computer-vision/visualizing-mnist-digit-averages.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Visualizing MNIST Digit Averages",
      "provenance": [],
      "authorship_tag": "ABX9TyPXZtrvVanD94nNUJ7iYZpn"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MSW--Hn0obwy"
      },
      "source": [
        "# Visualizing MNIST Digit Averages\n",
        "*By Carlos Santiago Bañón*\n",
        "\n",
        "**Year:** 2020\n",
        "\n",
        "**Technologies:** Python, NumPy, Matplotlib\n",
        "\n",
        "**Discipline(s):** Computer Vision\n",
        "\n",
        "**Keywords:** `computer-vision`, `mnist`\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "evDm-alRoguG"
      },
      "source": [
        "This notebook presents the average image for each digit in the MNIST dataset. For each $i = 0, 1, \\dots, 9$, the average representation of digit $i$ is computed and displayed."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7ZiM5EukpFTT"
      },
      "source": [
        "## 1. Import Statements\n",
        "\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eODBP8cGpEa1"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "from keras.datasets import mnist"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TqhbGh7BpPqf"
      },
      "source": [
        "## 2. Load the MNIST Dataset\n",
        "\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AaNBlrx1pSup"
      },
      "source": [
        "For the purposes of this computation, we need to import the MNIST dataset."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TZhl8-jGpWxI"
      },
      "source": [
        "# Load the MNIST dataset.\n",
        "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DM-EK2ZwpmJb"
      },
      "source": [
        "## 3. Compute the Average Image for Each MNIST Digit\n",
        "\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qV0Rt99zpy7z"
      },
      "source": [
        "def compute_avg_MNIST_dig():\n",
        "  \"\"\"\n",
        "  Compute the average image for each MNIST digit, where i = 0, 1, ..., 9.\n",
        "  \"\"\"\n",
        "\n",
        "  # Set up the arrays. Initialize to 0.\n",
        "  avg_dig = np.zeros((10, 28, 28))\n",
        "  dig_freq = np.zeros((10, 1, 1))\n",
        "\n",
        "  # For each i, add all the images and increment the frequency.\n",
        "  for i in np.arange(len(train_images)):\n",
        "    avg_dig[train_labels[i]] += train_images[i]\n",
        "    dig_freq += 1\n",
        "\n",
        "  avg_dig = avg_dig / dig_freq\n",
        "\n",
        "  return avg_dig"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j0IFdICBrT4l"
      },
      "source": [
        "## 4. Display the Averages\n",
        "\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k7zcY1TkuPB0"
      },
      "source": [
        "# Compute the average image for each MNIST digit.\n",
        "average = compute_avg_MNIST_dig()"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TuuCF2UGrgvV"
      },
      "source": [
        "def display_average_MNIST_digits():\n",
        "  \"\"\"\n",
        "  Display the average images computed by compute_avg_MNIST_dig().\n",
        "  \"\"\"\n",
        "\n",
        "  # Set the figure size.\n",
        "  plt.figure(figsize=(16, 16))\n",
        "\n",
        "  # Show every digit.\n",
        "  for i in np.arange(10):\n",
        "    plt.subplot(4, 4, 1 + i)\n",
        "    \n",
        "    # Remove the ticks.\n",
        "    plt.xticks([])\n",
        "    plt.yticks([])\n",
        "\n",
        "    plt.imshow(average[i])\n",
        "\n",
        "  plt.show()"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3v5Kvp_dsq0M",
        "outputId": "e2aad517-d79f-418d-f0e9-6397bfbb34e9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 677
        }
      },
      "source": [
        "# Display the images.\n",
        "display_average_MNIST_digits()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1152x1152 with 10 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}