main.ipynb

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      "name": "python3",
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      "name": "python"
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  "cells": [
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import struct\n",
        "from array import array\n",
        "from os.path import join\n",
        "import pandas as pd\n",
        "import random\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "import tensorflow as tf\n",
        "from tensorflow.keras.layers import Dense, Flatten, MaxPooling2D, Conv2D, Input\n",
        "from tensorflow.keras.models import Sequential, load_model\n",
        "from tensorflow.keras.losses import SparseCategoricalCrossentropy\n",
        "from tensorflow.keras.callbacks import ModelCheckpoint, EarlyStopping\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.metrics import confusion_matrix, multilabel_confusion_matrix, classification_report, accuracy_score\n",
        "import seaborn as sns"
      ],
      "metadata": {
        "id": "5pgpCirGX9SD"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Classifying MNIST Images With Various Neural Networks and Comparing Them\n",
        "- Thomas Armstrong\n",
        "- Approved by Max\n",
        "\n",
        "## Neural Networks Used\n",
        "- Dense\n",
        "- Convolutional\n",
        "\n",
        "In this tutorial, we'll be using a dense neural network and a convolutional neural network in order to classify MNIST images, and then comparing the results of the networks. \n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "jV3ZMZGzGHbu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## What are MNIST Images?\n",
        "\n",
        "---\n"
      ],
      "metadata": {
        "id": "8oN3p6irb6BN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "MNIST images are images of handwritten digits ranging from 0-9. The images are in 28 by 28 pixels, and are greyscale only, with a completely black background. There will also be some example images printed below, if this description is inadequate.\n",
        "\n",
        "This makes MNIST images great to use for machine learning. Images being greyscaled means that each pixel can be represented by one value, from 0 to 255. Then, the full representation of an MNIST image can be thought of as a 28x28 array. Values within the array would have values up to 255, indicating the pixel is completely white, and as low as 0, indicating the completely black background."
      ],
      "metadata": {
        "id": "bN6BCe0Mb8Bg"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Data Collection\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "xaFbQC4oPSOa"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "I found the MNIST data available from Kaggle [here](https://www.kaggle.com/datasets/hojjatk/mnist-dataset?resource=download).\n",
        "\n",
        "The user that posted the MNIST data also generously provided code to read in the data, which I found [here](https://www.kaggle.com/code/hojjatk/read-mnist-dataset/notebook).\n",
        "\n",
        "\n",
        "This allowed for a very simple data collection process, where I simply had to download the data myself, and direct the code to the proper file directory. \n",
        "\n",
        "In this notebook, I will be saving all of the data and saved models to my Google Drive."
      ],
      "metadata": {
        "id": "g0SBYx6bbx1I"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "T7YCYw5UEP7t"
      },
      "outputs": [],
      "source": [
        "file_dir = \"./drive/MyDrive/College/CMSC320/mnist/\""
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "MNIST Data from: https://www.kaggle.com/datasets/hojjatk/mnist-dataset?resource=download\n",
        "\n",
        "Code for reading the data: https://www.kaggle.com/code/hojjatk/read-mnist-dataset/notebook\n",
        "\n"
      ],
      "metadata": {
        "id": "dvDeoby5GCvo"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "cBdi0bvnX2I3"
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      "outputs": [],
      "source": [
        "\n",
        "\n",
        "#\n",
        "# MNIST Data Loader Class\n",
        "#\n",
        "class MnistDataloader(object):\n",
        "    def __init__(self, training_images_filepath,training_labels_filepath,\n",
        "                 test_images_filepath, test_labels_filepath):\n",
        "        self.training_images_filepath = training_images_filepath\n",
        "        self.training_labels_filepath = training_labels_filepath\n",
        "        self.test_images_filepath = test_images_filepath\n",
        "        self.test_labels_filepath = test_labels_filepath\n",
        "    \n",
        "    def read_images_labels(self, images_filepath, labels_filepath):        \n",
        "        labels = []\n",
        "        with open(labels_filepath, 'rb') as file:\n",
        "            magic, size = struct.unpack(\">II\", file.read(8))\n",
        "            if magic != 2049:\n",
        "                raise ValueError('Magic number mismatch, expected 2049, got {}'.format(magic))\n",
        "            labels = array(\"B\", file.read())        \n",
        "        \n",
        "        with open(images_filepath, 'rb') as file:\n",
        "            magic, size, rows, cols = struct.unpack(\">IIII\", file.read(16))\n",
        "            if magic != 2051:\n",
        "                raise ValueError('Magic number mismatch, expected 2051, got {}'.format(magic))\n",
        "            image_data = array(\"B\", file.read())        \n",
        "        images = []\n",
        "        for i in range(size):\n",
        "            images.append([0] * rows * cols)\n",
        "        for i in range(size):\n",
        "            img = np.array(image_data[i * rows * cols:(i + 1) * rows * cols])\n",
        "            img = img.reshape(28, 28)\n",
        "            images[i][:] = img            \n",
        "        \n",
        "        return images, labels\n",
        "            \n",
        "    def load_data(self):\n",
        "        x_train, y_train = self.read_images_labels(self.training_images_filepath, self.training_labels_filepath)\n",
        "        x_test, y_test = self.read_images_labels(self.test_images_filepath, self.test_labels_filepath)\n",
        "        return (x_train, y_train),(x_test, y_test)\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "#\n",
        "# Set file paths based on added MNIST Datasets\n",
        "#\n",
        "input_path = file_dir\n",
        "training_images_filepath = join(input_path, 'train-images-idx3-ubyte/train-images-idx3-ubyte')\n",
        "training_labels_filepath = join(input_path, 'train-labels-idx1-ubyte/train-labels-idx1-ubyte')\n",
        "test_images_filepath = join(input_path, 't10k-images-idx3-ubyte/t10k-images-idx3-ubyte')\n",
        "test_labels_filepath = join(input_path, 't10k-labels-idx1-ubyte/t10k-labels-idx1-ubyte')\n",
        "\n",
        "\n",
        "#\n",
        "# Load MNIST dataset\n",
        "#\n",
        "mnist_dataloader = MnistDataloader(training_images_filepath, training_labels_filepath, test_images_filepath, test_labels_filepath)\n",
        "(x_train, y_train), (x_test, y_test) = mnist_dataloader.load_data()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Preparing Data for Model Input\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "xx--cXyqu6sr"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Currently, each image is an array of 28 arrays. Generally, when passing the inputs into the model, we want each image to instead be a 2D array.\n",
        "\n",
        "This way, we pass an array of 2D arrays into the model, instead of an array of arrays of arrays.\n",
        "\n",
        "The model will expect each input to have a specific shape (in this case 28x28), which is difficult to determine when an input is an array of arrays.\n",
        "\n",
        "Here, you can see that each image is currently an array of arrays. This can be seen by the multiple array declarations instead of a single array declaration."
      ],
      "metadata": {
        "id": "bQYbsz4Sbual"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x_train[0]"
      ],
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        "colab": {
          "base_uri": "https://localhost:8080/"
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        "id": "rJcNxx__vBuO",
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          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "To convert the inputs into 2D arrays, we can use the [numpy stack function](https://numpy.org/doc/stable/reference/generated/numpy.stack.html):"
      ],
      "metadata": {
        "id": "UYRZAMx3xCO-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x_train = np.stack(x_train)\n",
        "y_train = np.stack(y_train)\n",
        "x_test = np.stack(x_test)\n",
        "y_test = np.stack(y_test)"
      ],
      "metadata": {
        "id": "FK5VNl5tYnbb"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Note that we even stack our labels. Although not as necessary, it keeps the datatypes uniform.\n",
        "\n",
        "Now, each input image is a 2D array:"
      ],
      "metadata": {
        "id": "HVFHlHq-xaZ-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x_train[0]"
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        "colab": {
          "base_uri": "https://localhost:8080/"
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        "id": "1LR04CSgxWmD",
        "outputId": "e28b39da-d7a6-42b1-a80d-fe01a5c8499f"
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              "          0,  45, 186, 253, 253, 150,  27,   0,   0,   0,   0,   0,   0,\n",
              "          0,   0],\n",
              "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
              "          0,   0,  16,  93, 252, 253, 187,   0,   0,   0,   0,   0,   0,\n",
              "          0,   0],\n",
              "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
              "          0,   0,   0,   0, 249, 253, 249,  64,   0,   0,   0,   0,   0,\n",
              "          0,   0],\n",
              "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
              "          0,  46, 130, 183, 253, 253, 207,   2,   0,   0,   0,   0,   0,\n",
              "          0,   0],\n",
              "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,  39,\n",
              "        148, 229, 253, 253, 253, 250, 182,   0,   0,   0,   0,   0,   0,\n",
              "          0,   0],\n",
              "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,  24, 114, 221,\n",
              "        253, 253, 253, 253, 201,  78,   0,   0,   0,   0,   0,   0,   0,\n",
              "          0,   0],\n",
              "       [  0,   0,   0,   0,   0,   0,   0,   0,  23,  66, 213, 253, 253,\n",
              "        253, 253, 198,  81,   2,   0,   0,   0,   0,   0,   0,   0,   0,\n",
              "          0,   0],\n",
              "       [  0,   0,   0,   0,   0,   0,  18, 171, 219, 253, 253, 253, 253,\n",
              "        195,  80,   9,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
              "          0,   0],\n",
              "       [  0,   0,   0,   0,  55, 172, 226, 253, 253, 253, 253, 244, 133,\n",
              "         11,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
              "          0,   0],\n",
              "       [  0,   0,   0,   0, 136, 253, 253, 253, 212, 135, 132,  16,   0,\n",
              "          0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
              "          0,   0],\n",
              "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
              "          0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
              "          0,   0],\n",
              "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
              "          0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
              "          0,   0],\n",
              "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
              "          0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
              "          0,   0]], dtype=uint8)"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Creation of Validation Dataset\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "bh85umUK99CI"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Currently, we have a train and a test dataset. I will also be creating a third validation set, that we will use during training to evaluate the model's performance on data it hasn't seen.\n",
        "\n",
        "- Train set: Used for training our models\n",
        "- Validation set: Used to validate the models during training\n",
        "- Test set: Used to evaluate our models' predictions after training\n",
        "\n",
        "This is useful because we are essentially double blinded to the test set before analysis. We've never seen any of the data within the set, and do not know how the model will perform with it.\n",
        "\n",
        "If we did not create a separate validation set, we would no longer be blinded to the test set, as we would use the test set during validation in model training.\n",
        "\n",
        "We'll be using sklearn's [train_test_split function](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html):"
      ],
      "metadata": {
        "id": "baDJgG1kbp_k"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x_train, x_valid, y_train, y_valid = train_test_split(x_train, y_train, test_size=0.1667, random_state=42)"
      ],
      "metadata": {
        "id": "nLc2_BWe2Xo3"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Showing Example Images\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "76DspcicpA2H"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The following code is used to show some example images from the dataset. It also came from [Kaggle](https://www.kaggle.com/code/hojjatk/read-mnist-dataset/notebook) as a part of data collection."
      ],
      "metadata": {
        "id": "DK4UNKDndN-x"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#\n",
        "# Helper function to show a list of images with their relating titles\n",
        "#\n",
        "%matplotlib inline\n",
        "def show_images(images, title_texts):\n",
        "    cols = 5\n",
        "    rows = int(len(images)/cols) + 1\n",
        "    plt.figure(figsize=(20,10))\n",
        "    index = 1    \n",
        "    for x in zip(images, title_texts):        \n",
        "        image = x[0]        \n",
        "        title_text = x[1]\n",
        "        plt.subplot(rows, cols, index)        \n",
        "        plt.imshow(image, cmap=plt.cm.gray)\n",
        "        if (title_text != ''):\n",
        "            plt.title(title_text, fontsize = 15);        \n",
        "        index += 1"
      ],
      "metadata": {
        "id": "x4F9toweYExK"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "By showing random sample images, we can see that the digits are not exactly the same. There is quite a bit of variation within digits."
      ],
      "metadata": {
        "id": "_lIJUp1y_6VR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#\n",
        "# Show some random training and test images \n",
        "#\n",
        "images_2_show = []\n",
        "titles_2_show = []\n",
        "for i in range(0, 5):\n",
        "    r = random.randint(1, len(x_train))\n",
        "    images_2_show.append(x_train[r])\n",
        "    titles_2_show.append('training image [' + str(r) + '] = ' + str(y_train[r]))    \n",
        "\n",
        "for i in range(0, 5):\n",
        "    r = random.randint(1, len(x_valid))\n",
        "    images_2_show.append(x_valid[r])        \n",
        "    titles_2_show.append('validation image [' + str(r) + '] = ' + str(y_valid[r]))    \n",
        "\n",
        "show_images(images_2_show, titles_2_show)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 418
        },
        "id": "LrbdNyN4YFeJ",
        "outputId": "1ba279a6-a9eb-44f6-e442-34e2b4a016c6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1440x720 with 10 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "As you can see, each image is 28x28 and in black and white. "
      ],
      "metadata": {
        "id": "jZDAgehYsLrW"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Initial Data Analysis\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "D83vujHrsZ1j"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "To ensure that there is no classification bias in the models, we should aim to have close to the same amount of each label present the training set.\n",
        "\n",
        "To check how many of each label we have, we'll make use of Numpy's [bincount function](https://numpy.org/doc/stable/reference/generated/numpy.bincount.html). This function takes an array of numbers, and returns an array where the indexes represent the numbers from the original array, and the values at each index are the number of occurrences.\n",
        "\n",
        "So, for example:\n",
        "```\n",
        "initial_array = np.array([0, 1, 2, 2, 2, 3, 3])\n",
        "bincounted_array = np.bincount(initial_array)\n",
        "\n",
        "bincounted_array[0] = 1\n",
        "bincounted_array[1] = 1\n",
        "bincounted_array[2] = 3\n",
        "bincounted_array[3] = 2\n",
        "```\n",
        "\n",
        "Another useful function is Numpy's [ptp function](https://numpy.org/doc/stable/reference/generated/numpy.ptp.html). This stands for peak-to-peak, and calculates the largest possible range from an array of values."
      ],
      "metadata": {
        "id": "ZFbhuqctbklc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "bincount = np.bincount(y_train)\n",
        "print(f\"Average number of inputs per label: {bincount.mean()}\")\n",
        "print(f\"Standard deviation of inputs per label: {bincount.std()}\")\n",
        "print(f\"Range of inputs per label: {bincount.max()} - {bincount.min()} = {np.ptp(bincount)}\")\n",
        "\n",
        "plt.title(\"Number of Images Per Label in Training Dataset\")\n",
        "plt.ylabel(\"Number of Images\")\n",
        "plt.xlabel(\"Label\")\n",
        "plt.bar(range(0, 10), bincount)\n",
        "plt.xticks(range(0, 10))\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "cgAghVuhx_q8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 349
        },
        "outputId": "f19f1cd9-ef4b-4085-b880-f99e5afc23b6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Average number of inputs per label: 4999.8\n",
            "Standard deviation of inputs per label: 278.88700220698706\n",
            "Range of inputs per label: 5649 - 4501 = 1148\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",
      "source": [
        "Overall, there is not a huge difference in number of images per label. The lowest number of images is 4501 for the label 5, and the highest number of images is 5649 for the label 1. Each of these are about two standard deviations off of the mean.\n",
        "\n",
        "This is likely not a huge enough difference to cause significantly harmful effects to our models during training."
      ],
      "metadata": {
        "id": "DgdwvCO37SUt"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "bincount = np.bincount(y_valid)\n",
        "print(f\"Average number of inputs per label: {bincount.mean()}\")\n",
        "print(f\"Standard deviation of inputs per label: {bincount.std()}\")\n",
        "print(f\"Range of inputs per label: {bincount.max()} - {bincount.min()} = {np.ptp(bincount)}\")\n",
        "\n",
        "plt.title(\"Number of Images Per Label in Validation Dataset\")\n",
        "plt.ylabel(\"Number of Images\")\n",
        "plt.xlabel(\"Label\")\n",
        "plt.xticks(range(0, 10))\n",
        "plt.bar(range(0, 10), bincount)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 349
        },
        "id": "K5Ban4hLCsMu",
        "outputId": "c4cd2612-9345-4560-f322-39456eac051c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Average number of inputs per label: 1000.2\n",
            "Standard deviation of inputs per label: 44.94619004988076\n",
            "Range of inputs per label: 1093 - 920 = 173\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",
      "source": [
        "Although not as important to check since it won't affect training, the validation dataset also has a decent number of images for each class."
      ],
      "metadata": {
        "id": "YcPyDlCQEacJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Creating a Dense Neural Network\n",
        "\n",
        "---\n",
        "\n"
      ],
      "metadata": {
        "id": "69HCbXWSFTtB"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "For this step, we're just going to make a densely connected neural network that takes the images as inputs, and returns an array of size 10, corresponding to the number of digits, where each value is the probability of the image being the digit associated with the index.\n",
        "\n",
        "An example output may look like: [0, 0, 0, 1, 0, 0, 0, 0, 0, 0]\n",
        "\n",
        "This can be seen in the model from the last layer we add, the Dense layer of size 10, with softmax activation.\n",
        "\n",
        "\n",
        "This would indicate the model is predicting the digit 3, since the probability in the index 3 is as high as possible.\n",
        "\n",
        "\n",
        "For the models in this notebook, I'll primarily be using TensorFlow and Keras. If you're new to TensorFlow, there's some tutorials [here](https://www.tensorflow.org/tutorials) that can get you started."
      ],
      "metadata": {
        "id": "-WJIckVBIJt7"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "d_model = Sequential()\n",
        "d_model.add(Flatten(input_shape=(28, 28, 1)))\n",
        "d_model.add(Dense(32, activation='relu'))\n",
        "d_model.add(Dense(16, activation='relu'))\n",
        "d_model.add(Dense(10, activation='softmax'))\n",
        "\n",
        "d_model.summary()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hAv1_d8qFZge",
        "outputId": "ef0668c4-2d59-4fd8-e422-452934dabbfb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model: \"sequential\"\n",
            "_________________________________________________________________\n",
            " Layer (type)                Output Shape              Param #   \n",
            "=================================================================\n",
            " flatten (Flatten)           (None, 784)               0         \n",
            "                                                                 \n",
            " dense (Dense)               (None, 32)                25120     \n",
            "                                                                 \n",
            " dense_1 (Dense)             (None, 16)                528       \n",
            "                                                                 \n",
            " dense_2 (Dense)             (None, 10)                170       \n",
            "                                                                 \n",
            "=================================================================\n",
            "Total params: 25,818\n",
            "Trainable params: 25,818\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Since we're passing the digit numbers into the model as our labels instead of one-hot encoded vectors, we use sparse categorical crossentropy instead of normal categorical crossentropy."
      ],
      "metadata": {
        "id": "0D5tW0CsPgHs"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "d_model.compile(optimizer='adam',\n",
        "              loss=SparseCategoricalCrossentropy(from_logits=False),\n",
        "              metrics=['accuracy'])"
      ],
      "metadata": {
        "id": "IzyIPOe5GJLh"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Here we create Keras' [EarlyStopping callback](https://keras.io/api/callbacks/early_stopping/). \n",
        "\n",
        "This will stop the model from training further when the model goes 1 epoch without a decrease in validation loss (the patience). Typically, we want to implement some kind of early stopping mechanism like this so that our model does not overfit to the training data. \n",
        "\n",
        "Although we could just reduce the number of epochs, this approach would prevent us from reaching the best model possible, as training could end before reaching our best accuracy."
      ],
      "metadata": {
        "id": "-dbdNv_YmT9c"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "callback = EarlyStopping(monitor='val_loss', patience=1, restore_best_weights=True)"
      ],
      "metadata": {
        "id": "Rgwl1zwkmUZn"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Below is the code that was used to generate our model. Note that you may receive different results when running this section over again. Therefore, I have saved a model that we will instead use for analysis as otherwise I would be doing new analysis on a model each time I had to run this code (which would be a lot of times as I reconnect to Google Colab's runtime)."
      ],
      "metadata": {
        "id": "h8JW6NVqaTYu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "d_history = d_model.fit(x=x_train, y=y_train,\n",
        "                    validation_data=(x_valid, y_valid),\n",
        "                    epochs=50,\n",
        "                    callbacks=[callback])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EYBoyGk5GLxV",
        "outputId": "09dac3d1-e99c-4a0f-cccc-28f62a33c268"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/50\n",
            "1563/1563 [==============================] - 3s 2ms/step - loss: 1.9037 - accuracy: 0.6142 - val_loss: 0.8486 - val_accuracy: 0.7244\n",
            "Epoch 2/50\n",
            "1563/1563 [==============================] - 2s 2ms/step - loss: 0.7127 - accuracy: 0.7707 - val_loss: 0.5500 - val_accuracy: 0.8490\n",
            "Epoch 3/50\n",
            "1563/1563 [==============================] - 2s 2ms/step - loss: 0.4930 - accuracy: 0.8709 - val_loss: 0.4873 - val_accuracy: 0.8840\n",
            "Epoch 4/50\n",
            "1563/1563 [==============================] - 2s 2ms/step - loss: 0.4089 - accuracy: 0.8960 - val_loss: 0.4054 - val_accuracy: 0.8949\n",
            "Epoch 5/50\n",
            "1563/1563 [==============================] - 2s 2ms/step - loss: 0.3637 - accuracy: 0.9072 - val_loss: 0.3825 - val_accuracy: 0.9094\n",
            "Epoch 6/50\n",
            "1563/1563 [==============================] - 3s 2ms/step - loss: 0.3317 - accuracy: 0.9148 - val_loss: 0.3545 - val_accuracy: 0.9149\n",
            "Epoch 7/50\n",
            "1563/1563 [==============================] - 2s 2ms/step - loss: 0.3002 - accuracy: 0.9212 - val_loss: 0.3453 - val_accuracy: 0.9090\n",
            "Epoch 8/50\n",
            "1563/1563 [==============================] - 3s 2ms/step - loss: 0.2834 - accuracy: 0.9245 - val_loss: 0.3255 - val_accuracy: 0.9178\n",
            "Epoch 9/50\n",
            "1563/1563 [==============================] - 2s 2ms/step - loss: 0.2695 - accuracy: 0.9285 - val_loss: 0.3148 - val_accuracy: 0.9214\n",
            "Epoch 10/50\n",
            "1563/1563 [==============================] - 2s 2ms/step - loss: 0.2615 - accuracy: 0.9306 - val_loss: 0.2828 - val_accuracy: 0.9242\n",
            "Epoch 11/50\n",
            "1563/1563 [==============================] - 2s 2ms/step - loss: 0.2523 - accuracy: 0.9319 - val_loss: 0.2995 - val_accuracy: 0.9266\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "This is the code to save the model and it's history. It's commented out so that the model is not overwritten each runthrough of the notebook. This allows our data analysis to be a bit more standardized."
      ],
      "metadata": {
        "id": "ot0aM0AYCBky"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "'''\n",
        "d_model.save(\"./drive/MyDrive/College/CMSC320/saved_model/dnn\", overwrite=True)\n",
        "\n",
        "hist_df = pd.DataFrame(d_history.history)\n",
        "with open(\"./drive/MyDrive/College/CMSC320/saved_model/dnn_history.csv\", mode='w') as f:\n",
        "    hist_df.to_csv(f)\n",
        "'''"
      ],
      "metadata": {
        "id": "e96IN1uYy1QV",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "94624bf9-cec6-49dc-f92a-96c552c5f1ee"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'\\nd_model.save(\"./drive/MyDrive/College/CMSC320/saved_model/dnn\", overwrite=True)\\n\\nhist_df = pd.DataFrame(d_history.history)\\nwith open(\"./drive/MyDrive/College/CMSC320/saved_model/dnn_history.csv\", mode=\\'w\\') as f:\\n    hist_df.to_csv(f)\\n'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Loading pretrained model for standardized results and analysis for when Colab dies\n",
        "\n",
        "d_model = load_model(\"./drive/MyDrive/College/CMSC320/saved_model/dnn\")\n",
        "d_history = pd.read_csv(\"./drive/MyDrive/College/CMSC320/saved_model/dnn_history.csv\")"
      ],
      "metadata": {
        "id": "JVOrIaMMH4xR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Evaluating Dense Neural Network Training\n",
        "\n",
        "---\n"
      ],
      "metadata": {
        "id": "xTa8rrrwY06W"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(d_history['accuracy'], label='accuracy')\n",
        "plt.plot(d_history['val_accuracy'], label = 'val_accuracy')\n",
        "plt.title(\"Accuracy of Dense Neural Network During Training\")\n",
        "plt.xlabel('Epoch')\n",
        "plt.ylabel('Accuracy')\n",
        "plt.ylim([0, 1])\n",
        "plt.legend(loc='lower right')\n",
        "\n",
        "test_loss, test_acc = d_model.evaluate(x_valid,  y_valid, verbose=2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "id": "AfhGdD0fH88l",
        "outputId": "72c8a711-b0ce-4e15-94d0-63812dea550c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "313/313 - 0s - loss: 0.3627 - accuracy: 0.9038 - 389ms/epoch - 1ms/step\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",
      "source": [
        "Here we can see the training accuracy and validation accuracy begin to converge after about 1 epoch.\n",
        "\n",
        "As expected, our validation accuracy decreased at the end of training. This is a result of our EarlyStopping callback from earlier - training will stop when the model begins to perform worse than previously.\n",
        "\n",
        "Fortunately though, thanks to setting `restore_best_weights=True` in the callback, the model returns to the weights from the epoch before validation loss began to increase.\n"
      ],
      "metadata": {
        "id": "VKcwx9aTdusW"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(d_history['loss'], label='loss')\n",
        "plt.plot(d_history['val_loss'], label = 'val_loss')\n",
        "plt.title(\"Loss of Dense Neural Network During Training\")\n",
        "plt.xlabel('Epoch')\n",
        "plt.ylabel('Loss')\n",
        "plt.ylim([0, 2])\n",
        "plt.legend(loc='upper right')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "h5oeQpdNxYTn",
        "outputId": "c95793a5-23d2-44c3-fc16-faaad2764728"
      },
      "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",
      "source": [
        "Like the accuracy graph, the loss graph also indicates the model was beginning to experience some overfitting at the end of training, as the validation loss began to increase."
      ],
      "metadata": {
        "id": "JRO0HnhCzgNJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Evaluating Dense Neural Network Predictions\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "FmpDYoh_3Lnt"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "\n",
        "One important way to evaluate the model is to see how its number of predictions vary from the true number of digits.\n",
        "\n",
        "Using the test dataset, we will get the model's predictions, and then compare the two. We also make use of Numpy's [argmax function](https://numpy.org/doc/stable/reference/generated/numpy.argmax.html), which returns the index of the largest value in an array. \n",
        "\n",
        "In this case, that will get us an exact prediction from the model in single digit form."
      ],
      "metadata": {
        "id": "EuT825DvcFH8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "y_test_preds = np.argmax(d_model.predict(x_test), axis=1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "usQMxz0WIgu6",
        "outputId": "536d60bd-552a-41ba-dc43-f2951bf585ed"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "313/313 [==============================] - 0s 1ms/step\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "pred_bincount = np.bincount(y_test_preds)\n",
        "truth_bincount = np.bincount(y_test)\n",
        "plt.title(\"Difference in Num Predictions and Num True Labels in Testing Dataset\")\n",
        "plt.ylabel(\"Diff in Num Preds and Num True Labels\")\n",
        "plt.xlabel(\"Label\")\n",
        "plt.xticks(range(0, 10))\n",
        "plt.gca().axhline(y=0, color=\"black\")\n",
        "plt.bar(range(0, 10), pred_bincount - truth_bincount)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "VQGWM9KzKH_2",
        "outputId": "3d280639-1776-4a97-b854-d5622cbe29c8"
      },
      "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",
      "source": [
        "In the above graph, we're comparing the difference in number of predictions versus the number of true labels for each digit in the test set.\n",
        "\n",
        "Positive values indicate more predictions than actual labels for that digit.\n",
        "\n",
        "\n",
        "\n",
        "As it turns out, our model is significantly overclassifying things as the digit 8, and underclassifying things as the digits 1 and 2.\n",
        "\n",
        "One possible improvement that could be made to the network could be to add some dropout layers. This could help ensure the nodes in the network learn different features, instead of multiple nodes learning similar features from the digits. This could possibly allow the model to learn more significant features from the digits 1 and 2, improving our underclassification."
      ],
      "metadata": {
        "id": "WsUARy25auWl"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "---\n",
        "We should also look into how the model is misclassifying results. We know that we're underclassifying 1 and 2 and overclassifying 8, but how? What true digits are being predicted into what labels?\n",
        "\n",
        "\n",
        "To start, we'll make a confusion matrix that shows where our true digits are ending up. I found [this resource](https://www.stackvidhya.com/plot-confusion-matrix-in-python-and-why/) to be quite helpful to learn how to make a confusion matrix.\n",
        "\n"
      ],
      "metadata": {
        "id": "7jKVw-zP5Zl3"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "cf_matr = confusion_matrix(y_test, y_test_preds)\n",
        "\n",
        "ax = sns.heatmap(cf_matr, annot=True, fmt='0', cmap='Blues')\n",
        "fig = plt.gcf()\n",
        "fig.set_figheight(10)\n",
        "fig.set_figwidth(15)\n",
        "\n",
        "ax.set_ylabel(\"True Digit\")\n",
        "ax.set_xlabel(\"Predicted Digit\")\n",
        "ax.set_title(\"Confusion Matrix of True Digits vs. Predicted Digits\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 621
        },
        "id": "JZKR_PGSLMto",
        "outputId": "3051b146-f6d2-433b-f05d-5a15b0e910d9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1080x720 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "From the confusion matrix, we can see that we're often predicting 1 and 2 as 8s. This would explain why we were often underclassifying 1 and 2, while overclassifying 8.\n",
        "\n",
        "We can also see that we're predicting:\n",
        "- 5s as 3s\n",
        "- 5s as 8s\n",
        "- 8s as 5s\n",
        "- 9s as 4s\n",
        "\n",
        "\n",
        "Although, to be honest, I find it hard to gain insights from a confusion matrix this big.\n",
        "So, we'll also make some bar graphs of the misclassifications."
      ],
      "metadata": {
        "id": "uEr0b91EP46t"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "---\n",
        "\n",
        "To start, we'll make a dictionary where each key represents the true labels, and the values will store lists with what the model predicted the key to be."
      ],
      "metadata": {
        "id": "1OE3e-v7O3yG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "misclassifications = {}\n",
        "for i in range(len(y_test)):\n",
        "    true_label = y_test[i]\n",
        "    pred_label = y_test_preds[i]\n",
        "\n",
        "    if true_label != pred_label:\n",
        "        misclassifications.setdefault(true_label, [])\n",
        "        misclassifications.get(true_label).append(pred_label)"
      ],
      "metadata": {
        "id": "P0QLf8sw6MK0"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Next, we'll graph them so that it's easier to interpret:"
      ],
      "metadata": {
        "id": "DHBel_zwEIKT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots(2, 5)\n",
        "fig.set_figheight(15)\n",
        "fig.set_figwidth(30)\n",
        "\n",
        "\n",
        "for i in range(0, 5):\n",
        "    ax[0, i].set_title(f\"Misclassifications When True Label Was {i}\")\n",
        "    ax[0, i].set_ylabel(\"Number of Misclassifications\")\n",
        "    ax[0, i].set_xlabel(\"Label Predicted Instead of True\")\n",
        "    ax[0, i].set_ylim([0, 80])\n",
        "    ax[0, i].set_xticks(range(0, 10))\n",
        "\n",
        "    ax[0, i].bar(range(0, 10), np.bincount(misclassifications.get(i), minlength=10))\n",
        "\n",
        "\n",
        "for i in range(5, 10):\n",
        "    ax[1, i-5].set_title(f\"Misclassifications When True Label Was {i}\")\n",
        "    ax[1, i-5].set_ylabel(\"Number of Misclassifications\")\n",
        "    ax[1, i-5].set_xlabel(\"Label Predicted Instead of True\")\n",
        "    ax[1, i-5].set_ylim([0, 80])\n",
        "    ax[1, i-5].set_xticks(range(0, 10))\n",
        "\n",
        "    ax[1, i-5].bar(range(0, 10), np.bincount(misclassifications.get(i), minlength=10))\n",
        "\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 893
        },
        "id": "qQTI15WE7btf",
        "outputId": "15097ea5-d3e5-452f-95bf-3c4d90ee79d4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 2160x1080 with 10 Axes>"
            ],
            "image/png": 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          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Here, we can see the same trends as the confusion matrix, but a bit clearer. Our model struggles a lot with predicting 5s, often confusing them with 3s and 8s, and vice versa.\n",
        "\n",
        "We are also predicting 1s and 2s as 8, although we're not predicting 8s as 1 and 2.\n",
        "\n",
        "In certain instances, we're also predicting digits that are visually similar.\n",
        "We're also predicting 5s instead of 6s often, and a decent number of 9s and 4s are getting mixed up.\n",
        "\n"
      ],
      "metadata": {
        "id": "uoiBNsgOByd2"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## The Numbers\n",
        "---\n",
        "\n"
      ],
      "metadata": {
        "id": "QTz0AbQfdVfm"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "We've yet to look indepth at the metrics of accuracy, precision and recall of the model. \n",
        "\n",
        "First, we'll start with the accuracy of each digit, which unfortunately isn't provided by a neat sklearn function. Instead, we'll get it from the confusion matrix, by dividing the diagonals (the number of true positives) by the total number of labels for each number."
      ],
      "metadata": {
        "id": "8es-bMiGdqOH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "cf_matr.diagonal()/cf_matr.sum(axis=1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RRY-lgx0Y2Vt",
        "outputId": "372afe78-05f4-44c2-eef6-3f5795d18002"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.98163265, 0.94713656, 0.88565891, 0.8960396 , 0.93686354,\n",
              "       0.82286996, 0.91962422, 0.90758755, 0.8973306 , 0.87512389])"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the array above, the index corresponds to the digit.\n",
        "\n",
        "We can see that our accuracy for 5 (82%) is quite bad compared to every other accuracy. This makes sense as we we predicted almost 70 3s and 50 8s instead of 5, so our overall number of true positives for 5 is going to be subpar."
      ],
      "metadata": {
        "id": "e2F_7mGMeiZm"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Next, we'll look at our precision and recall scores for each label.\n",
        "\n",
        "Sklearn provides a great [classification_report function](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.classification_report.html) that calculates them all for us:"
      ],
      "metadata": {
        "id": "GvjOAQUMgRsN"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(classification_report(y_test, y_test_preds))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VmNPk1J2ZCeA",
        "outputId": "ebef543b-44d7-4536-fe95-59b337e26232"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "              precision    recall  f1-score   support\n",
            "\n",
            "           0       0.95      0.98      0.96       980\n",
            "           1       0.99      0.95      0.97      1135\n",
            "           2       0.93      0.89      0.91      1032\n",
            "           3       0.90      0.90      0.90      1010\n",
            "           4       0.90      0.94      0.92       982\n",
            "           5       0.82      0.82      0.82       892\n",
            "           6       0.94      0.92      0.93       958\n",
            "           7       0.95      0.91      0.93      1028\n",
            "           8       0.79      0.90      0.84       974\n",
            "           9       0.91      0.88      0.89      1009\n",
            "\n",
            "    accuracy                           0.91     10000\n",
            "   macro avg       0.91      0.91      0.91     10000\n",
            "weighted avg       0.91      0.91      0.91     10000\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Our precisions for 5 and 8 are comparatively low: 82% and 79% respectively. So, when we're predicting 5 or 8 for an image, only 82% and 79% of them are actually 5s and 8s. This lowers my certainty in the model that the classification is correct when it returns a 5 or 8.\n",
        "\n",
        "The only below average recall from the model is of 5 at 82% again. Of the digits labeled 5 in our test set, the model only predicted 82% of them. This tells me the model has some difficulty determining what a 5 should look like.\n",
        "\n"
      ],
      "metadata": {
        "id": "Y794RNsOgrci"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Overall, the dense neural network can classify relatively well, but has some difficulty especially with the digits 5 and 8."
      ],
      "metadata": {
        "id": "X0n-NCPWD1Wa"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Creating the Convolutional Neural Network\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "aBFJCn0gZkwk"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Hopefully, the convolutional network can better extract features than the dense network due to its convolutional and pooling layers. This should result in less misclassifications of similar digits like what we saw in the dense network.\n",
        "\n",
        "This model follows the base model found from another TensorFlow tutorial [here](https://www.tensorflow.org/tutorials/images/cnn).\n",
        "\n",
        "Just like the dense neural network, the input to this model will be our same input images, and our outputs will be arrays of size 10 where each value is the probability of the image being the digit associated with the index.\n"
      ],
      "metadata": {
        "id": "uZ8hNrexgsn8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "c_model = Sequential()\n",
        "c_model.add(Conv2D(28, (4, 4), activation='relu', input_shape=(28, 28, 1)))\n",
        "c_model.add(MaxPooling2D((2, 2)))\n",
        "c_model.add(Conv2D(16, (2, 2), activation='relu'))\n",
        "c_model.add(MaxPooling2D((2, 2)))\n",
        "c_model.add(Conv2D(8, (2, 2), activation='relu'))\n",
        "c_model.add(Flatten())\n",
        "c_model.add(Dense(16, activation='relu'))\n",
        "c_model.add(Dense(10, activation='softmax'))\n",
        "\n",
        "c_model.summary()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NjF8ObYPZmae",
        "outputId": "446e8b86-403b-4dfe-9086-89e81a0bd06f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model: \"sequential_1\"\n",
            "_________________________________________________________________\n",
            " Layer (type)                Output Shape              Param #   \n",
            "=================================================================\n",
            " conv2d (Conv2D)             (None, 25, 25, 28)        476       \n",
            "                                                                 \n",
            " max_pooling2d (MaxPooling2D  (None, 12, 12, 28)       0         \n",
            " )                                                               \n",
            "                                                                 \n",
            " conv2d_1 (Conv2D)           (None, 11, 11, 16)        1808      \n",
            "                                                                 \n",
            " max_pooling2d_1 (MaxPooling  (None, 5, 5, 16)         0         \n",
            " 2D)                                                             \n",
            "                                                                 \n",
            " conv2d_2 (Conv2D)           (None, 4, 4, 8)           520       \n",
            "                                                                 \n",
            " flatten_1 (Flatten)         (None, 128)               0         \n",
            "                                                                 \n",
            " dense_3 (Dense)             (None, 16)                2064      \n",
            "                                                                 \n",
            " dense_4 (Dense)             (None, 10)                170       \n",
            "                                                                 \n",
            "=================================================================\n",
            "Total params: 5,038\n",
            "Trainable params: 5,038\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Note how this convolutional network has only a fifth of the parameters of the dense one."
      ],
      "metadata": {
        "id": "8sPisBIiSYdw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "c_model.compile(optimizer='adam',\n",
        "              loss=SparseCategoricalCrossentropy(from_logits=False),\n",
        "              metrics=['accuracy'])"
      ],
      "metadata": {
        "id": "H-4QAbzmcuio"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Just like before, we'll be using Keras' [EarlyStopping callback](https://keras.io/api/callbacks/early_stopping/) to ensure our model is trained the best it can without overfitting:"
      ],
      "metadata": {
        "id": "BF3i2bqHYzPl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "callback = EarlyStopping(monitor='val_loss', patience=1, restore_best_weights=True)"
      ],
      "metadata": {
        "id": "2kHcM2dzXqvZ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Once again, this is the code to generate the model. We will be loading a model that was trained using this code later, to standardize analysis."
      ],
      "metadata": {
        "id": "9pSus7oybOIZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "c_history = c_model.fit(x=x_train, y=y_train,\n",
        "                    validation_data=(x_valid, y_valid),\n",
        "                    epochs=50,\n",
        "                    callbacks=[callback])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hlzscepydSFu",
        "outputId": "8ecb4d6c-472c-41cd-e098-daec0e6287ca"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/50\n",
            "1563/1563 [==============================] - 22s 14ms/step - loss: 0.6654 - accuracy: 0.8191 - val_loss: 0.1710 - val_accuracy: 0.9499\n",
            "Epoch 2/50\n",
            "1563/1563 [==============================] - 21s 13ms/step - loss: 0.1445 - accuracy: 0.9573 - val_loss: 0.1305 - val_accuracy: 0.9611\n",
            "Epoch 3/50\n",
            "1563/1563 [==============================] - 22s 14ms/step - loss: 0.1084 - accuracy: 0.9675 - val_loss: 0.0943 - val_accuracy: 0.9708\n",
            "Epoch 4/50\n",
            "1563/1563 [==============================] - 21s 13ms/step - loss: 0.0856 - accuracy: 0.9747 - val_loss: 0.0735 - val_accuracy: 0.9766\n",
            "Epoch 5/50\n",
            "1563/1563 [==============================] - 21s 13ms/step - loss: 0.0770 - accuracy: 0.9766 - val_loss: 0.0844 - val_accuracy: 0.9753\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "'''\n",
        "c_model.save(\"./drive/MyDrive/College/CMSC320/saved_model/cnn\", overwrite=True)\n",
        "\n",
        "hist_df = pd.DataFrame(c_history.history)\n",
        "with open(\"./drive/MyDrive/College/CMSC320/saved_model/cnn_history.csv\", mode='w') as f:\n",
        "    hist_df.to_csv(f)\n",
        "'''"
      ],
      "metadata": {
        "id": "k-iceF-wdlzi",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6b25972a-d35d-4288-e099-dd3ebe951e72"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "WARNING:absl:Found untraced functions such as _jit_compiled_convolution_op, _jit_compiled_convolution_op, _jit_compiled_convolution_op while saving (showing 3 of 3). These functions will not be directly callable after loading.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Loading pretrained model for standardized results and analysis\n",
        "\n",
        "c_model = load_model(\"./drive/MyDrive/College/CMSC320/saved_model/cnn\")\n",
        "c_history = pd.read_csv(\"./drive/MyDrive/College/CMSC320/saved_model/cnn_history.csv\")"
      ],
      "metadata": {
        "id": "eH0kwrxnPEd6"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Evaluating Convolutional Neural Network Training\n",
        "\n",
        "\n",
        "---\n",
        "\n"
      ],
      "metadata": {
        "id": "1ZZG-Z1CQh2R"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(c_history['accuracy'], label='accuracy')\n",
        "plt.plot(c_history['val_accuracy'], label = 'val_accuracy')\n",
        "plt.title(\"Accuracy of Convolutional Neural Network During Training\")\n",
        "plt.xlabel('Epoch')\n",
        "plt.ylabel('Accuracy')\n",
        "plt.ylim([0, 1])\n",
        "plt.legend(loc='lower right')\n",
        "\n",
        "test_loss, test_acc = c_model.evaluate(x_test,  y_test, verbose=2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "id": "vk4-GDMnmMVw",
        "outputId": "efd25925-6c80-4ed1-de13-e4bf958c7f80"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "313/313 - 1s - loss: 0.0730 - accuracy: 0.9775 - 1s/epoch - 5ms/step\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",
      "source": [
        "Despite having a fifth of the parameters, the accuracy of the convolutional network surpassed that of the dense network during training. This is likely due to convolutional networks' improved ability to extract features from their inputs.\n",
        "\n",
        "However, you might be able to get the dense network to have similar levels of accuracy, given the appropriate tweaks to the model's hyperparameters and addition of some dropout.\n",
        "\n",
        "By about the end of the first epoch, accuracy and validation accuracy converged to pretty close to their max values during training. "
      ],
      "metadata": {
        "id": "EFWwlxbFQwhS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(c_history['loss'], label='loss')\n",
        "plt.plot(c_history['val_loss'], label = 'val_loss')\n",
        "plt.title(\"Loss of Convolutional Neural Network During Training\")\n",
        "plt.xlabel('Epoch')\n",
        "plt.ylabel('Loss')\n",
        "plt.ylim([0, 1])\n",
        "plt.legend(loc='upper right')\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "45LmNfoQnJ2D",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "2f326930-5183-4447-b864-3a75ea16a318"
      },
      "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",
      "source": [
        "The loss of the convolutional network stayed much smaller than the loss of the dense network. The dense network started with a loss of almost 2, whereas the convolutional network started at less than 1."
      ],
      "metadata": {
        "id": "MwRa5OUJTq2J"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Evaluating Convolutional Neural Network Predictions\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "nzJYpD5hVLgF"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Just like with the dense network, let's see how it's predictions on the test set vary from the true digits."
      ],
      "metadata": {
        "id": "W0s9RVxbVLgH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "y_test_preds = np.argmax(c_model.predict(x_test), axis=1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8340d958-8b96-47c6-a3f6-51b9306e7434",
        "id": "RL25Rj_bVLgI"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "313/313 [==============================] - 2s 5ms/step\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Looking at the differences in number of predictions vs number of true labels again:"
      ],
      "metadata": {
        "id": "ok7BA89VVLgJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "pred_bincount = np.bincount(y_test_preds)\n",
        "truth_bincount = np.bincount(y_test)\n",
        "plt.title(\"Difference in Num Predictions and Num True Labels in Testing Dataset\")\n",
        "plt.ylabel(\"Diff in Num Preds and Num True Labels\")\n",
        "plt.xlabel(\"Label\")\n",
        "plt.gca().axhline(y=0, color=\"black\")\n",
        "plt.xticks(range(0, 10))\n",
        "plt.bar(range(0, 10), pred_bincount - truth_bincount)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "c275da11-0baf-4943-a49d-4330a2357633",
        "id": "xzX1w11LVLgK"
      },
      "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",
      "source": [
        "Again, positive values indicate more predictions than actual labels for that digit.\n",
        "\n",
        "We've predicted the digit 1 about 25 more occurrences than it actually appears, and also predicted the digits 0 and 2 a bit more as well.\n",
        "\n",
        "We're also not predicting the digits 3, 7, 8 and 9 as much as we should be.\n",
        "\n",
        "However, we do have some improvement over the dense network. The dense network predicted the digit 8 about **125** instances more than the true number of 8s.\n",
        "\n",
        "Our convolutional network does not reach such high differences for any label, which may indicate that that it is performing better."
      ],
      "metadata": {
        "id": "4q1vgUINVLgK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "---\n",
        "Taking a further look into how we're misclassifying results again, we'll start with a confusion matrix:"
      ],
      "metadata": {
        "id": "1Hd1qPESVLgL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "cf_matr = confusion_matrix(y_test, y_test_preds)\n",
        "\n",
        "ax = sns.heatmap(cf_matr, annot=True, fmt='0', cmap='Blues')\n",
        "fig = plt.gcf()\n",
        "fig.set_figheight(10)\n",
        "fig.set_figwidth(15)\n",
        "\n",
        "ax.set_ylabel(\"True Digit\")\n",
        "ax.set_xlabel(\"Predicted Digit\")\n",
        "ax.set_title(\"Confusion Matrix of True Digits vs. Predicted Digits\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 621
        },
        "id": "Hm5mxWzsuydo",
        "outputId": "66cf383b-d306-4472-d96a-8f352b38a39e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1080x720 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Compared to the dense network, we have a lot fewer classifications off of the diagonals. Previously, we could identify instances of 50 or more classifications in a category that was not along the diagonal, indicating an incorrect prediction.\n",
        "\n",
        "With this confusion matrix, the highest instances of misclassifications appear to be:\n",
        "- 14 predictions of 7 as 2\n",
        "- 12 predictions of 8 as 0\n",
        "- 12 predictions of 3 as 5\n",
        "- 11 predictions of 7 as 1\n",
        "- 10 predictions of 9 as 4\n",
        "\n",
        "We'll also look at the misclassifications for each label, to make it clearer:"
      ],
      "metadata": {
        "id": "l5IImQSUu5GG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "misclassifications = {}\n",
        "for i in range(len(y_test)):\n",
        "    true_label = y_test[i]\n",
        "    pred_label = y_test_preds[i]\n",
        "\n",
        "    if true_label != pred_label:\n",
        "        misclassifications.setdefault(true_label, [])\n",
        "        misclassifications.get(true_label).append(pred_label)"
      ],
      "metadata": {
        "id": "mmO_pQ-GVLgL"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots(2, 5)\n",
        "fig.set_figheight(15)\n",
        "fig.set_figwidth(30)\n",
        "\n",
        "\n",
        "for i in range(0, 5):\n",
        "    ax[0, i].set_title(f\"Misclassifications When True Label Was {i}\")\n",
        "    ax[0, i].set_ylabel(\"Number of Misclassifications\")\n",
        "    ax[0, i].set_xlabel(\"Label Predicted Instead of True\")\n",
        "    ax[0, i].set_ylim([0, 80])\n",
        "    ax[0, i].set_xticks(range(0, 10))\n",
        "\n",
        "    ax[0, i].bar(range(0, 10), np.bincount(misclassifications.get(i), minlength=10))\n",
        "\n",
        "\n",
        "for i in range(5, 10):\n",
        "    ax[1, i-5].set_title(f\"Misclassifications When True Label Was {i}\")\n",
        "    ax[1, i-5].set_ylabel(\"Number of Misclassifications\")\n",
        "    ax[1, i-5].set_xlabel(\"Label Predicted Instead of True\")\n",
        "    ax[1, i-5].set_ylim([0, 80])\n",
        "    ax[1, i-5].set_xticks(range(0, 10))\n",
        "\n",
        "    ax[1, i-5].bar(range(0, 10), np.bincount(misclassifications.get(i), minlength=10))\n",
        "\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 893
        },
        "outputId": "734ac549-8fa4-4b7f-ce68-63a53e0579fd",
        "id": "pUXjUeONVLgN"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 2160x1080 with 10 Axes>"
            ],
            "image/png": 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/rLNW9p7O6mx0dnadnXwqi9/HZPFzvdvxzDlKdFZno7Nz7Owjk5yaxQvBf3x62+n1MLgK0FqtjdbOsbXXn77WS7N4oPfyJN+/zlrZezqrs9HZ2XW2uz/Y3e/feps2f6h3fz20I6q6V+3xCAAAAAAAAFdN9ugCAAAAAABgloYOuqrqZ6rqzVX1z1X1V9MxKk+vqtdU1Tuq6pnTMSsBOAw6CzCe1gKMpbMAY+kssN8NG3RV1fWTPCzJge7+2iRXy+J4m49N8sTuvlkWx5988Kg1AOxnOgswntYCjKWzAGPpLLAJRh+68Ngk16qqY5N8SZILk9w5ixftS5Kzktx78BoA9jOdBRhPawHG0lmAsXQW2NeOHXXF3f3eqvovSf41yaeSvDTJuUku7u7LprO9J8n1l12+qh6S5CFJcvzxx3/DLW5xi1FLBdjRueee+6HuPvVor2MZnQX2C60FGEtnAcbSWYDxVrV22KCrqk5Ocq8kpye5OMmzk3zPupfv7jOTnJkkBw4c6HPOOWfEMgFWqqoLjvYadqKzwH6htQBj6SzAWDoLMN6q1o48dOF3JnlXd1/U3Z9L8pwkd0hy0rSbbJLcIMl7B64BYD/TWYDxtBZgLJ0FGEtngX1v5KDrX5Pcrqq+pKoqyV2SnJfkFUnuO53njCTPH7gGgP1MZwHG01qAsXQWYCydBfa9YYOu7n5NFi9o+Pokb5pu68wkv5DkEVX1jiTXTfLUUWsA2M90FmA8rQUYS2cBxtJZYBMMe42uJOnuRyd59EGb35nkm0beLsCm0FmA8bQWYCydBRhLZ4H9buShCwEAAAAAAGAYgy4AAAAAAABmyaALAAAAAACAWTLoAgAAAAAAYJYMugAAAAAAAJglgy4AAAAAAABmyaALAAAAAACAWTLoAgAAAAAAYJYMugAAAAAAAJglgy4AAAAAAABmyaALAAAAAACAWTLoAgAAAAAAYJYMugAAAAAAAJglgy4AAAAAAABmyaALAAAAAACAWTLoAgAAAAAAYJYMugAAAAAAAJglgy4AAAAAAABmyaALAAAAAACAWTLoAgAAAAAAYJYMugAAAAAAAJglgy4AAAAAAABmyaALAAAAAACAWTLoAgAAAAAAYJYMugAAAAAAAJglgy4AAAAAAABmyaALAAAAAACAWTLoAgAAAAAAYJYMugAAAAAAAJglgy4AAAAAAABmyaALAAAAAACAWTLoAgAAAAAAYJYMugAAAAAAAJglgy4AAAAAAABmyaALAAAAAACAWTLoAgAAAAAAYJYMugAAAAAAAJglgy4AAAAAAABmadigq6q+uqreuO3tkqr66ao6papeVlVvn96fPGoNAPuZzgKMp7UAY+kswFg6C2yCYYOu7n5bd9+mu2+T5BuSfDLJc5M8KsnLu/vmSV4+nQbgEOkswHhaCzCWzgKMpbPAJtirQxfeJcm/dPcFSe6V5Kxp+1lJ7r1HawDYz3QWYDytBRhLZwHG0llgX9qrQdcPJ/mr6ePrdfeF08fvT3K9ZReoqodU1TlVdc5FF120F2sEmDOdBRhPawHG0lmAsXQW2JeGD7qq6upJ7pnk2Qd/rrs7SS+7XHef2d0HuvvAqaeeOniVAPOlswDjaS3AWDoLMJbOAvvZXuzRdbckr+/uD0ynP1BVpyXJ9P6De7AGgP1MZwHG01qAsXQWYCydBfatvRh0/Uiu2CU2SV6Q5Izp4zOSPH8P1gCwn+kswHhaCzCWzgKMpbPAvjV00FVVxye5a5LnbNv8mCR3raq3J/nO6TQAh0FnAcbTWoCxdBZgLJ0F9rtjR155d38iyXUP2vbhJHcZebsAm0JnAcbTWoCxdBZgLJ0F9ru9OHQhAAAAAAAAHHEGXQAAAAAAAMySQRcAAAAAAACzZNAFAAAAAADALBl0AQAAAAAAMEsGXQAAAAAAAMySQRcAAAAAAACzZNAFAAAAAADALBl0AQAAAAAAMEsGXQAAAAAAAMySQRcAAAAAAACzZNAFAAAAAADALBl0AQAAAAAAMEsGXQAAAAAAAMySQRcAAAAAAACzZNAFAAAAAADALBl0AQAAAAAAMEsGXQAAAAAAAMySQRcAAAAAAACzZNAFAAAAAADALBl0AQAAAAAAMEsGXQAAAAAAAMySQRcAAAAAAACzZNAFAAAAAADALBl0AQAAAAAAMEsGXQAAAAAAAMySQRcAAAAAAACzZNAFAAAAAADALBl0AQAAAAAAMEsGXQAAAAAAAMySQRcAAAAAAACzZNAFAAAAAADALBl0AQAAAAAAMEsGXQAAAAAAAMySQRcAAAAAAACzZNAFAAAAAADALBl0AQAAAAAAMEtDB11VdVJVnV1Vb62qt1TV7avqlKp6WVW9fXp/8sg1AOxnOgswntYCjKWzAGPpLLDfjd6j60lJXtLdt0hy6yRvSfKoJC/v7psnefl0GoDDo7MA42ktwFg6CzCWzgL72rBBV1VdJ8kdkzw1Sbr7s919cZJ7JTlrOttZSe49ag0A+5nOAoyntQBj6SzAWDoLbIKRe3SdnuSiJH9aVW+oqj+uquOTXK+7L5zO8/4k11t24ap6SFWdU1XnXHTRRQOXCTBbOgswntYCjKWzAGPpLLDvjRx0HZvk65P81+6+bZJP5KBdYLu7k/SyC3f3md19oLsPnHrqqQOXCTBbOgswntYCjKWzAGPpLLDvjRx0vSfJe7r7NdPps7OI6geq6rQkmd5/cOAaAPYznQUYT2sBxtJZgLF0Ftj3hg26uvv9Sd5dVV89bbpLkvOSvCDJGdO2M5I8f9QaAPYznQUYT2sBxtJZgLF0FtgExw6+/ocmeVpVXT3JO5M8KIvh2rOq6sFJLkhyv8FrANjPdBZgPK0FGEtnAcbSWWBfGzro6u43Jjmw5FN3GXm7AJtCZwHG01qAsXQWYCydBfa7ka/RBQAAAAAAAMMYdAEAAAAAADBLBl0AAAAAAADMkkEXAAAAAAAAs2TQBQAAAAAAwCwZdAEAAAAAADBLBl0AAAAAAADMkkEXAAAAAAAAs2TQBQAAAAAAwCwZdAEAAAAAADBLBl0AAAAAAADMkkEXAAAAAAAAs2TQBQAAAAAAwCwZdAEAAAAAADBLBl0AAAAAAADMkkEXAAAAAAAAs2TQBQAAAAAAwCztOuiqqq+sqmtMH39HVT2sqk4avzSAzaG1AGPpLMBYOgswntYCLLfOHl1/neTzVXWzJGcmuWGSpw9dFcDm0VqAsXQWYCydBRhPawGWWGfQdXl3X5bk+5P8fnf/XJLTxi4LYONoLcBYOgswls4CjKe1AEusM+j6XFX9SJIzkrxo2nbcuCUBbCStBRhLZwHG0lmA8bQWYIl1Bl0PSnL7JL/d3e+qqtOT/MXYZQFsHK0FGEtnAcbSWYDxtBZgiWN3O0N3n5fkYdtOvyvJY0cuCmDTaC3AWDoLMJbOAoyntQDL7Troqqo7JPm1JDeezl9JurtvOnZpAJtDawHG0lmAsXQWYDytBVhu10FXkqcm+Zkk5yb5/NjlAGwsrQUYS2cBxtJZgPG0FmCJdQZdH+vuFw9fCcBm01qAsXQWYCydBRhPawGWWGfQ9YqqelyS5yT5zNbG7n79sFUBbB6tBRhLZwHG0lmA8bQWYIl1Bl3fPL0/sG1bJ7nzkV8OwMbSWoCxdBZgLJ0FGE9rAZbYddDV3Xfai4UAbDKtBRhLZwHG0lmA8bQWYLljdjtDVV2nqp5QVedMb4+vquvsxeIANoXWAoylswBj6SzAeFoLsNyug64kf5Lk0iT3m94uSfKnIxcFsIG0FmAsnQUYS2cBxtNagCXWeY2ur+zuH9h2+ter6o2jFgSwobQWYCydBRhLZwHG01qAJdbZo+tTVfWtWyeq6g5JPjVuSQAbSWsBxtJZgLF0FmA8rQVYYp09uv5DkrOm471Wko8keeDIRQFsIK0FGEtnAcbSWYDxtBZgiV0HXd39xiS3rqoTp9OXDF8VwIbRWoCxdBZgLJ0FGE9rAZbbcdBVVT/W3X9ZVY84aHuSpLufMHhtAPue1gKMpbMAY+kswHhaC7Daqj26jp/en7Dkcz1gLQCbSGsBxtJZgLF0FmA8rQVYYcdBV3c/Zfrwb7v7f2z/3PRCh7uqqvOTXJrk80ku6+4DVXVKkmcmuUmS85Pcr7s/esgrB9gHrmxrdRZgNfdpAcbSWYDxPHYAsNoxa5zn99fctpM7dfdtuvvAdPpRSV7e3TdP8vLpNMCmuzKt1VmA3blPCzCWzgKM57EDgCVWvUbX7ZN8S5JTDzr+64lJrnYlbvNeSb5j+visJH+f5BeuxPUBzNag1uoswMR9WoCxdBZgPI8dAKy2ao+uqye5dhbDsBO2vV2S5L5rXn8neWlVnVtVD5m2Xa+7L5w+fn+S6y27YFU9pKrOqapzLrroojVvDmB2rmxrdRZgNfdpAcbSWYDxPHYAsMKq1+h6ZZJXVtWfdfcFh3n939rd762qL0vysqp660G30VW19AUTu/vMJGcmyYEDB7yoIrAvHYHW6izACu7TAoylswDjeewAYLUdB13bfLKqHpfkVkmuubWxu++82wW7+73T+w9W1XOTfFOSD1TVad19YVWdluSDh7d0gH3lsFqrswBrc58WYCydBRjPYwcAS6w6dOGWpyV5a5LTk/x6kvOTvG63C1XV8VV1wtbHSb4ryT8neUGSM6aznZHk+Ye8aoD955Bbq7MAh8R9WoCxdBZgPI8dACyxzh5d1+3up1bVw7ftJrvrndUsjuv63Kraup2nd/dLpss+q6oenOSCJPc73MUD7COH01qdBVif+7QAY+kswHgeOwBYYp1B1+em9xdW1d2TvC/JKbtdqLvfmeTWS7Z/OMldDmWRABvgkFurswCHxH1agLF0FmA8jx0ALLHOoOu3quo6SR6Z5PeTnJjkZ4auCmDzaC3AWDoLMJbOAoyntQBL7Dro6u4XTR9+LMmdxi4HYDNpLcBYOgswls4CjKe1AMsds9sZquqsqjpp2+mTq+pPxi4LYLNoLcBYOgswls4CjKe1AMvtOuhK8u+6++KtE9390SS3HbckgI2ktQBj6SzAWDoLMJ7WAiyxzqDrmKo6eetEVZ2S9V7bC4D1aS3AWDoLMJbOAoyntQBLrBPCxyd5dVU9O0kluW+S3x66KoDNo7UAY+kswFg6CzCe1gIsseugq7v/vKrOSXLnadN9uvu8scsC2CxaCzCWzgKMpbMA42ktwHI7Drqq6sTuvmTaBfb9SZ6+7XOndPdH9mKBAPuZ1gKMpbMAY+kswHhaC7Daqj26np7kHknOTdLbttd0+qYD1wWwKbQWYCydBRhLZwHG01qAFVYNuh4zvf+a7v70XiwGYANpLcBYOgswls4CjKe1ACscs+JzT5re/8+9WAjAhtJagLF0FmAsnQUYT2sBVli1R9fnqurMJDeoqicf/Mnufti4ZQFsDK0FGEtnAcbSWYDxtBZghVWDrnsk+c4k353F8V8BOPK0FmAsnQUYS2cBxtNagBV2HHR194eSPKOq3tLd/2sP1wSwMbQWYCydBRhLZwHG01qA1XYcdFXVz3f37yb58arqgz9vl1iAK09rAcbSWYCxdBZgPK0FWG3VoQvfMr0/Zy8WArChtBZgLJ0FGEtnAcbTWoAVVh268IXT+7O2tlXVMUmu3d2X7MHaAPY9rQUYS2cBxtJZgPG0FmC1Y3Y7Q1U9vapOrKrjk/xzkvOq6ufGLw1gc2gtwFg6CzCWzgKMp7UAy+066Epyy+mZAfdO8uIkpyd5wNBVAWwerQUYS2cBxtJZgPG0FmCJdQZdx1XVcVkE9AXd/bkk/+ZFDwG4UrQWYCydBRhLZwHG01qAJdYZdD0lyflJjk/yqqq6cRLHfgU4srQWYCydBRhLZwHG01qAJY7d7Qzd/eQkT9626YKqutO4JQFsHq0FGEtnAcbSWYDxtBZguV336Kqqh08vclhV9dSqen2SO+/B2gA2htYCjKWzAGPpLMB4Wguw3DqHLvz304scfleSk7N4gcPHDF0VwObRWoCxdBZgLJ0FGE9rAZZYZ9BV0/vvTfIX3f3mbdsAODK0FmAsnQUYS2cBxtNagCXWGXSdW1UvzSKgf1NVJyS5fOyyADaO1gKMpbMAY+kswHhaC5+nFsMAACAASURBVLDEsWuc58FJbpPknd39yaq6bpIHjV0WwMbRWoCxdBZgLJ0FGE9rAZbYddDV3ZdX1buSfFVVXXMP1gSwcbQWYCydBRhLZwHG01qA5XYddFXVjyd5eJIbJHljktsleXWSO49dGsDm0FqAsXQWYCydBRhPawGWW+c1uh6e5BuTXNDdd0py2yQXD10VwObRWoCxdBZgLJ0FGE9rAZZYZ9D16e7+dJJU1TW6+61JvnrssgA2jtYCjKWzAGPpLMB4WguwxK6HLkzynqo6Kcnzkrysqj6a5IKxywLYOFoLMJbOAoylswDjaS3AErsOurr7+6cPf62qXpHkOkleMnRVABtGawHG0lmAsXQWYDytBVhux0FXVZ2yZPObpvfXTvKRISsC2CBaCzCWzgKMpbMA42ktwGqr9ug6N0knqW3btk53kpsOXBfAptBagLF0FmAsnQUYT2sBVthx0NXdp+/lQgA2kdYCjKWzAGPpLMB4Wguw2jG7naGqvr+qrrPt9ElVde+xywLYLFoLMJbOAoylswDjaS3AcrsOupI8urs/tnWiuy9O8uhxSwLYSFoLMJbOAoylswDjaS3AEusMupadZ9Vre32RqrpaVb2hql40nT69ql5TVe+oqmdW1dXXvS6AfeywW6uzAGvRWYCxPHYAMJ77tABLrDPoOqeqnlBVXzm9PTGLF0Bc18OTvGXb6ccmeWJ33yzJR5M8+BCuC2C/ujKt1VmA3ekswFgeOwAYz31agCXWGXQ9NMlnkzxzevt0kp9a58qr6gZJ7p7kj6fTleTOSc6eznJWEseRBTjM1uoswNp0FmAsjx0AjOc+LcASu+7a2t2fSPKoZLGLa5Ljp23r+L0kP5/khOn0dZNc3N2XTaffk+T6yy5YVQ9J8pAkudGNbrTmzQHM05Vorc4CrOFodHa6La0FNoLHDgDG89gBwHK77tFVVU+vqhOr6vgkb0pyXlX93BqXu0eSD3b3oRyq4Au6+8zuPtDdB0499dTDuQqA2Tic1uoswPqORmcTrQU2h8cOAMbz2AHAcuscuvCW3X1JFruvvjjJ6UkesMbl7pDknlV1fpJnZLE77JOSnFRVW3uS3SDJew910QD70OG0VmcB1qezAGN57ABgPPdpAZZYZ9B1XFUdl0VAX9Ddn0vSu12ou3+xu2/Q3TdJ8sNJ/q6775/kFUnuO53tjCTPP6yVA+wvh9xanQU4JDoLMJbHDgDGc58WYIl1Bl1PSXJ+kuOTvKqqbpzkkitxm7+Q5BFV9Y4sjgf71CtxXQD7xZFsrc4C/Fs6CzCWxw4AxnOfFmCJ6t71CVb/9kJVx257scLhDhw40Oecc85e3RzAF1TVud194Cjd9p61VmeBo+lotdZ9WmBT6CzAWB47ABhvVWuPXbZxutCPdfdfVtUjdjjLE47I6gA2mNYCjKWzAGPpLMB4Wguw2o6Drix2gU2SE/ZiIQAbSmsBxtJZgLF0FmA8rQVYYcdBV3c/ZXr/63u3HIDNorUAY+kswFg6CzCe1gKsturQhU9edcHuftiRXw7AZtFagLF0FmAsnQUYT2sBVlt16MKfTPLPSZ6V5H1Jak9WBLBZtBZgLJ0FGEtnAcbTWoAVVg26Tkvyg0l+KMllSZ6Z5OzuvngvFgawIbQWYCydBRhLZwHG01qAFY7Z6RPd/eHu/m/dfackD0pyUpLzquoBe7Y6gH1OawHG0lmAsXQWYDytBVht1R5dSZKq+vokP5LkrklenOTc0YsC2DRaCzCWzgKMpbMA42ktwHI7Drqq6jeS3D3JW5I8I8kvdvdle7UwgE2gtQBj6SzAWDoLMJ7WAqy2ao+uX07yriS3nt5+p6qSxYsddnf/u/HLA9j3tBZgLJ0FGEtnAcbTWoAVVg26Tt+zVQBsLq0FGEtnAcbSWYDxtBZghR0HXd19wV4uBGATaS3AWDoLMJbOAoyntQCrHXO0FwAAAAAAAACHw6ALAAAAAACAWdpx0FVVL5/eP3bvlgOwWbQWYCydBRhLZwHG01qA1XZ8ja4kp1XVtyS5Z1U9I0lt/2R3v37oygA2g9YCjKWzAGPpLMB4WguwwqpB168m+ZUkN0jyhIM+10nuPGpRABtEawHG0lmAsXQWYDytBVhhx0FXd5+d5Oyq+pXu/s09XBPAxtBagLF0FmAsnQUYT2sBVlu1R1eSpLt/s6rumeSO06a/7+4XjV0WwGbRWoCxdBZgLJ0FGE9rAZY7ZrczVNV/TvLwJOdNbw+vqt8ZvTCATaK1AGPpLMBYOgswntYCLLfrHl1J7p7kNt19eZJU1VlJ3pDkl0YuDGDDaC3AWDoLMJbOAoyntQBL7LpH1+SkbR9fZ8RCANBagMF0FmAsnQUYT2sBDrLOHl3/OckbquoVSSqLY8A+auiqADaP1gKMpbMAY+kswHhaC7DEroOu7v6rqvr7JN84bfqF7n7/0FUBbBitBRhLZwHG0lmA8bQWYLl19uhKd1+Y5AWD1wKw0bQWYCydBRhLZwHG01qAf2vd1+gCAAAAAACAqxSDLgAAAAAAAGZp5aCrqq5WVW/dq8UAbCKtBRhLZwHG0lmA8bQWYGcrB13d/fkkb6uqG+3RegA2jtYCjKWzAGPpLMB4Wguws2PXOM/JSd5cVa9N8omtjd19z2GrAtg8Wgswls4CjKWzAONpLcAS6wy6fmX4KgDQWoCxdBZgLJ0FGE9rAZbYddDV3a+sqhsnuXl3/21VfUmSq41fGsDm0FqAsXQWYCydBRhPawGWW/kaXUlSVf93krOTPGXadP0kzxu5KIBNo7UAY+kswFg6CzCe1gIst+ugK8lPJblDkkuSpLvfnuTLRi4KYANpLcBYOgswls4CjKe1AEusM+j6THd/dutEVR2bpMctCWAjaS3AWDoLMJbOAoyntQBLrDPoemVV/VKSa1XVXZM8O8kLxy4LYONoLcBYOgswls4CjKe1AEusM+h6VJKLkrwpyU8k+e9JfnnkogA2kNYCjKWzAGPpLMB4WguwxLG7naG7L6+qs5K8JotdYd/W3bvuEltV10zyqiTXmG7n7O5+dFWdnuQZSa6b5NwkD9i+yy3AJjqc1uoswPrcpwUYS2cBxvPYAcByu+7RVVV3T/IvSZ6c5A+SvKOq7rbGdX8myZ27+9ZJbpPke6rqdkkem+SJ3X2zJB9N8uDDXTzAfnGYrdVZgDW5Twswls4CjOexA4Dl1jl04eOT3Km7v6O7vz3JnZI8cbcL9cLHp5PHTW+d5M5Jzp62n5Xk3oe8aoD955Bbq7MAh8R9WoCxdBZgPI8dACyxzqDr0u5+x7bT70xy6TpXXlVXq6o3Jvlgkpdl8YyDi7v7suks70ly/R0u+5CqOqeqzrnooovWuTmAOTus1uoswNrcpwUYS2cBxvPYAcASO75GV1XdZ/rwnKr670melcW0/weTvG6dK+/uzye5TVWdlOS5SW6x7sK6+8wkZybJgQMHdj2uN8AcXdnW6izAau7TAoylswDjeewAYLUdB11Jvm/bxx9I8u3Txxcludah3Eh3X1xVr0hy+yQnVdWx0zMGbpDkvYdyXQD7zBFprc4C7Mh9WoCxdBZgPI8dAKyw46Crux90Za64qk5N8rkpoNdKctcsXuTwFUnum+QZSc5I8vwrczsAc3ZlWquzALtznxZgLJ0FGM9jBwCrrdqjK0lSVacneWiSm2w/f3ffc5eLnpbkrKq6WhavBfas7n5RVZ2X5BlV9VtJ3pDkqYe5doB94zBbq7MAa3KfFmAsnQUYz2MHAMvtOuhK8rwsQvfCJJeve8Xd/b+T3HbJ9ncm+aZ1rwdgQxxya3UW4JC4Twswls4CjOexA4Al1hl0fbq7nzx8JQCbTWsBxtJZgLF0FmA8rQVYYp1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          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Here we're using the same scale as what was used for the dense network, to make comparison easy. The convolutional network is definitely misclassifying less often.\n",
        "\n",
        "With the convolutional network, we don't get anywhere close to the number of misclassifications that the dense network had for many of its labels.\n",
        "\n",
        "The most significant cases in the convolutional network are when we incorrectly predict a different digit in about 10 instances, whereas the dense network would sometimes incorrectly predict a digit in about 65 instances instead of the true digit.\n"
      ],
      "metadata": {
        "id": "JrHg0bZOVLgO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## The Numbers\n",
        "---\n",
        "\n"
      ],
      "metadata": {
        "id": "DEbOeOJezN9g"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Following the same pattern as the dense network, we'll now look at our metrics.\n",
        "\n",
        "Starting with the accuracy again:"
      ],
      "metadata": {
        "id": "0uunqw-hzN9h"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "cf_matr.diagonal()/cf_matr.sum(axis=1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c449a714-262a-43fe-a988-a95fc304839c",
        "id": "JJurCPTMzN9i"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.99183673, 0.99559471, 0.98158915, 0.96732673, 0.98065173,\n",
              "       0.97757848, 0.98538622, 0.96595331, 0.96406571, 0.96333003])"
            ]
          },
          "metadata": {},
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the array above, the index corresponds to the digit.\n",
        "\n",
        "Our accuracy for each digit is quite a bit higher than that of the dense network. Previously, we had some accuracies in the 80-90% range, but the convolutional network has an accuracies greater than 96% for all labels.\n",
        "\n",
        "The digits the convolutional network has the least accuracy for are 7 and 8 (although their accuracies are ~96%)."
      ],
      "metadata": {
        "id": "oH_27B8nzN9j"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Next, we'll look at our precision and recall scores for each label.\n",
        "\n",
        "Using Sklearn's [classification_report function](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.classification_report.html) again:"
      ],
      "metadata": {
        "id": "PUzEDPU4zN9j"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(classification_report(y_test, y_test_preds))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ff8e36ec-dcc5-44ae-b1a7-6d95b431b9f1",
        "id": "op_yPOmhzN9k"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "              precision    recall  f1-score   support\n",
            "\n",
            "           0       0.97      0.99      0.98       980\n",
            "           1       0.97      1.00      0.98      1135\n",
            "           2       0.97      0.98      0.97      1032\n",
            "           3       0.98      0.97      0.98      1010\n",
            "           4       0.98      0.98      0.98       982\n",
            "           5       0.98      0.98      0.98       892\n",
            "           6       0.98      0.99      0.98       958\n",
            "           7       0.98      0.97      0.97      1028\n",
            "           8       0.98      0.96      0.97       974\n",
            "           9       0.98      0.96      0.97      1009\n",
            "\n",
            "    accuracy                           0.98     10000\n",
            "   macro avg       0.98      0.98      0.98     10000\n",
            "weighted avg       0.98      0.98      0.98     10000\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The convolutional network also has much greater precision than the dense network. Where the dense network had some precisions in the 82s and 79s, our lowest precision in the convolutional network is 97%. We can be fairly certain that when the model predicts a digit, it is a correct prediction.\n",
        "\n",
        "The recall of our convolutional network also tells a similar story - the recalls range from 96% to 100%, while the recalls of the dense network were closer to 90%, going as low as 82%. Recalls this high tell us our model is predicting a high number of digits correctly, as the recall is the ratio of true positives to to the total number of positive labels.\n",
        "\n"
      ],
      "metadata": {
        "id": "oIGmICBGzN9k"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Conclusion\n",
        "\n",
        "---\n",
        "\n"
      ],
      "metadata": {
        "id": "oQ7GljB3zN9k"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The dense network, all things considered, performed fairly well. With accuracies, precisions and recalls ~ 90%, it could predict 0s well, but had difficulties with 5s and 8s.\n",
        "\n",
        "The convolutional network outperformed the dense network, having accuracies, precisions and recalls of ~ 98%. It has some slight trouble predicting the digit 7, but could still do so better than the dense network.\n",
        "\n",
        "The convolutional network was able to perform better because of its convolutional layers, which are better suited for extracting features from images than a traditional dense network. Dense networks must rely purely on adjustments during training in order to learn features from images."
      ],
      "metadata": {
        "id": "842uVyzgi0S0"
      }
    }
  ]
}