUREwyXoIyIaLkEfEdFwCfqIiIarFfSSpktaLmmFpLkd5p8h6S5JSyT9WNKUMn2ipKfK9CWSvtLtDYiIiK0b8laCkkYB84FjgTXAYkn9tpe1FLvM9ldK+RnAF4HpZd59tg/tbrMjIqKuOnv004AVtlfafgZYCMxsLWD7iZbRPQF3r4kRETEcdYJ+LLC6ZXxNmbYFSWdKug+4EPgvLbMmSbpT0s2SjuxUgaTZkgYkDaxbt24bmh8REUPp2sFY2/Ntvwb4OPDJMvkhYILtw4CzgcskvaLDshfbnmp7al9fX7eaFBER1Av6tcD4lvFxZdpgFgInANh+2vZjZfh24D7gtdvX1IiI2B51gn4xMFnSJEmjgVlAf2sBSZNbRt8F3Fum95WDuUg6CJgMrOxGwyMiop4hz7qxvUnSHOAaYBSwwPZSSfOAAdv9wBxJxwAbgQ3AqWXxo4B5kjYCzwFn2F7fiw2JiIjOhgx6ANuLgEVt085tGT5rkOWuAq4aTgMjImJ48svYiIiGS9BHRDRcgj4iouES9BERDZegj4houAR9RETDJegjIhouQR8R0XAJ+oiIhkvQR0Q0XII+IqLhEvQREQ2XoI+IaLgEfUREwyXoIyIaLkEfEdFwCfqIiIarFfSSpktaLmmFpLkd5p8h6S5JSyT9WNKUlnnnlOWWS3pHNxsfERFDGzLoy8295wPHA1OAk1uDvLjM9httHwpcCHyxLDuF6mbihwDTgYs23yw8IiJGRp09+mnACtsrbT8DLARmthaw/UTL6J6Ay/BMYKHtp23fD6wo64uIiBFS5+bgY4HVLeNrgCPaC0k6EzgbGA28vWXZW9qWHdth2dnAbIAJEybUaXdERNTUtYOxtufbfg3wceCT27jsxban2p7a19fXrSZFRAT1gn4tML5lfFyZNpiFwAnbuWxERHRZnaBfDEyWNEnSaKqDq/2tBSRNbhl9F3BvGe4HZknaTdIkYDJw2/CbHRERdQ3ZR297k6Q5wDXAKGCB7aWS5gEDtvuBOZKOATYCG4BTy7JLJV0BLAM2AWfafrZH2xIRER3UORiL7UXAorZp57YMn7WVZT8LfHZ7GxgREcOTX8ZGRDRcgj4iouES9BERDZegj4houAR9RETDJegjIhouQR8R0XAJ+oiIhkvQR0Q0XII+IqLhEvQREQ2XoI+IaLgEfUREwyXoIyIaLkEfEdFwCfqIiIarFfSSpktaLmmFpLkd5p8taZmkn0n6oaQDW+Y9K2lJefS3LxsREb015B2mJI0C5gPHAmuAxZL6bS9rKXYnMNX2k5L+HLgQeG+Z95TtQ7vc7oiIqKnOHv00YIXtlbafARYCM1sL2L7R9pNl9BZgXHebGRER26tO0I8FVreMrynTBnM6cHXL+O6SBiTdIumE7WhjREQMQ62bg9cl6QPAVOCPWyYfaHutpIOAGyTdZfu+tuVmA7MBJkyY0M0mRUTs9Ors0a8FxreMjyvTtiDpGOATwAzbT2+ebntt+bsSuAk4rH1Z2xfbnmp7al9f3zZtQEREbF2doF8MTJY0SdJoYBawxdkzkg4DvkoV8o+2TN9P0m5leAzwFqD1IG5ERPTYkF03tjdJmgNcA4wCFtheKmkeMGC7H/gCsBfwXUkAD9ieAbwe+Kqk56g+VC5oO1snIiJ6rFYfve1FwKK2aee2DB8zyHI/Ad44nAZGRMTw5JexERENl6CPiGi4BH1ERMMl6CMiGi5BHxHRcAn6iIiGS9BHRDRcgj4iouES9BERDZegj4houAR9RETDJegjIhouQR8R0XAJ+oiIhkvQR0Q0XII+IqLhEvQREQ1XK+glTZe0XNIKSXM7zD9b0jJJP5P0Q0kHtsw7VdK95XFqNxsfERFDGzLoJY0C5gPHA1OAkyVNaSt2JzDV9h8AVwIXlmX3B84DjgCmAedJ2q97zY+IiKHU2aOfBqywvdL2M8BCYGZrAds32n6yjN4CjCvD7wCus73e9gbgOmB6d5oeERF11An6scDqlvE1ZdpgTgeu3pZlJc2WNCBpYN26dTWaFBERdXX1YKykDwBTgS9sy3K2L7Y91fbUvr6+bjYpImKnVyfo1wLjW8bHlWlbkHQM8Alghu2nt2XZiIjonTpBvxiYLGmSpNHALKC/tYCkw4CvUoX8oy2zrgGOk7RfOQh7XJkWEREjZJehCtjeJGkOVUCPAhbYXippHjBgu5+qq2Yv4LuSAB6wPcP2ekmfpvqwAJhne31PtiQiIjoaMugBbC8CFrVNO7dl+JitLLsAWLC9DYyIiOHJL2MjIhouQR8R0XAJ+oiIhkvQR0Q0XII+IqLhEvQREQ2XoI+IaLgEfUREwyXoIyIaLkEfEdFwCfqIiIZL0EdENFyCPiKi4RL0ERENl6CPiGi4BH1ERMMl6CMiGq5W0EuaLmm5pBWS5naYf5SkOyRtknRi27xnJS0pj/72ZSMioreGvJWgpFHAfOBYYA2wWFK/7WUtxR4ATgP+ssMqnrJ9aBfaGhER26HOPWOnAStsrwSQtBCYCTwf9LZXlXnP9aCNERExDHW6bsYCq1vG15Rpde0uaUDSLZJO6FRA0uxSZmDdunXbsOqIiBjKSByMPdD2VOB9wJckvaa9gO2LbU+1PbWvr28EmhQRsfOoE/RrgfEt4+PKtFpsry1/VwI3AYdtQ/siImKY6gT9YmCypEmSRgOzgFpnz0jaT9JuZXgM8BZa+vYjIqL3hgx625uAOcA1wD3AFbaXSponaQaApDdJWgOcBHxV0tKy+OuBAUk/BW4ELmg7WyciInqszlk32F4ELGqbdm7L8GKqLp325X4CvHGYbYyIiGHIL2MjIhouQR8R0XAJ+oiIhkvQR0Q0XII+IqLhEvQREQ2XoI+IaLgEfUREwyXoIyIaLkEfEdFwCfqIiIZL0EdENFyCPiKi4RL0ERENl6CPiGi4BH1ERMMl6CMiGq5W0EuaLmm5pBWS5naYf5SkOyRtknRi27xTJd1bHqd2q+EREVHPkEEvaRQwHzgemAKcLGlKW7EHgNOAy9qW3R84DzgCmAacJ2m/4Tc7IiLqqrNHPw1YYXul7WeAhcDM1gK2V9n+GfBc27LvAK6zvd72BuA6YHoX2h0RETXVCfqxwOqW8TVlWh21lpU0W9KApIF169bVXHVERNTxojgYa/ti21NtT+3r69vRzYmIaJQ6Qb8WGN8yPq5Mq2M4y0ZERBfUCfrFwGRJkySNBmYB/TXXfw1wnKT9ykHY48q0iIgYIUMGve1NwByqgL4HuML2UknzJM0AkPQmSWuAk4CvSlpall0PfJrqw2IxMK9Mi4iIEbJLnUK2FwGL2qad2zK8mKpbptOyC4AFw2hjREQMw4viYGxERPROgj4iouES9BERDZegj4houAR9RETDJegjIhouQR8R0XAJ+oiIhkvQR0Q0XII+IqLhEvQREQ1X61o3MbiJc3/Qk/WuuuBdPVlvROx8skcfEdFwCfqIiIZL181LTK+6iqBzd9FI1xfdl+7FaFzQ50390rYzfLDkPdpdO8N7ZrgaF/QRsWMleF98avXRS5ouabmkFZLmdpi/m6TvlPm3SppYpk+U9JSkJeXxle42PyIihjLkHr2kUcB84FhgDbBYUr/tZS3FTgc22D5Y0izg88B7y7z7bB/a5XZHdE26UqLp6uzRTwNW2F5p+xlgITCzrcxM4NIyfCVwtCR1r5kREbG96gT9WGB1y/iaMq1jGdubgF8BryzzJkm6U9LNko7sVIGk2ZIGJA2sW7dumzYgIiK2rtfn0T8ETLB9GHA2cJmkV7QXsn2x7am2p/b19fW4SRERO5c6Qb8WGN8yPq5M61hG0i7APsBjtp+2/RiA7duB+4DXDrfRERFRX52gXwxMljRJ0mhgFtDfVqYfOLUMnwjcYNuS+srBXCQdBEwGVnan6RERUceQZ93Y3iRpDnANMApYYHuppHnAgO1+4BLgm5JWAOupPgwAjgLmSdoIPAecYXt9LzYkIiI6q/WDKduLgEVt085tGf4dcFKH5a4CrhpmGyMiYhhyUbOIiIZL0EdENFyCPiKi4RL0ERENl6CPiGi4BH1ERMMl6CMiGi5BHxHRcAn6iIiGS9BHRDRcgj4iouES9BERDZegj4houAR9RETDJegjIhouQR8R0XAJ+oiIhqsV9JKmS1ouaYWkuR3m7ybpO2X+rZImtsw7p0xfLukd3Wt6RETUMWTQl5t7zweOB6YAJ0ua0lbsdGCD7YOBvwM+X5adQnX/2EOA6cBFm28WHhERI6POHv00YIXtlbafARYCM9vKzAQuLcNXAkdLUpm+0PbTtu8HVpT1RUTECJHtrReQTgSm2/5wGT8FOML2nJYyd5cya8r4fcARwPnALba/VaZfAlxt+8q2OmYDs8vo64Dlw9+0WsYAvxyhulJfM+pMfS/t+nZEnSNV34G2+zrN2GUEKh+S7YuBi0e6XkkDtqemvpdmfTuiztT30q5vR9S5I7axXZ2um7XA+JbxcWVaxzKSdgH2AR6ruWxERPRQnaBfDEyWNEnSaKqDq/1tZfqBU8vwicANrvqE+oFZ5aycScBk4LbuND0iIuoYsuvG9iZJc4BrgFHAAttLJc0DBmz3A5cA35S0AlhP9WFAKXcFsAzYBJxp+9kebcv2GOnuotT30q8z9b2069sRde6IbdzCkAdjIyLipS2/jI2IaLgEfUREw+2UQT/UJR16UN8CSY+W3xv0nKTxkm6UtEzSUkln9bi+3SXdJumnpb5P9bK+lnpHSbpT0vdHoK5Vku6StETSQK/rK3XuK+lKST+XdI+kN/ewrteVbdv8eELSR3tVX6nzL8r75W5Jl0vavcf1nVXqWtqrbev0vy5pf0nXSbq3/N2vF3Vvle2d6kF1QPk+4CBgNPBTYEqP6zwKOBy4e4S28dXA4WV4b+Bfe7mNgIC9yvCuwK3AH43Adp4NXAZ8fwTqWgWMGYnXr6XOS4EPl+HRwL4jVO8o4GGqH+D0qo6xwP3Ay8v4FcBpPazvDcDdwB5UJ6FcDxzcg3pe8L8OXAjMLcNzgc+P5PvI9k65R1/nkg5dZftHVGcjjQjbD9m+owz/GriH6h+rV/XZ9m/K6K7l0dOj/JLGAe8CvtbLenYUSftQhcYlALafsf34CFV/NHCf7V/0uJ5dgJeX397sATzYw7peD9xq+0nbm4CbgT/pdiWD/K+3XiLmUuCEbtc7lJ0x6McCq1vG19DDENzRypVED6Pay+5lPaMkLQEeBa6z3dP6gC8Bfw081+N6NjNwraTbyyU7em0SsA74eume+pqkPUegXqhOj768lxXYXgv8LfAA8BDwK9vX9rDKu4EjJb1S0h7AO9nyx5y99CrbD5Xhh4FXjVC9z9sZg36nIWkv4Crgo7af6GVdtp+1fSjVr5+nSXpDr+qS9G7gUdu396qODt5q+3Cqq7ieKemoHte3C1UXwP+2fRjwW6qv/T1VfhQ5A/huj+vZj2pPdxJwALCnpA/0qj7b91BdVfda4J+AJcCI/6bHVf/NiJ/TvjMG/U5xWQZJu1KF/Ldt//1I1Vu6F26kuix1r7wFmCFpFVXX29slfauH9W3eA8X2o8D36P1VWNcAa1q+GV1JFfy9djxwh+1HelzPMcD9ttfZ3gj8PfAfelmh7Uts/3vbRwEbqI5djYRHJL0aoPx9dITqfd7OGPR1LunwklYuEX0JcI/tL45AfX2S9i3DLweOBX7eq/psn2N7nO2JVK/fDbZ7tjcoaU9Je28eBo6j6groGdsPA6slva5MOprqF+a9djI97rYpHgD+SNIe5f16NNWxpJ6R9Hvl7wSq/vnLellfi9ZLxJwK/OMI1fu8F8XVK0eSB7mkQy/rlHQ58DZgjKQ1wHm2L+lhlW8BTgHuKv3mAP/V9qIe1fdq4FJVN5V5GXCF7Z6f8jiCXgV8r8ojdgEus/1PI1Dvfwa+XXZIVgIf7GVl5UPsWODPelkPgO1bJV0J3EF1eZQ76f2lAq6S9EpgI9XlWLp+cLvT/zpwAXCFpNOBXwDv6Xa9Q7arnPITERENtTN23URE7FQS9BERDZegj4houAR9RETDJegjIhouQR8R0XAJ+oiIhvv/UUk7HK3n0TAAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ADQMb2X6ruMT",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 280
        },
        "outputId": "a4e7aed3-a97f-4c39-e2af-849529ab47ac"
      },
      "source": [
        "unique_y4, counts_y4 = np.unique(train_labels[:, 3], return_counts=True)\n",
        "plt.bar(unique_y4, counts_y4/sum(counts_y4))\n",
        "plt.xticks(unique_y4, unique_y4)\n",
        "plt.title(f\"Class Distribution of the fourth column\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vYuwvAWQru7I",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 280
        },
        "outputId": "a2b31265-09cb-40d8-905b-978ae5ee0b60"
      },
      "source": [
        "unique_y5, counts_y5 = np.unique(train_labels[:, 4], return_counts=True)\n",
        "plt.bar(unique_y5, counts_y5/sum(counts_y5))\n",
        "plt.xticks(unique_y5, unique_y5)\n",
        "plt.title(f\"Class Distribution of the fifth column\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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PiChEAj0iohAJ9IiIQiTQIyIKkUCPiChEAj0iohAJ9IiIQiTQIyIKkUCPiChEAj0iohAJ9IiIQiTQIyIKkUCPiChEAj0iohCNAl3SYknbJY1IWj3BuBdJsqSFg2sxIiKa6BvokqYBa4ElwAJghaQFPcYdB7wBuGrQTUZERH9NttAXASO2d9i+C1gPLOsx7h3Ae4BfDbC/iIhoqEmgzwR2dUzvruf9lqSnALNtf2GiFUlaKWmTpE2jo6OTbjYiIsZ3wAdFJT0AeD/wpn5jba+zvdD2wqGhoQMtHRERHZoE+h5gdsf0rHremOOAJwJfkbQTeDownAOjERFTq0mgbwTmS5onaTqwHBgeW2j7Z7Zn2J5rey7wLWCp7U2tdBwRET31DXTb+4BVwGXANuAS21skrZG0tO0GIyKimSOaDLK9AdjQNe/cccaeduBtRUTEZOWTohERhUigR0QUIoEeEVGIBHpERCES6BERhUigR0QUIoEeEVGIBHpERCES6BERhUigR0QUIoEeEVGIBHpERCES6BERhUigR0QUIoEeEVGIBHpERCES6BERhWgU6JIWS9ouaUTS6h7LXyvp+5I2S/q6pAWDbzUiIibSN9AlTQPWAkuABcCKHoF9ke3fsf1k4L3A+wfeaURETKjJFvoiYMT2Dtt3AeuBZZ0DbP+8Y/IYwINrMSIimmhykeiZwK6O6d3A07oHSXodcDYwHXhOrxVJWgmsBJgzZ85ke42IiAkM7KCo7bW2Hw28GThnnDHrbC+0vXBoaGhQpSMigmaBvgeY3TE9q543nvXACw+kqYiImLwmgb4RmC9pnqTpwHJguHOApPkdk88Hfji4FiMioom++9Bt75O0CrgMmAacb3uLpDXAJtvDwCpJZwB7gduAV7TZdERE7K/JQVFsbwA2dM07t+P+GwbcV0RETFI+KRoRUYgEekREIRLoERGFSKBHRBQigR4RUYgEekREIRLoERGFSKBHRBQigR4RUYgEekREIRLoERGFSKBHRBQigR4RUYgEekREIRLoERGFSKBHRBQigR4RUYhGgS5psaTtkkYkre6x/GxJWyV9T9L/lXTS4FuNiIiJ9A10SdOAtcASYAGwQtKCrmHfBRbafhJwKfDeQTcaERETa7KFvggYsb3D9l3AemBZ5wDbV9j+ZT35LWDWYNuMiIh+mgT6TGBXx/Tuet54XgX8W68FklZK2iRp0+joaPMuIyKir4EeFJX0J8BC4H29ltteZ3uh7YVDQ0ODLB0Rcdg7osGYPcDsjulZ9bx7kXQG8DfA79v+9WDai4iIpppsoW8E5kuaJ2k6sBwY7hwg6RTgn4Cltm8afJsREdFP30C3vQ9YBVwGbAMusb1F0hpJS+th7wOOBT4labOk4XFWFxERLWmyywXbG4ANXfPO7bh/xoD7ioiISconRSMiCpFAj4goRAI9IqIQCfSIiEIk0CMiCpFAj4goRAI9IqIQCfSIiEIk0CMiCpFAj4goRAI9IqIQCfSIiEIk0CMiCpFAj4goRAI9IqIQCfSIiEIk0CMiCtEo0CUtlrRd0oik1T2WP1vS1ZL2SXrx4NuMiIh++ga6pGnAWmAJsABYIWlB17DrgbOAiwbdYERENNPkmqKLgBHbOwAkrQeWAVvHBtjeWS/7TQs9RkREA012ucwEdnVM767nTZqklZI2Sdo0Ojp6X1YRERHjmNKDorbX2V5oe+HQ0NBUlo6IKF6TQN8DzO6YnlXPi4iI+5Emgb4RmC9pnqTpwHJguN22IiJisvoGuu19wCrgMmAbcIntLZLWSFoKIOmpknYDLwH+SdKWNpuOiIj9NTnLBdsbgA1d887tuL+RaldMREQcJPmkaEREIRLoERGFSKBHRBQigR4RUYgEekREIRLoERGFSKBHRBQigR4RUYgEekREIRLoERGFSKBHRBQigR4RUYgEekREIRLoERGFaPT1uYe7uau/0Nq6d777+a2tOw4vbb1O8xo9dBySgX44BOxU/+cspd54NUuvdzCU8pq5vzyfg5BdLhERhWgU6JIWS9ouaUTS6h7LHyjpk/XyqyTNHXSjERExsb6BLmkasBZYAiwAVkha0DXsVcBttk8GPgC8Z9CNRkTExJpsoS8CRmzvsH0XsB5Y1jVmGXBhff9S4HRJGlybERHRj2xPPEB6MbDY9qvr6ZcDT7O9qmPMtfWY3fX0j+oxN3etayWwsp58LLB9UA+kjxnAzX1HpV7qHZx6B6Nm6h269U6yPdRrwZSe5WJ7HbBuKmsCSNpke2Hqpd79sd7BqJl6h3a98TTZ5bIHmN0xPaue13OMpCOA44FbBtFgREQ00yTQNwLzJc2TNB1YDgx3jRkGXlHffzHwZffblxMREQPVd5eL7X2SVgGXAdOA821vkbQG2GR7GDgP+JikEeBWqtC/P5nq3Typl3r395qpd2jX66nvQdGIiDg05JOiERGFSKBHRBSi6EDv95UFLdQ7X9JN9Xn5bdeaLekKSVslbZH0himoeZSkb0u6pq759rZr1nWnSfqupM9PQa2dkr4vabOkTVNQ7yGSLpX0H5K2SXpGi7UeWz+usdvPJf1FW/U66r6xfr1cK+liSUe1XO8Nda0tbTy+Xv/PJZ0g6YuSflj/+9BB123EdpE3qgO4PwIeBUwHrgEWtFzz2cBTgGun4PE9AnhKff844AdT8PgEHFvfPxK4Cnj6FDzWs4GLgM9PQa2dwIy263TUuxB4dX1/OvCQKao7DbiR6kMqbdaZCfwYeFA9fQlwVov1nghcCxxNddLHl4CTB1xjv//nwHuB1fX91cB7puo11HkreQu9yVcWDJTtK6nO8mmd7RtsX13fvwPYRvWfp82atn1nPXlkfWv1qLqkWcDzgY+0WedgkHQ8VTicB2D7Ltu3T1H504Ef2b5uCmodATyo/ozK0cBPWqz1eOAq27+0vQ/4KvDfBllgnP/nnV9/ciHwwkHWbKrkQJ8J7OqY3k3LgXew1N9ueQrVFnPbtaZJ2gzcBHzRdts1Pwj8FfCbluuMMXC5pO/UX1XRpnnAKPDRepfSRyQd03LNMcuBi9suYnsP8PfA9cANwM9sX95iyWuBZ0l6mKSjgedx7w9GtuVE2zfU928ETpyCmvspOdAPC5KOBT4N/IXtn7ddz/bdtp9M9YnhRZKe2FYtSS8AbrL9nbZq9PBM20+h+nbR10l6dou1jqB66/6/bZ8C/ILq7Xqr6g8ILgU+NQW1Hkq19ToPeCRwjKQ/aaue7W1U3/Z6OfDvwGbg7rbqjdODafmd63hKDvQmX1lwSJN0JFWYf8L2Z6aydr1r4ApgcYtlTgWWStpJtcvsOZI+3mK9sS1KbN8EfJZq111bdgO7O97lXEoV8G1bAlxt+6dTUOsM4Me2R23vBT4D/Nc2C9o+z/bv2X42cBvV8aW2/VTSIwDqf2+agpr7KTnQm3xlwSGr/nri84Bttt8/RTWHJD2kvv8g4EzgP9qqZ/sttmfZnkv1+/uy7da27iQdI+m4sfvAc6newrfC9o3ALkmPrWedDmxtq16HFUzB7pba9cDTJR1dv2ZPpzre0xpJD6//nUO1//yiNuvVOr/+5BXAv0xBzf0cktcUbcLjfGVBmzUlXQycBsyQtBt4q+3zWip3KvBy4Pv1Pm2Av7a9oaV6UJ1Zc2F90ZMHAJfYbv1Uwil0IvDZ+qv8jwAusv3vLdd8PfCJeqNjB/DKNovVf6jOBP6szTpjbF8l6VLgamAf8F3a/5j8pyU9DNgLvG7QB5p7/T8H3g1cIulVwHXASwdZs3Fv9Wk2ERFxiCt5l0tExGElgR4RUYgEekREIRLoERGFSKBHRBQigR4RUYgEekREIf4/cLCqfXXxt+sAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SlLoNgfSoKD2"
      },
      "source": [
        "### **1.2.4 Calculate the bounds of the images**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NF7LOKX5oJRk"
      },
      "source": [
        "def lowerBound(x):\n",
        "  N = x.shape[1]\n",
        "  D = x.shape[0]\n",
        "  lowerBounds = [0]*D\n",
        "  bound = x[0, 0]\n",
        "  for i in list(range(0, D)):\n",
        "    for j in list(range(0, N)):\n",
        "      if torch.all(torch.eq(x[i, j], bound)):\n",
        "        lowerBounds[i] = j + 1\n",
        "      else:\n",
        "        break\n",
        "  return min(lowerBounds)\n",
        "  \n",
        "def upperBound(x):\n",
        "  N = x.shape[1]\n",
        "  D = x.shape[0]\n",
        "  upperBounds = [64]*D\n",
        "  bound = x[0, 0]\n",
        "  for i in list(range(0, D)):\n",
        "    for j in list(range(0, N)):\n",
        "      if torch.all(torch.eq(x[i, 63-j], bound)):\n",
        "        upperBounds[i] = 63-j\n",
        "      else:\n",
        "        break\n",
        "  return max(upperBounds)"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aDiUbLpdIdkF"
      },
      "source": [
        "def leftBound(x):\n",
        "  N = x.shape[2]\n",
        "  D = x.shape[0]\n",
        "  leftBounds = [0]*D\n",
        "  bound = x[0, :, 0]\n",
        "  for i in list(range(0, D)):\n",
        "    for j in list(range(0, N)):\n",
        "      if torch.all(torch.eq(x[i, :, j], bound)):\n",
        "        leftBounds[i] = j + 1\n",
        "      else:\n",
        "        break\n",
        "  return min(leftBounds)\n",
        "  \n",
        "def rightBound(x):\n",
        "  N = x.shape[2]\n",
        "  D = x.shape[0]\n",
        "  rightBounds = [64]*D\n",
        "  bound = x[0, :, 0]\n",
        "  for i in list(range(0, D)):\n",
        "    for j in list(range(0, N)):\n",
        "      if torch.all(torch.eq(x[i, :, 63 - j], bound)):\n",
        "        rightBounds[i] = 63 - j\n",
        "      else:\n",
        "        break\n",
        "  return max(rightBounds)"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "metobBdpqBXv",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3669fe40-bdfb-4480-e4fa-16e9da48abbd"
      },
      "source": [
        "u = upperBound(X_train)\n",
        "l = lowerBound(X_train)\n",
        "l2 = leftBound(X_train)\n",
        "r = rightBound(X_train)\n",
        "\n",
        "print(\"Upper bound: \", u,\", Lower bound:\", l, \", Left bound: \", l2,\", Right bound:\", r)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Upper bound:  38 , Lower bound: 26 , Left bound:  2 , Right bound: 62\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g7ghhGf6wzaV"
      },
      "source": [
        "### **1.2.5 Partitioning the data**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 108
        },
        "id": "iEzyQ6MNoBnr",
        "outputId": "93109aad-ac60-494a-ca0a-724cf834c871"
      },
      "source": [
        "images=[]\n",
        "titles=[]\n",
        "images.append(np.array(train_images[0], dtype='float').reshape(64,64))\n",
        "titles.append(\"img_1\")\n",
        "images.append(np.array(train_images[2], dtype='float').reshape(64,64))\n",
        "titles.append(\"img_2\")\n",
        "images.append(np.array(train_images[5], dtype='float').reshape(64,64))\n",
        "titles.append(\"img_3\")\n",
        "images.append(np.array(train_images[9], dtype='float').reshape(64,64))\n",
        "titles.append(\"img_4\")\n",
        "images.append(np.array(train_images[26], dtype='float').reshape(64,64))\n",
        "titles.append(\"img_5\")\n",
        "\n",
        "for i in range(5):\n",
        "    plt.subplot(1,5,i+1),plt.imshow(images[i])\n",
        "    plt.title(titles[i])\n",
        "    plt.xticks([]),plt.yticks([])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 5 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "JK0E9O98qRmR",
        "outputId": "386d1a2c-4c3f-4af7-decb-e79a8409fad6"
      },
      "source": [
        "x_try = X_train[0].reshape(64, 64)\n",
        "#x_try = np.float32(x_try).reshape(64, 64)\n",
        "plt.imshow(x_try)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7efd2f594fd0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Uiuu_L9T4XJ7"
      },
      "source": [
        "def leftBound_digit(x, initial_column):\n",
        "  N = x.shape[1] #column\n",
        "  leftBound = 0\n",
        "  bound = torch.full(x[:, 0].shape, 0.2)\n",
        "  for i in list(range(initial_column, N)):\n",
        "    if torch.all(torch.le(x[:, i], bound)):\n",
        "      leftBound = i + 1\n",
        "    else:\n",
        "      break\n",
        "  return leftBound"
      ],
      "execution_count": 123,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gCell7HW-kbp"
      },
      "source": [
        "def rightBound_digit(x, initial_column):\n",
        "  N = x.shape[1] #column\n",
        "  leftBound = 0\n",
        "  bound = torch.full(x[:, 0].shape, 0.2)\n",
        "  for i in list(range(initial_column, N)):\n",
        "    if torch.all(torch.le(x[:, i], bound)) == False:\n",
        "      leftBound = i + 1\n",
        "    else:\n",
        "      break\n",
        "  return leftBound"
      ],
      "execution_count": 124,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1-vRjRk4AmA8"
      },
      "source": [
        "l1_1 = leftBound_digit(x_try, 0)\n",
        "l1_2 = rightBound_digit(x_try, l1_1)\n",
        "l2_1 = leftBound_digit(x_try, l1_2)\n",
        "l2_2 = rightBound_digit(x_try, l2_1)\n",
        "l3_1 = leftBound_digit(x_try, l2_2)\n",
        "l3_2 = rightBound_digit(x_try, l3_1)\n",
        "l4_1 = leftBound_digit(x_try, l3_2)\n",
        "l4_2 = rightBound_digit(x_try, l4_1)"
      ],
      "execution_count": 125,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "IxDFAMsCB4wZ",
        "outputId": "bb33678e-1d96-46bb-e520-f6b738e4930b"
      },
      "source": [
        "plt.imshow(x_try[26:38 ,l1_1:l1_2])"
      ],
      "execution_count": 126,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7efd268136d8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 126
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fu5bW5h1VHLw",
        "outputId": "354c5524-ecff-4154-ef79-7b47ecdd0a7e"
      },
      "source": [
        "np.array(x_try[26:38 ,l1_1])"
      ],
      "execution_count": 163,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.        , 0.        , 0.        , 0.        , 0.        ,\n",
              "       0.        , 0.        , 0.00784314, 0.40392157, 0.45882353,\n",
              "       0.05098039, 0.        ], dtype=float32)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 163
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "Kf5QRoi1CAgT",
        "outputId": "0b15ba1e-1740-4854-858e-aebaa96d1a90"
      },
      "source": [
        "plt.imshow(x_try[26:38 ,l2_1:l2_2])"
      ],
      "execution_count": 128,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7efd267e3c18>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 128
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iR6KrnzNWrrJ",
        "outputId": "f0579914-e9e7-49c7-d3cc-f5a5c5045eb8"
      },
      "source": [
        "np.array(x_try[26:38 ,l2_1+1])"
      ],
      "execution_count": 160,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.        , 0.        , 0.        , 0.        , 0.08627451,\n",
              "       0.43529412, 0.01960784, 0.06666667, 0.85490197, 0.21960784,\n",
              "       0.        , 0.        ], dtype=float32)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 160
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "b0hz_-SaCVem",
        "outputId": "77ad410c-44c1-418d-ad77-bc3de4bc913f"
      },
      "source": [
        "plt.imshow(x_try[26:38 ,l3_1:l3_2])"
      ],
      "execution_count": 129,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7efd26ea5128>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 129
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wzXMdP5LV6rF",
        "outputId": "4fc347f5-1099-4e2d-8eaf-93da4f106d91"
      },
      "source": [
        "np.array(x_try[26:38 ,l3_1])"
      ],
      "execution_count": 131,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.        , 0.        , 0.        , 0.        , 0.        ,\n",
              "       0.01176471, 0.16470589, 0.28235295, 0.5921569 , 0.44705883,\n",
              "       0.0627451 , 0.        ], dtype=float32)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 131
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "3AXJcCZ3CYN-",
        "outputId": "1cc9fc1f-39e4-4939-fab4-be655d164992"
      },
      "source": [
        "plt.imshow(x_try[26:38 ,l4_1:l4_2])"
      ],
      "execution_count": 132,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7efd26b3ce10>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 132
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AtY_2IPmKnb_",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "29836d49-1a0f-40f5-dc35-a09270929b16"
      },
      "source": [
        "l5_1 = leftBound_digit(x_try, l4_2)\n",
        "l5_2 = rightBound_digit(x_try, l5_1)\n",
        "print(\" l5_1: \", l5_1, \"l5_2: \", l5_2) #think about how to handle this\n",
        "'''\n",
        "if(l == 64 && r == 0):\n",
        "  the digit = torch.zeros((12, 12))\n",
        "'''"
      ],
      "execution_count": 133,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            " l5_1:  64 l5_2:  0\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'\\nif(l == 64 && r == 0):\\n  the digit = torch.zeros((12, 12))\\n'"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 133
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WZERYd8TFhhl",
        "outputId": "c6d24ea2-d9d1-426b-b2aa-f49fab573fbe"
      },
      "source": [
        "x_try[26:38,l1_1:l1_2].shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([12, 10])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YUkU-fLjFk3T"
      },
      "source": [
        "x_try1 = torch.zeros((12, 12))\n",
        "x_try1[0:12, 0: x_try[26:38,l1_1:l1_2].shape[1]] = x_try[26:38,l1_1:l1_2]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tEj4F2uAMStH"
      },
      "source": [
        "x_try2 = torch.zeros((12, 12))\n",
        "x_try2[0:12, 0: x_try[26:38,l2_1:l2_2].shape[1]] = x_try[26:38,l2_1:l2_2]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H22HWh-pMTBQ"
      },
      "source": [
        "x_try3 = torch.zeros((12, 12))\n",
        "x_try3[0:12, 0: x_try[26:38,l3_1:l3_2].shape[1]] = x_try[26:38,l3_1:l3_2]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ExqiRQdnMTTP"
      },
      "source": [
        "x_try4 = torch.zeros((12, 12))\n",
        "x_try4[0:12, 0: x_try[26:38,l4_1:l4_2].shape[1]] = x_try[26:38,l4_1:l4_2]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5r_J7KSwMnCc"
      },
      "source": [
        "x_try5 = torch.zeros((12, 12))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uULnY2VxM6KA",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0fc3274b-c6d2-4e8a-b565-6bc483ac833c"
      },
      "source": [
        "x_try0 = torch.stack((x_try1, x_try2, x_try3, x_try4, x_try5))\n",
        "x_try0.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([5, 12, 12])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 108
        },
        "id": "cnSIGZZlHScx",
        "outputId": "4576c162-fbfa-4ba3-d242-9f586cb1b635"
      },
      "source": [
        "for i in range(5):\n",
        "    plt.subplot(1,5,i+1),plt.imshow(x_try0[i, :, :])\n",
        "    plt.title(titles[i])\n",
        "    plt.xticks([]),plt.yticks([])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 5 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V2wzc_uZZCTk"
      },
      "source": [
        "def partition_image(x):\n",
        "  x = x.reshape(64, 64)\n",
        "  l = leftBound_digit(x, 0)\n",
        "  r = rightBound_digit(x, l)\n",
        "  x_1 = torch.zeros((14, 14))\n",
        "  x_1[0:12, 0: x[26:38,l:r].shape[1]] = x[26:38,l:r]\n",
        "\n",
        "  l = leftBound_digit(x, r)\n",
        "  if l == 64: #i.e. one digit\n",
        "    x_2 = torch.zeros((14, 14))\n",
        "    x_3 = torch.zeros((14, 14))\n",
        "    x_4 = torch.zeros((14, 14))\n",
        "    x_5 = torch.zeros((14, 14))\n",
        "  else:\n",
        "    r = rightBound_digit(x, l)\n",
        "    x_2 = torch.zeros((14, 14))\n",
        "    x_2[0:12, 0: x[26:38,l:r].shape[1]] = x[26:38,l:r]\n",
        "\n",
        "    l = leftBound_digit(x, r)\n",
        "\n",
        "    if l == 64: #i.e. two digits\n",
        "      x_3 = torch.zeros((14, 14))\n",
        "      x_4 = torch.zeros((14, 14))\n",
        "      x_5 = torch.zeros((14, 14))\n",
        "    else:\n",
        "      r = rightBound_digit(x, l)\n",
        "      x_3 = torch.zeros((14, 14))\n",
        "      x_3[0:12, 0: x[26:38,l:r].shape[1]] = x[26:38,l:r]\n",
        "      l = leftBound_digit(x, r)\n",
        "\n",
        "      if l == 64: #i.e. three digits\n",
        "        x_4 = torch.zeros((14, 14))\n",
        "        x_5 = torch.zeros((14, 14))\n",
        "      else:\n",
        "        r = rightBound_digit(x, l)\n",
        "        x_4 = torch.zeros((14, 14))\n",
        "        x_4[0:12, 0: x[26:38,l:r].shape[1]] = x[26:38,l:r]\n",
        "        l = leftBound_digit(x, r)\n",
        "\n",
        "        if l == 64:  #i.e. four digits\n",
        "          x_5 = torch.zeros((14, 14))\n",
        "        else: #i.e. five digits\n",
        "          r = rightBound_digit(x, l)\n",
        "          x_5 = torch.zeros((14, 14))\n",
        "          x_5[0:12, 0: x[26:38,l:r].shape[1]] = x[26:38,l:r]\n",
        "    \n",
        "  x_0 = torch.stack((x_1, x_2, x_3, x_4, x_5))\n",
        "\n",
        "  return x_0"
      ],
      "execution_count": 134,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ltEpUY3XGNm7"
      },
      "source": [
        "#this code checks the accuracy per image\n",
        "def partition_image_number_of_digits_accuracy(x):\n",
        "  x = x.reshape(64, 64)\n",
        "  l = leftBound_digit(x, 0)\n",
        "  r = rightBound_digit(x, l)\n",
        "  l = leftBound_digit(x, r)\n",
        "  if l == 64: #i.e. one digit\n",
        "    n = 1\n",
        "  else:\n",
        "    r = rightBound_digit(x, l)\n",
        "    l = leftBound_digit(x, r)\n",
        "\n",
        "    if l == 64: #i.e. two digits\n",
        "      n = 2\n",
        "    else:\n",
        "      r = rightBound_digit(x, l)\n",
        "      l = leftBound_digit(x, r)\n",
        "\n",
        "      if l == 64: #i.e. three digits\n",
        "        n = 3\n",
        "      else:\n",
        "        r = rightBound_digit(x, l)\n",
        "        l = leftBound_digit(x, r)\n",
        "\n",
        "        if l == 64:  #i.e. four digits\n",
        "          n = 4\n",
        "        else: #i.e. five digits\n",
        "          r = rightBound_digit(x, l)\n",
        "          n = 5\n",
        "  return n"
      ],
      "execution_count": 135,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wnM0GDqqGjac"
      },
      "source": [
        "def accuracy_check(x, y):\n",
        "  D = x.shape[0]\n",
        "  Y_true = torch.zeros(D)\n",
        "  for i in list(range(0, D)):\n",
        "    n = 0\n",
        "    for c in y[i]:\n",
        "      if c != 10:\n",
        "        n = n + 1\n",
        "    Y_true[i] = n\n",
        "\n",
        "  correct = 0\n",
        "  incorrect = 0\n",
        "  for i in list(range(0, D)):\n",
        "    if Y_true[i] == partition_image_number_of_digits_accuracy(x[i]):\n",
        "      correct = correct + 1\n",
        "    else:\n",
        "      incorrect = incorrect +1\n",
        "  return correct/(incorrect+correct)"
      ],
      "execution_count": 136,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LIbR-6lBJEOd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "50aff262-af0f-43bb-e301-625af309d77b"
      },
      "source": [
        "accuracy_check(X_train, train_labels)"
      ],
      "execution_count": 137,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.997375"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 137
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "A-wkegnYllIf"
      },
      "source": [
        "#The accuracy is 0.994 when set threshold = 0\n",
        "#The accuracy is 0.996 when set threshold = 0.25"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LyWvd72NPzTA"
      },
      "source": [
        "def incorrect_list(x, y):\n",
        "  D = x.shape[0]\n",
        "  Y_true = torch.zeros(D)\n",
        "  for i in list(range(0, D)):\n",
        "    n = 0\n",
        "    for c in y[i]:\n",
        "      if c != 10:\n",
        "        n = n + 1\n",
        "    Y_true[i] = n\n",
        "\n",
        "  correct = 0\n",
        "  incorrect = []\n",
        "  for i in list(range(0, D)):\n",
        "    if Y_true[i] == partition_image_number_of_digits_accuracy(x[i]):\n",
        "      correct = correct + 1\n",
        "    else:\n",
        "      incorrect.append(i)\n",
        "  return incorrect"
      ],
      "execution_count": 138,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dnJa-EH6QZdE"
      },
      "source": [
        "incorrect_digits = incorrect_list(X_train, train_labels)"
      ],
      "execution_count": 139,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rkW7qQviQOfG",
        "outputId": "bcfee2cd-a9d0-4b8f-8194-e6af54d288d8"
      },
      "source": [
        "print(np.array(incorrect_digits))"
      ],
      "execution_count": 151,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[  678  1576  2110  3254  3771  3878  3883  4011  4447  4639  4890  5011\n",
            "  5809  5892  6708  7021  8597  8698  8941  9070  9722  9860 10545 10792\n",
            " 11090 11622 12806 13824 14131 14150 14748 14896 15874 16268 16488 16553\n",
            " 16984 17030 17310 18127 18772 18861 19104 19660 20243 20666 21407 21578\n",
            " 21692 21839 21917 22832 22864 23438 24124 24360 24786 24809 25190 25273\n",
            " 25292 25376 25913 26042 26601 27695 27704 27942 28690 28919 29189 29444\n",
            " 29616 29623 29800 30120 30169 30386 30907 31392 31598 32187 32383 32557\n",
            " 32752 32944 33049 33167 33354 34909 35422 36550 36780 36787 37239 37607\n",
            " 37859 38355 38495 38753 38965 39331 39693 40349 40780 40917 41084 41329\n",
            " 41479 41913 42324 42451 43557 44071 44245 44650 45009 45074 45089 45187\n",
            " 45719 46256 46543 46742 47255 47595 48072 48985 49179 49303 49305 50225\n",
            " 50737 50840 51106 51592 52326 52705 53779 54048 54282 54814 54831 55088\n",
            " 55823 55847 55849]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "c9JeLScMP9Ec",
        "outputId": "4a577b72-92e5-4069-c7f2-c51064609ba8"
      },
      "source": [
        "digits = []\n",
        "passed = 0\n",
        "for i in range(0, 56000):\n",
        "  x = len(findDigits(train_images[i]))\n",
        "  n = 0\n",
        "  for c in train_labels[i]:\n",
        "    if c != 10:\n",
        "      n = n + 1\n",
        "  \n",
        "  if n == x:\n",
        "    passed = passed + 1\n",
        "  else:\n",
        "    digits.append(i)\n",
        "\n",
        "print(np.array(digits))"
      ],
      "execution_count": 152,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[  264  1530  3344  3709  4142  4155  4757  5245  7023  7348  7491  7958\n",
            "  9140 10223 11408 11739 12629 13291 13551 16801 17768 18127 20220 22505\n",
            " 22884 23959 26042 27399 28246 29910 31619 32954 33640 33935 35350 37873\n",
            " 39165 39721 41435 42162 42649 44362 46295 46373 48651 49483 50935 53330\n",
            " 54436 55359]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kJquEQIjaHYM"
      },
      "source": [
        "bad_cases = []\n",
        "for i in list(range(0, np.array(incorrect_digits).shape[0])):\n",
        "  for j in list(range(0, np.array(digits).shape[0])):\n",
        "    if np.array(incorrect_digits)[i] == np.array(digits)[j]:\n",
        "      bad_cases.append(np.array(digits)[j])"
      ],
      "execution_count": 156,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kIhmk7BgatGW",
        "outputId": "876e7d90-a832-4994-c7ae-6e962a6ae518"
      },
      "source": [
        "print(np.array(bad_cases))"
      ],
      "execution_count": 157,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[18127 26042]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "PhyDB1LFbHpo",
        "outputId": "40b22b1f-b7c5-46f6-b24c-fb82f6fb5c82"
      },
      "source": [
        "plt.imshow(X_train[18127].reshape(64, 64))"
      ],
      "execution_count": 158,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7efd1d60e080>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 158
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAD7CAYAAACscuKmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAATOUlEQVR4nO3dfZBddX3H8fcnu5sHAiEPQAhJICghEaUEugIWx0oQG9EBpBRBbNNOxqiDDo5WBe1U+jSVaatStToR0Djy6AMPMhaJMY5iMbAQQCCEkEBI1pBFTCBEWLK73/5xT+65Z2eXvdn7lPj7vGYy+zvn/O6eb/buZ8/j/R1FBGb2x29Mqwsws+Zw2M0S4bCbJcJhN0uEw26WCIfdLBE1hV3SIknrJD0p6bJ6FWVm9afRXmeX1AY8AZwJbAHuAy6KiMfqV56Z1Ut7Da89GXgyIjYCSLoROAcYNuxjNS7GM7GGVZrZa3mFXbwavRpqWS1hnwlsrpjeApzyWi8Yz0RO0Rk1rNLMXsvqWDnsslrCXhVJS4GlAOM5oNGrM7Nh1HKCrhuYXTE9K5tXEBHLIqIzIjo7GFfD6sysFrWE/T5grqSjJY0FLgRur09ZZlZvo96Nj4g+SR8FfgK0AddGxKN1q8zM6qqmY/aI+DHw4zrVYmYN5DvozBLhsJslwmE3S4TDbpYIh90sEQ67WSIcdrNEOOxmiXDYzRLhsJslwmE3S4TDbpYIh90sEQ67WSIcdrNEOOxmiXDYzRLhsJslwmE3S4TDbpYIh90sEQ67WSIcdrNEOOxmiXDYzRIxYtglXSupR9IjFfOmSlohaX32dUpjyzSzWlWzZf82sGjQvMuAlRExF1iZTZvZPmzEsEfEL4DfD5p9DrA8ay8Hzq1zXWZWZ6M9Zp8eEVuz9rPA9DrVY2YNUvMJuogIIIZbLmmppC5JXbvprXV1ZjZKow37NkkzALKvPcN1jIhlEdEZEZ0djBvl6sysVqMN++3A4qy9GLitPuWYWaNUc+ntBuAeYJ6kLZKWAF8AzpS0HnhHNm1m+7D2kTpExEXDLDqjzrWYWQP5DjqzRDjsZolw2M0S4bCbJcJhN0uEw26WCIfdLBEOu1kiHHazRDjsZolw2M0S4bCbJcJhN0uEw26WCIfdLBEOu1kiHHazRDjsZolw2M0S4bCbJcJhN0uEw26WCIfdLBEOu1kiHHazRFTz+KfZklZJekzSo5IuzeZPlbRC0vrs65TGl2tmo1XNlr0P+GREHAecClwi6TjgMmBlRMwFVmbTZraPGjHsEbE1Ih7I2juBtcBM4BxgedZtOXBuo4o0s9rt1TG7pDnAicBqYHpEbM0WPQtMr2tlZlZXVYdd0oHAD4CPR8SLlcsiIoAY5nVLJXVJ6tpNb03FmtnoVRV2SR2Ugn5dRPwwm71N0oxs+QygZ6jXRsSyiOiMiM4OxtWjZjMbhWrOxgu4BlgbEV+sWHQ7sDhrLwZuq395ZlYv7VX0OQ34a+A3kh7M5n0W+AJws6QlwCbggsaUaGb1MGLYI+JuQMMsPqO+5ZhZo/gOOrNEOOxmiXDYzRLhsJslwmE3S4TDbpYIh90sEQ67WSIcdrNEOOxmiXDYzRLhsJslwmE3S4TDbpYIh90sEQ67WSIcdrNEVDMsVcu1H31Uud07Z9qw/dpe7stfs/l3hWV93b+tf2G10nADAAEx5GC9zVFZVyvrsLrylt0sEQ67WSL2i934x/95arn9mc47y+3egY5Cv2d6837zJ2wtLLvxg4vK7TF3P0irxGkLyu3Orz5QWPb87onl9ubFs8rt/rXr616H2vO3futHTy4se/15+frW/2huuT3zpy8U+sVDj+cTA/11rnB4Y8aPL0zrqPxn1TdtYmFZ265X89c9X/Fsk76+Qr+BXX/I2zt31qPMfY637GaJcNjNEuGwmyVivzhmn/exjeX2rR1vzBfEQKFfHHFouT3/puIx+4aL8ufMzb27zgXuhe63HVBu3zX94cKy/or/z5mzl5bbHWvrsOJBl/l6PvjmcvuSD91aWPbGcVvK7baP5OdIrn/fqYV+v7z2lHL7sK/fU1xfnS/ZtR+ePyR40/8cUlh25JTt5fbkju2FZe+Ylv/wJo7JHyy6qbf4PW6+On/eyRE3FM+RDOzIz1WooxiZMYfl36d/ykHl9ovHHlTot2vG8NvVmT95Lv8eDTg/s0c1z3obL+leSQ9JelTSP2Xzj5a0WtKTkm6SNLZhVZpZzarZje8FFkbECcACYJGkU4ErgS9FxDHAdmBJ48o0s1pV86y3AF7KJjuyfwEsBN6fzV8OXAF8vf4lQn/FbtSYBceV2+svPrjQ79Kzflxu/82k7sKyFQvy3aOdc44st/uefqZudVbj5fmvNHV9e7QfOaswPf8D+WWz6//+3YVlm9/RVm4fsibf/X9pZvFQoP/tFZeout5UXOG9vxltqbmKQ491nzq63D5q0qC7Id+7q9x88aVdhUW3Tquoa9KBeft3xd396Tvyw5Axqw4vLDtp8svl9gFjXi0sO7h9c7ndofzy4y+2H1vod8/q+eX2Bxb+srDs+pPzQ6rXvZ+Gqfb57G3ZE1x7gBXABmBHROy5WLkFmNmYEs2sHqoKe0T0R8QCYBZwMjB/hJeUSVoqqUtS1256R36BmTXEXl16i4gdwCrgLcBkSXsOA2YB3cO8ZllEdEZEZwfjhupiZk0w4jG7pEOB3RGxQ9IE4ExKJ+dWAecDNwKLgdsaVeSYg/LLGId/Iz9GuvLwawv9/vbhxeX28tvPKizb9RcvldvHfzc/5tv1viMK/er96bjK21IBTp/3xLB9n9idH8+P786Ph+txI2r32bML00/lpzc4alXx9uF5GyuOyLq3lZtx3hsL/aauyC+vbTi/eKnpdffV/sm5tjfkt+pef95Xyu0Lf/TRQr9jX8rfsxh0G2z/tp58orL9Ggb+qvg9Hjj0DcP21Yv5OYJ4Kf8d63+heGvxMawut7+z7M8Ky9on7q6qrlpVc519BrBcUhulPYGbI+IOSY8BN0r6V2ANcE0D6zSzGlVzNv5h4MQh5m+kdPxuZvuB/eIOuspPJD19xUnl9mUbDi30m755U/6aV9YVlh16U76bOfvn+a7XrZ8q/r065uN1HuTixOIu4GdmfKNiqvgJrX/pzi+BxTP1rePFecWDgdl35rvWA3/4Q7HzMHdxTfnOvcUZbfklur6lJxQWtVde3nxqE6Ox9fT87rTf9+eXzf5j0Q2Fflds/kC5fcR/1n4nX/9zzxVnDJ4ejYrLiAuPL94SuWr1mwb3bgjfG2+WCIfdLBH7xW585cAIY++8r9zem7PUlQMS/O9T+W7T8Sc+Vej3cp3HX+v50wML08d25Lvu2/uLu8+//bdjyu1xO++jrgb9VyZse3m4RcMbNEBFVEwf8uvir9KWc/Iz+od/eXS78Yd/K79K8N/X5R/C2fSR4lWB//pQfm74K989vbCsb+uzo1p3I/UOFH9WMak5Z+O9ZTdLhMNulgiH3SwR+8cxe4X2Wfmx4OP/flhh2cDOfADKiZsGHRflV4n45klfLbeXfPeSQr+jYhu1qhzn/sOXDn9j4Ul3XlqYnnfXmnK73qO1j+9pK0zvODY/d3DwKE8PjDkgH4hj55zissnrigOLjMbAKxWfpXg5P8cwcWvxp7NroOI27AnFwSj3GRXnf3716NzCombdQectu1kiHHazROx3u/ED0yaV259/848Ky86amF/iOWhMcZSsdbvzy0Tn/eoj5faxX9tQ6FePD51sOTs/1Fgy6ZbCsmf68sttM1YWd60Hf4ijno68szgWevdn8//ptHvmFOt4oWJ89Sn5ACG9R04t9Ov+cD6QQ9/u4qAcU76Q38FY7Q592+TiYCQbP5EPVFL5iIB/eO/3Cv0++72Ly+05T/26yrU1WcUl3bcf/3hh0d0bX9+UErxlN0uEw26WCIfdLBH73zH7Q/knhm7885MKy64/8l3ldt/E4nPgxm7Nj0OP2ZAPhtjfgOPkCc/nR6mff674abDruvKx1ufdsqawrJEPR477HytMt63K6+i/ujjQwgu9U8rt+VPyAR8O7thc6PfSVflAiVNvLv5fBl7Z+4E1B3a9XJiemA9fT99ZO8rtZZ/7y0K/ObdUfBpvP3jE9Ngxxd+5MRsmNGW93rKbJcJhN0uEoom7PZM0NU7RGSN3/GMy6LFL++Ru5uAaq7Uv/l/2A89cURyDbmJ3/nOc9s17BnffK6tjJS/G74d8Q71lN0uEw26WiP3ubPx+Z3/Y1d0favwjcuQV/9eS9XrLbpYIh90sEQ67WSIcdrNEVB327LHNayTdkU0fLWm1pCcl3SRp7Ejfw8xaZ2+27JcClY+yuBL4UkQcA2wHltSzMDOrr6rCLmkW8G7g6mxawELg+1mX5cC5jSjQzOqj2i37l4FPkw86Mg3YERF7Pr6zBZg51AvNbN8wYtglvQfoiYj7R7MCSUsldUnq2k3vyC8ws4ao5g6604CzJZ0FjAcmAVcBkyW1Z1v3WUD3UC+OiGXAMih9EKYuVZvZXhtxyx4Rl0fErIiYA1wI/CwiLgZWAedn3RYDww+QbmYtV8t19s8An5D0JKVj+GtG6G9mLbRXH4SJiJ8DP8/aG4GT61+SmTWC76AzS4TDbpYIh90sEQ67WSIcdrNEOOxmiXDYzRLhsJslwmE3S4TDbpYIh90sEQ67WSIcdrNEOOxmiXDYzRLhsJslwmE3S4TDbpYIh90sEQ67WSIcdrNEOOxmiXDYzRLhsJslwmE3S0RVT4SR9DSwE+gH+iKiU9JU4CZgDvA0cEFEbG9MmWZWq73Zsp8eEQsiojObvgxYGRFzgZXZtJnto2rZjT8HWJ61lwPn1l6OmTVKtWEP4C5J90tams2bHhFbs/azwPS6V2dmdVPtU1zfGhHdkg4DVkh6vHJhRISkGOqF2R+HpQDjOaCmYs1s9KraskdEd/a1B7iF0qOat0maAZB97RnmtcsiojMiOjsYV5+qzWyvjRh2SRMlHbSnDbwTeAS4HVicdVsM3NaoIs2sdtXsxk8HbpG0p//1EXGnpPuAmyUtATYBFzSuTDOr1Yhhj4iNwAlDzH8eOKMRRZlZ/fkOOrNEOOxmiXDYzRLhsJslwmE3S4TDbpYIh90sEQ67WSIcdrNEOOxmiXDYzRLhsJslwmE3S4TDbpYIh90sEQ67WSIcdrNEOOxmiXDYzRLhsJslwmE3S4TDbpYIh90sEQ67WSIcdrNEVBV2SZMlfV/S45LWSnqLpKmSVkhan32d0uhizWz0qt2yXwXcGRHzKT0Kai1wGbAyIuYCK7NpM9tHVfMU14OBtwHXAETEqxGxAzgHWJ51Ww6c26gizax21WzZjwaeA74laY2kq7NHN0+PiK1Zn2cpPe3VzPZR1YS9HTgJ+HpEnAjsYtAue0QEEEO9WNJSSV2SunbTW2u9ZjZK1YR9C7AlIlZn09+nFP5tkmYAZF97hnpxRCyLiM6I6OxgXD1qNrNRGDHsEfEssFnSvGzWGcBjwO3A4mzeYuC2hlRoZnXRXmW/jwHXSRoLbAT+jtIfipslLQE2ARc0pkQzq4eqwh4RDwKdQyw6o77lmFmj+A46s0Q47GaJcNjNEuGwmyXCYTdLhMNulgiH3SwRKt3W3qSVSc9RugHnEOB3TVvx0PaFGsB1DOY6iva2jqMi4tChFjQ17OWVSl0RMdRNOknV4DpcRzPr8G68WSIcdrNEtCrsy1q03kr7Qg3gOgZzHUV1q6Mlx+xm1nzejTdLRFPDLmmRpHWSnpTUtNFoJV0rqUfSIxXzmj4UtqTZklZJekzSo5IubUUtksZLulfSQ1kd/5TNP1rS6uz9uSkbv6DhJLVl4xve0ao6JD0t6TeSHpTUlc1rxe9Iw4Ztb1rYJbUBXwPeBRwHXCTpuCat/tvAokHzWjEUdh/wyYg4DjgVuCT7GTS7ll5gYUScACwAFkk6FbgS+FJEHANsB5Y0uI49LqU0PPkerarj9IhYUHGpqxW/I40btj0imvIPeAvwk4rpy4HLm7j+OcAjFdPrgBlZewawrlm1VNRwG3BmK2sBDgAeAE6hdPNG+1DvVwPXPyv7BV4I3AGoRXU8DRwyaF5T3xfgYOApsnNp9a6jmbvxM4HNFdNbsnmt0tKhsCXNAU4EVreilmzX+UFKA4WuADYAOyKiL+vSrPfny8CngYFselqL6gjgLkn3S1qazWv2+9LQYdt9go7XHgq7ESQdCPwA+HhEvNiKWiKiPyIWUNqyngzMb/Q6B5P0HqAnIu5v9rqH8NaIOInSYeYlkt5WubBJ70tNw7aPpJlh7wZmV0zPyua1SlVDYdebpA5KQb8uIn7YyloAovR0n1WUdpcnS9ozLmEz3p/TgLMlPQ3cSGlX/qoW1EFEdGdfe4BbKP0BbPb7UtOw7SNpZtjvA+ZmZ1rHAhdSGo66VZo+FLYkUXqM1tqI+GKrapF0qKTJWXsCpfMGaymF/vxm1RERl0fErIiYQ+n34WcRcXGz65A0UdJBe9rAO4FHaPL7Eo0etr3RJz4GnWg4C3iC0vHh55q43huArcBuSn89l1A6NlwJrAd+CkxtQh1vpbQL9jDwYPbvrGbXAvwJsCar4xHgH7P5rwPuBZ4EvgeMa+J79HbgjlbUka3voezfo3t+N1v0O7IA6Mrem1uBKfWqw3fQmSXCJ+jMEuGwmyXCYTdLhMNulgiH3SwRDrtZIhx2s0Q47GaJ+H/FwwxuZc2M+gAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iPqW80yej0Jc",
        "outputId": "dc9d9e2c-bcd8-4c99-c47e-ad51995a910f"
      },
      "source": [
        "np.array(X_train[18127][26:38, 49])"
      ],
      "execution_count": 171,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.        ],\n",
              "       [0.        ],\n",
              "       [0.03529412],\n",
              "       [0.36078432],\n",
              "       [0.00392157],\n",
              "       [0.        ],\n",
              "       [0.        ],\n",
              "       [0.        ],\n",
              "       [0.        ],\n",
              "       [0.        ],\n",
              "       [0.        ],\n",
              "       [0.        ]], dtype=float32)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 171
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "H5XLoawdkFbd",
        "outputId": "5a81d662-c7d5-4f1e-8b61-e0a62babb279"
      },
      "source": [
        "np.array(X_train[18127][26:38, 50])"
      ],
      "execution_count": 166,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.        ],\n",
              "       [0.        ],\n",
              "       [0.        ],\n",
              "       [0.05882353],\n",
              "       [0.7058824 ],\n",
              "       [0.05882353],\n",
              "       [0.        ],\n",
              "       [0.        ],\n",
              "       [0.        ],\n",
              "       [0.        ],\n",
              "       [0.        ],\n",
              "       [0.        ]], dtype=float32)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 166
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "EnjjiZnibUIW",
        "outputId": "3b7226e6-9f9f-4227-9379-36e6cda48d34"
      },
      "source": [
        "plt.imshow(X_train[26042].reshape(64, 64))"
      ],
      "execution_count": 159,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7efd1d55ee80>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 159
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0ODg26ddbpGP"
      },
      "source": [
        "def leftBound_digit_1(x, initial_column):\n",
        "  N = x.shape[1] #column\n",
        "  leftBound = 0\n",
        "  bound = torch.full(x[:, 0].shape, 0.361)\n",
        "  for i in list(range(initial_column, N)):\n",
        "    if torch.all(torch.le(x[:, i], bound)):\n",
        "      leftBound = i + 1\n",
        "    else:\n",
        "      break\n",
        "  return leftBound\n",
        "\n",
        "\n",
        "def rightBound_digit_1(x, initial_column):\n",
        "  N = x.shape[1] #column\n",
        "  leftBound = 0\n",
        "  bound = torch.full(x[:, 0].shape, 0.361)\n",
        "  for i in list(range(initial_column, N)):\n",
        "    if torch.all(torch.le(x[:, i], bound)) == False:\n",
        "      leftBound = i + 1\n",
        "    else:\n",
        "      break\n",
        "  return leftBound\n",
        "\n",
        "def partition_image_number_of_digits_accuracy_1(x):\n",
        "  x = x.reshape(64, 64)\n",
        "  l = leftBound_digit_1(x, 0)\n",
        "  r = rightBound_digit_1(x, l)\n",
        "  l = leftBound_digit_1(x, r)\n",
        "  if l == 64: #i.e. one digit\n",
        "    n = 1\n",
        "  else:\n",
        "    r = rightBound_digit_1(x, l)\n",
        "    l = leftBound_digit_1(x, r)\n",
        "\n",
        "    if l == 64: #i.e. two digits\n",
        "      n = 2\n",
        "    else:\n",
        "      r = rightBound_digit_1(x, l)\n",
        "      l = leftBound_digit_1(x, r)\n",
        "\n",
        "      if l == 64: #i.e. three digits\n",
        "        n = 3\n",
        "      else:\n",
        "        r = rightBound_digit_1(x, l)\n",
        "        l = leftBound_digit_1(x, r)\n",
        "\n",
        "        if l == 64:  #i.e. four digits\n",
        "          n = 4\n",
        "        else: #i.e. five digits\n",
        "          r = rightBound_digit_1(x, l)\n",
        "          n = 5\n",
        "  return n\n",
        "\n",
        "def accuracy_check_1(x, y):\n",
        "  D = x.shape[0]\n",
        "  Y_true = torch.zeros(D)\n",
        "  for i in list(range(0, D)):\n",
        "    n = 0\n",
        "    for c in y[i]:\n",
        "      if c != 10:\n",
        "        n = n + 1\n",
        "    Y_true[i] = n\n",
        "\n",
        "  correct = 0\n",
        "  incorrect = 0\n",
        "  for i in list(range(0, D)):\n",
        "    if Y_true[i] == partition_image_number_of_digits_accuracy_1(x[i]):\n",
        "      correct = correct + 1\n",
        "    else:\n",
        "      incorrect = incorrect +1\n",
        "  return correct/(incorrect+correct)\n"
      ],
      "execution_count": 172,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xpqYIlvgbppk",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "032d1774-3cc5-4bd3-93df-6b46613fab1e"
      },
      "source": [
        "accuracy_check_1(X_train, train_labels)"
      ],
      "execution_count": 173,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9857142857142858"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 173
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9LTsJ1nkcJSG"
      },
      "source": [
        "def dataset_images_partition(x):\n",
        "  D = x.shape[0]\n",
        "  X_new = []\n",
        "  for i in list(range(0, D)):\n",
        "    X_new.append(partition_image(x[i]))\n",
        "  return X_new"
      ],
      "execution_count": 174,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vn4Xzl_pc-gc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "outputId": "09d2dbca-1e99-4cc3-d915-2f4ca5cd4bec"
      },
      "source": [
        "dataset_images_partition(X_train)"
      ],
      "execution_count": 175,
      "outputs": [
        {
          "output_type": "error",
          "ename": "RuntimeError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-175-0cc045ae06cb>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mdataset_images_partition\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_train\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;32m<ipython-input-174-ada3dab71ad1>\u001b[0m in \u001b[0;36mdataset_images_partition\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m      3\u001b[0m   \u001b[0mX_new\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m   \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mD\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m     \u001b[0mX_new\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpartition_image\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m   \u001b[0;32mreturn\u001b[0m \u001b[0mX_new\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-134-b191555e9dea>\u001b[0m in \u001b[0;36mpartition_image\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m     35\u001b[0m         \u001b[0mr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrightBound_digit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ml\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     36\u001b[0m         \u001b[0mx_4\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m14\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m14\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 37\u001b[0;31m         \u001b[0mx_4\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m12\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m26\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m38\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0ml\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m26\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m38\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0ml\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     38\u001b[0m         \u001b[0ml\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mleftBound_digit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     39\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mRuntimeError\u001b[0m: The expanded size of the tensor (14) must match the existing size (18) at non-singleton dimension 1.  Target sizes: [12, 14].  Tensor sizes: [12, 18]"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EXEBynfEmG3q"
      },
      "source": [
        "#The above runtime error occur because some of the digits fail to be separated."
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dRUoe-A8Wgs2"
      },
      "source": [
        "## **2. Neural Network Models**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JwL0Rac0jUB9"
      },
      "source": [
        "#classification\n",
        "#subset data into groups\n",
        "\n",
        "from sklearn.model_selection import KFold\n",
        "cross_validation = KFold(n_splits=5)\n",
        "#cross_validation.split(X, y=None, groups=None)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WjFthGpUerBl"
      },
      "source": [
        "'''\n",
        "logistic: https://towardsdatascience.com/logistic-regression-on-mnist-with-pytorch-b048327f8d19\n",
        "clustering: https://www.dlology.com/blog/how-to-do-unsupervised-clustering-with-keras/ \n",
        "'''"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vbZFVFikWsSP"
      },
      "source": [
        "## **3. Performance**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GD5KC8MyW1LV"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "awQVg43K4J4j"
      },
      "source": [
        "## **4. Application to the Testing Images**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rY9D20DVmalq"
      },
      "source": [
        "scaled_test_images = data_normalized(test_images)\n",
        "X_test = torch.from_numpy(scaled_test_images)"
      ],
      "execution_count": 176,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rwFu5rjLmiJQ"
      },
      "source": [
        "X_test_partition = dataset_images_partition(X_test)"
      ],
      "execution_count": 178,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ygGpajwDnGbZ",
        "outputId": "2a27980a-5407-4f8c-d8e4-ca6844074d01",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 162
        }
      },
      "source": [
        "#convert above to a tensor"
      ],
      "execution_count": 181,
      "outputs": [
        {
          "output_type": "error",
          "ename": "ValueError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-181-2c6a4e480bfa>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mX_test_part\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFloatTensor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_test_partition\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;31mValueError\u001b[0m: only one element tensors can be converted to Python scalars"
          ]
        }
      ]
    }
  ]
}