SuperBasicImageClassification_Conv.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/jansoe/AICA/blob/main/SuperBasicImageClassification_Conv.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kJLb0L98ur9d"
      },
      "source": [
        "# A simple Artifical Neural Network"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2D8gzaqdFm3J"
      },
      "source": [
        "import tensorflow as tf\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OOh2DRwrLoJN"
      },
      "source": [
        "## The Data\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7aOlul7618kS"
      },
      "source": [
        "Our toy data: The MNIST dastaset (handwritten digit recognition)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6FK0XF6p1tJv",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3341f6f2-0b58-4b12-c1a8-299fbe9f8a82"
      },
      "source": [
        "mnist = tf.keras.datasets.mnist\n",
        "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()\n",
        "\n",
        "# scaling the pixel values to the range (-1, 1) \n",
        "train_images = (train_images/255 - 0.5) * 2\n",
        "test_images = (test_images/255 - 0.5) * 2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n",
            "11490434/11490434 [==============================] - 2s 0us/step\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ipAYhZWdjaKs",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 452
        },
        "outputId": "afe7a607-dfde-4739-d175-9ba92c67531e"
      },
      "source": [
        "_ = plt.imshow(test_images[2], cmap=plt.cm.gray)\n",
        "_ = plt.title('Label: %s'%test_labels[2])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c4gvGiq8qxOo",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2fd74543-ed5f-4a96-9508-13c5aa10722c"
      },
      "source": [
        "train_images.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lRX-plXXq5Ta"
      },
      "source": [
        "The training data conatins 60.000 samples of handwritten digits. \n",
        "The data is inherently 2D (28x28 pixel).\n",
        "\n",
        "For our first network we will create now a simple 1D-Vector by flattening the images and thus discarding the 2D neighbourhood structure."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9RaVzw2Vq4d8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8b8c3d30-3335-42a0-dad6-087c12701640"
      },
      "source": [
        "train_images_flat = train_images.reshape((-1, 28*28))\n",
        "test_images_flat = test_images.reshape((-1, 28*28))\n",
        "\n",
        "train_images_flat.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000, 784)"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 76
        },
        "id": "2yGULPVcKjQt",
        "outputId": "d74a39a7-d942-481e-e872-23601bc4495b"
      },
      "source": [
        "plt.figure(figsize=(20,0.1))\n",
        "_ = plt.imshow(test_images_flat[2].reshape(1, -1), cmap=plt.cm.gray, aspect='auto')\n",
        "_ = plt.title('Label: %s'%test_labels[2])\n",
        "_ = plt.yticks([])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 2000x10 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FOOqKQWLL2A0"
      },
      "source": [
        "## The most simple Network "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FVjU-G023yYc"
      },
      "source": [
        "All features (pixel values) are mapped to probabilities for all 10 labels\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Mc5JrZik2cqa"
      },
      "source": [
        "# A Dense Layer ist an all-to-all conection of input and output neurons\n",
        "out_layer = tf.keras.layers.Dense(\n",
        "    input_shape=(784,),             \n",
        "    units=10,                      # output: 10 units for 10 categories\n",
        "    activation='softmax',          # softmax-activation, so that probabilities sum up to 1\n",
        "    name = 'probabilities'\n",
        ")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "C9vs1_u279O2"
      },
      "source": [
        "model1 = tf.keras.models.Sequential()\n",
        "model1.add(out_layer)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tGv2G8eN_5tD",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 201
        },
        "outputId": "3b01704d-b35c-4312-e905-0e31a9450c1c"
      },
      "source": [
        "tf.keras.utils.plot_model(model1, show_shapes=True)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YUuXfMJEMVdt",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c69a39e9-33e7-432b-94f6-9a8a28c8554a"
      },
      "source": [
        "model1.summary()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model: \"sequential\"\n",
            "_________________________________________________________________\n",
            " Layer (type)                Output Shape              Param #   \n",
            "=================================================================\n",
            " probabilities (Dense)       (None, 10)                7850      \n",
            "                                                                 \n",
            "=================================================================\n",
            "Total params: 7,850\n",
            "Trainable params: 7,850\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Dow5veHRA1wX"
      },
      "source": [
        "For training the model we need to specify the loss to minimize, and the procedure to do this.\n",
        "\n",
        "For our case of `multiclass-classification` we can use the loss of `categorical_crossentropy`, which measures how many bits of uncertainty are left to obtain the true labels given our prediction.\n",
        "\n",
        "We use **sparse**`_categorical_crossentropy` because our labels are encoded sparse i.e. as integers 0,1,..,9 and not as binary **one-hot** labels: (1,0,0,0,0,0,0,0,0,0,0), (0,1,0,0,0,0,0,0,0,0,0), ...,  (0,0,0,0,0,0,0,0,0,0,1)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "D3Nad9XbA8XW"
      },
      "source": [
        "model1.compile(\n",
        "    loss = 'sparse_categorical_crossentropy', \n",
        "    optimizer = 'SGD',      # optimization procdure\n",
        "    metrics = ['accuracy']  # Monitoring training\n",
        ")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MB4gy14O-LzI"
      },
      "source": [
        "Now we can fit our data to the model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SVZUPHhm8LOD",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c8ac0508-7a31-462b-ce7d-a2ff63cc99d7"
      },
      "source": [
        "history = model1.fit(\n",
        "    x = train_images_flat, \n",
        "    y = train_labels,\n",
        "    batch_size = 16,\n",
        "    validation_data = (test_images_flat, test_labels),\n",
        "    epochs = 20  # one epoche is one sweep through the training data\n",
        ")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/20\n",
            "3750/3750 [==============================] - 25s 5ms/step - loss: 0.4497 - accuracy: 0.8695 - val_loss: 0.3308 - val_accuracy: 0.9031\n",
            "Epoch 2/20\n",
            "3750/3750 [==============================] - 13s 3ms/step - loss: 0.3299 - accuracy: 0.9053 - val_loss: 0.3080 - val_accuracy: 0.9157\n",
            "Epoch 3/20\n",
            "3750/3750 [==============================] - 10s 3ms/step - loss: 0.3108 - accuracy: 0.9100 - val_loss: 0.2983 - val_accuracy: 0.9148\n",
            "Epoch 4/20\n",
            "3750/3750 [==============================] - 12s 3ms/step - loss: 0.3008 - accuracy: 0.9133 - val_loss: 0.2960 - val_accuracy: 0.9127\n",
            "Epoch 5/20\n",
            "3750/3750 [==============================] - 10s 3ms/step - loss: 0.2942 - accuracy: 0.9158 - val_loss: 0.2839 - val_accuracy: 0.9183\n",
            "Epoch 6/20\n",
            "3750/3750 [==============================] - 10s 3ms/step - loss: 0.2896 - accuracy: 0.9178 - val_loss: 0.2844 - val_accuracy: 0.9200\n",
            "Epoch 7/20\n",
            "3750/3750 [==============================] - 10s 3ms/step - loss: 0.2862 - accuracy: 0.9185 - val_loss: 0.2866 - val_accuracy: 0.9182\n",
            "Epoch 8/20\n",
            "3750/3750 [==============================] - 10s 3ms/step - loss: 0.2830 - accuracy: 0.9193 - val_loss: 0.2830 - val_accuracy: 0.9175\n",
            "Epoch 9/20\n",
            "3750/3750 [==============================] - 10s 3ms/step - loss: 0.2804 - accuracy: 0.9208 - val_loss: 0.2776 - val_accuracy: 0.9211\n",
            "Epoch 10/20\n",
            "3750/3750 [==============================] - 10s 3ms/step - loss: 0.2788 - accuracy: 0.9214 - val_loss: 0.2890 - val_accuracy: 0.9206\n",
            "Epoch 11/20\n",
            "3750/3750 [==============================] - 10s 3ms/step - loss: 0.2766 - accuracy: 0.9214 - val_loss: 0.2910 - val_accuracy: 0.9170\n",
            "Epoch 12/20\n",
            "3750/3750 [==============================] - 11s 3ms/step - loss: 0.2750 - accuracy: 0.9223 - val_loss: 0.2738 - val_accuracy: 0.9243\n",
            "Epoch 13/20\n",
            "3750/3750 [==============================] - 12s 3ms/step - loss: 0.2734 - accuracy: 0.9240 - val_loss: 0.2844 - val_accuracy: 0.9200\n",
            "Epoch 14/20\n",
            "3750/3750 [==============================] - 11s 3ms/step - loss: 0.2718 - accuracy: 0.9236 - val_loss: 0.2821 - val_accuracy: 0.9208\n",
            "Epoch 15/20\n",
            "3750/3750 [==============================] - 10s 3ms/step - loss: 0.2704 - accuracy: 0.9240 - val_loss: 0.2741 - val_accuracy: 0.9213\n",
            "Epoch 16/20\n",
            "3750/3750 [==============================] - 11s 3ms/step - loss: 0.2699 - accuracy: 0.9244 - val_loss: 0.2879 - val_accuracy: 0.9178\n",
            "Epoch 17/20\n",
            "3750/3750 [==============================] - 10s 3ms/step - loss: 0.2678 - accuracy: 0.9251 - val_loss: 0.2711 - val_accuracy: 0.9232\n",
            "Epoch 18/20\n",
            "3750/3750 [==============================] - 10s 3ms/step - loss: 0.2673 - accuracy: 0.9253 - val_loss: 0.2716 - val_accuracy: 0.9245\n",
            "Epoch 19/20\n",
            "3750/3750 [==============================] - 10s 3ms/step - loss: 0.2661 - accuracy: 0.9259 - val_loss: 0.2766 - val_accuracy: 0.9213\n",
            "Epoch 20/20\n",
            "3750/3750 [==============================] - 10s 3ms/step - loss: 0.2654 - accuracy: 0.9255 - val_loss: 0.2756 - val_accuracy: 0.9224\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "id": "8N-PpsB1Gm4h",
        "outputId": "fd76e540-076a-488e-e1d9-eed51cf5f480"
      },
      "source": [
        "plt.plot(history.history['accuracy'], label='Training')\n",
        "plt.plot(history.history['val_accuracy'], label='Validation')\n",
        "plt.ylim([.8, .95])\n",
        "plt.ylabel('Accuracy')\n",
        "plt.xlabel('Epoch')\n",
        "plt.legend()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f7e5a154970>"
            ]
          },
          "metadata": {},
          "execution_count": 13
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HkyCMsdtgJrW"
      },
      "source": [
        "## Getting Deeper  \n",
        "\n",
        "Additional `hidden layers` increase complexity and thus expressiveness of the network."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8L0RpGCv-c3e"
      },
      "source": [
        "hidden_layer = tf.keras.layers.Dense( \n",
        "    input_shape = (28*28,), \n",
        "    units=200,            # 200 units als intermediate-output\n",
        "    activation = 'relu',  # one of the most popular activation functions \n",
        "    name = 'hidden'\n",
        ") "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q6jmSNym-cxC"
      },
      "source": [
        "# unser outputlayer wie oben\n",
        "out_layer = tf.keras.layers.Dense( \n",
        "    units=10,                      \n",
        "    activation='softmax',  \n",
        "    name= 'out'\n",
        ")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eSx3lZlr-cpQ"
      },
      "source": [
        "model2 = tf.keras.models.Sequential()\n",
        "\n",
        "model2.add(hidden_layer)\n",
        "model2.add(out_layer)\n",
        "\n",
        "model2.compile(\n",
        "    loss = 'sparse_categorical_crossentropy',  # Klassifizierungsfehler\n",
        "    metrics = ['accuracy'],  # Anteil korrekt klassifizierter Samples des Validierungsdatensatzes\n",
        ")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-GOOX3F3Et-t",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "outputId": "172ce007-e08a-410a-ba9a-131d31ba08e5"
      },
      "source": [
        "tf.keras.utils.plot_model(model2, show_shapes=True)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LuniAJBoMEbs",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "621cc461-913e-4310-9fe9-10a0b4df9640"
      },
      "source": [
        "model2.summary()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model: \"sequential_1\"\n",
            "_________________________________________________________________\n",
            " Layer (type)                Output Shape              Param #   \n",
            "=================================================================\n",
            " hidden (Dense)              (None, 200)               157000    \n",
            "                                                                 \n",
            " out (Dense)                 (None, 10)                2010      \n",
            "                                                                 \n",
            "=================================================================\n",
            "Total params: 159,010\n",
            "Trainable params: 159,010\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2P0A9eM7FLs-",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "44f011bd-ed6f-49fe-e6a2-c98bed3a4f90"
      },
      "source": [
        "history = model2.fit(\n",
        "    x = train_images_flat, \n",
        "    y = train_labels,\n",
        "    validation_data = (test_images_flat, test_labels),\n",
        "    epochs = 20\n",
        ")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/20\n",
            "1875/1875 [==============================] - 7s 3ms/step - loss: 0.3183 - accuracy: 0.9021 - val_loss: 0.1668 - val_accuracy: 0.9501\n",
            "Epoch 2/20\n",
            "1875/1875 [==============================] - 5s 3ms/step - loss: 0.1584 - accuracy: 0.9528 - val_loss: 0.1443 - val_accuracy: 0.9622\n",
            "Epoch 3/20\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.1255 - accuracy: 0.9643 - val_loss: 0.1273 - val_accuracy: 0.9654\n",
            "Epoch 4/20\n",
            "1875/1875 [==============================] - 5s 3ms/step - loss: 0.1084 - accuracy: 0.9692 - val_loss: 0.1570 - val_accuracy: 0.9586\n",
            "Epoch 5/20\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.1029 - accuracy: 0.9709 - val_loss: 0.1488 - val_accuracy: 0.9636\n",
            "Epoch 6/20\n",
            "1875/1875 [==============================] - 5s 3ms/step - loss: 0.0910 - accuracy: 0.9756 - val_loss: 0.1247 - val_accuracy: 0.9691\n",
            "Epoch 7/20\n",
            "1875/1875 [==============================] - 5s 3ms/step - loss: 0.0873 - accuracy: 0.9764 - val_loss: 0.1265 - val_accuracy: 0.9721\n",
            "Epoch 8/20\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.0808 - accuracy: 0.9796 - val_loss: 0.1565 - val_accuracy: 0.9681\n",
            "Epoch 9/20\n",
            "1875/1875 [==============================] - 5s 3ms/step - loss: 0.0749 - accuracy: 0.9805 - val_loss: 0.1459 - val_accuracy: 0.9709\n",
            "Epoch 10/20\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.0700 - accuracy: 0.9812 - val_loss: 0.1326 - val_accuracy: 0.9735\n",
            "Epoch 11/20\n",
            "1875/1875 [==============================] - 5s 3ms/step - loss: 0.0671 - accuracy: 0.9823 - val_loss: 0.1473 - val_accuracy: 0.9699\n",
            "Epoch 12/20\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.0619 - accuracy: 0.9845 - val_loss: 0.1438 - val_accuracy: 0.9717\n",
            "Epoch 13/20\n",
            "1875/1875 [==============================] - 5s 3ms/step - loss: 0.0605 - accuracy: 0.9845 - val_loss: 0.1573 - val_accuracy: 0.9718\n",
            "Epoch 14/20\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.0554 - accuracy: 0.9861 - val_loss: 0.1523 - val_accuracy: 0.9730\n",
            "Epoch 15/20\n",
            "1875/1875 [==============================] - 5s 3ms/step - loss: 0.0531 - accuracy: 0.9861 - val_loss: 0.1589 - val_accuracy: 0.9732\n",
            "Epoch 16/20\n",
            "1875/1875 [==============================] - 5s 3ms/step - loss: 0.0504 - accuracy: 0.9870 - val_loss: 0.1588 - val_accuracy: 0.9736\n",
            "Epoch 17/20\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.0450 - accuracy: 0.9884 - val_loss: 0.1718 - val_accuracy: 0.9707\n",
            "Epoch 18/20\n",
            "1875/1875 [==============================] - 5s 3ms/step - loss: 0.0464 - accuracy: 0.9883 - val_loss: 0.2146 - val_accuracy: 0.9686\n",
            "Epoch 19/20\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.0410 - accuracy: 0.9891 - val_loss: 0.1695 - val_accuracy: 0.9746\n",
            "Epoch 20/20\n",
            "1875/1875 [==============================] - 5s 3ms/step - loss: 0.0416 - accuracy: 0.9895 - val_loss: 0.1685 - val_accuracy: 0.9755\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lxYWbfMrozxz"
      },
      "source": [
        "\n",
        "### Experiments Suggestions\n",
        "Observe the train and validation error \n",
        "- in/decrease the number of neurons in the `hidden layer` (getting wider)\n",
        "- with a second `hidden layer 2` (getting deeper) \n"
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "rBTrHCP3Mzfh"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Lha1ZoUkuRKz"
      },
      "source": [
        "## Convolutional Neural Networks (CNN)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6BhjT8aLDD6z"
      },
      "source": [
        "![Förderprogramm LINK der Stiftung Niedersachsen - Aufgabensammlung 1](https://raw.githubusercontent.com/vdumoulin/conv_arithmetic/master/gif/padding_strides.gif) https://github.com/vdumoulin/conv_arithmetic"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BOKrT5XbDscs"
      },
      "source": [
        "Convolutional Neural Networks reflect the inherent 2D-structure of images.\n",
        "\n",
        "Every convolution filter \"looks\" for a specific local feature in across the image "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aagPdunD3Dp0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9cccef6e-6c0e-4423-d5de-e666630d3b9d"
      },
      "source": [
        "input_layer = tf.keras.layers.Conv2D(\n",
        "    input_shape = (28, 28, 1),    # our input shape (1 colour channel)\n",
        "    filters = 24,                 # how many filter/feature we want to learn\n",
        "    kernel_size = (5,5),          # filtersize\n",
        "    activation= 'relu',\n",
        "    strides=2\n",
        ")\n",
        "\n",
        "hidden_convolution = tf.keras.layers.Conv2D(\n",
        "    filters = 48,                  \n",
        "    kernel_size = (5,5),\n",
        "    activation= 'relu',\n",
        "    strides=2\n",
        ")\n",
        "\n",
        "flatten_layer = tf.keras.layers.Flatten()\n",
        "\n",
        "intermediate_layer = tf.keras.layers.Dense( \n",
        "    units = 256,\n",
        "    activation = 'relu',\n",
        ")\n",
        "\n",
        "out_layer = tf.keras.layers.Dense( \n",
        "    units=10,                     \n",
        "    activation='softmax',           \n",
        "    name = 'out'\n",
        ")\n",
        "\n",
        "\n",
        "model3 = tf.keras.models.Sequential()\n",
        "model3.add(input_layer)\n",
        "model3.add(hidden_convolution)\n",
        "model3.add(intermediate_layer)\n",
        "model3.add(flatten_layer)\n",
        "model3.add(out_layer)\n",
        "\n",
        "model3.compile(\n",
        "    loss = 'sparse_categorical_crossentropy',\n",
        "    # a more sophisticated optimizer than SGD\n",
        "    optimizer = tf.keras.optimizers.Adam(learning_rate=1E-4), \n",
        "    metrics = ['accuracy'],                    \n",
        ")\n",
        "\n",
        "tf.keras.utils.plot_model(model3, show_shapes=True)\n",
        "model3.summary()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model: \"sequential_2\"\n",
            "_________________________________________________________________\n",
            " Layer (type)                Output Shape              Param #   \n",
            "=================================================================\n",
            " conv2d (Conv2D)             (None, 12, 12, 24)        624       \n",
            "                                                                 \n",
            " conv2d_1 (Conv2D)           (None, 4, 4, 48)          28848     \n",
            "                                                                 \n",
            " dense (Dense)               (None, 4, 4, 256)         12544     \n",
            "                                                                 \n",
            " flatten (Flatten)           (None, 4096)              0         \n",
            "                                                                 \n",
            " out (Dense)                 (None, 10)                40970     \n",
            "                                                                 \n",
            "=================================================================\n",
            "Total params: 82,986\n",
            "Trainable params: 82,986\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CxfhtUK4Ofsm"
      },
      "source": [
        "A `Conv2D`-layer works on 2D data with multiple channels. In our case (MNIST) we have only one color channel (grey) which we need to explicitly add in the data \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nAczXSNUO7gT"
      },
      "source": [
        "train_images_ch = train_images.reshape(-1, 28, 28, 1)\n",
        "test_images_ch = test_images.reshape(-1, 28, 28, 1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wySN86igB3nm"
      },
      "source": [
        "now we can train the model\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wQ9Cpe-W3Toa",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "69a3f56f-5266-45ee-9732-0b5faf036666"
      },
      "source": [
        "history = model3.fit(\n",
        "    x = train_images_ch, \n",
        "    y = train_labels,\n",
        "    validation_data = (test_images_ch, test_labels),\n",
        "    epochs = 20\n",
        ")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/20\n",
            "1875/1875 [==============================] - 14s 4ms/step - loss: 0.4180 - accuracy: 0.8858 - val_loss: 0.1471 - val_accuracy: 0.9564\n",
            "Epoch 2/20\n",
            "1875/1875 [==============================] - 7s 4ms/step - loss: 0.1215 - accuracy: 0.9644 - val_loss: 0.0781 - val_accuracy: 0.9754\n",
            "Epoch 3/20\n",
            "1875/1875 [==============================] - 8s 4ms/step - loss: 0.0809 - accuracy: 0.9761 - val_loss: 0.0592 - val_accuracy: 0.9815\n",
            "Epoch 4/20\n",
            "1875/1875 [==============================] - 7s 4ms/step - loss: 0.0636 - accuracy: 0.9812 - val_loss: 0.0483 - val_accuracy: 0.9855\n",
            "Epoch 5/20\n",
            "1875/1875 [==============================] - 8s 4ms/step - loss: 0.0533 - accuracy: 0.9838 - val_loss: 0.0444 - val_accuracy: 0.9862\n",
            "Epoch 6/20\n",
            "1875/1875 [==============================] - 7s 4ms/step - loss: 0.0459 - accuracy: 0.9862 - val_loss: 0.0417 - val_accuracy: 0.9859\n",
            "Epoch 7/20\n",
            "1875/1875 [==============================] - 7s 4ms/step - loss: 0.0412 - accuracy: 0.9878 - val_loss: 0.0362 - val_accuracy: 0.9883\n",
            "Epoch 8/20\n",
            "1875/1875 [==============================] - 8s 4ms/step - loss: 0.0360 - accuracy: 0.9891 - val_loss: 0.0379 - val_accuracy: 0.9879\n",
            "Epoch 9/20\n",
            "1875/1875 [==============================] - 8s 4ms/step - loss: 0.0324 - accuracy: 0.9901 - val_loss: 0.0339 - val_accuracy: 0.9886\n",
            "Epoch 10/20\n",
            "1875/1875 [==============================] - 8s 4ms/step - loss: 0.0294 - accuracy: 0.9905 - val_loss: 0.0319 - val_accuracy: 0.9890\n",
            "Epoch 11/20\n",
            "1875/1875 [==============================] - 8s 4ms/step - loss: 0.0264 - accuracy: 0.9922 - val_loss: 0.0355 - val_accuracy: 0.9880\n",
            "Epoch 12/20\n",
            "1875/1875 [==============================] - 8s 4ms/step - loss: 0.0239 - accuracy: 0.9928 - val_loss: 0.0341 - val_accuracy: 0.9886\n",
            "Epoch 13/20\n",
            "1875/1875 [==============================] - 8s 4ms/step - loss: 0.0217 - accuracy: 0.9936 - val_loss: 0.0330 - val_accuracy: 0.9878\n",
            "Epoch 14/20\n",
            "1875/1875 [==============================] - 8s 4ms/step - loss: 0.0190 - accuracy: 0.9943 - val_loss: 0.0318 - val_accuracy: 0.9898\n",
            "Epoch 15/20\n",
            "1875/1875 [==============================] - 8s 4ms/step - loss: 0.0177 - accuracy: 0.9944 - val_loss: 0.0329 - val_accuracy: 0.9903\n",
            "Epoch 16/20\n",
            "1875/1875 [==============================] - 8s 4ms/step - loss: 0.0159 - accuracy: 0.9950 - val_loss: 0.0317 - val_accuracy: 0.9898\n",
            "Epoch 17/20\n",
            "1875/1875 [==============================] - 8s 4ms/step - loss: 0.0143 - accuracy: 0.9956 - val_loss: 0.0293 - val_accuracy: 0.9910\n",
            "Epoch 18/20\n",
            "1875/1875 [==============================] - 7s 4ms/step - loss: 0.0128 - accuracy: 0.9962 - val_loss: 0.0325 - val_accuracy: 0.9888\n",
            "Epoch 19/20\n",
            "1875/1875 [==============================] - 7s 4ms/step - loss: 0.0112 - accuracy: 0.9968 - val_loss: 0.0349 - val_accuracy: 0.9890\n",
            "Epoch 20/20\n",
            "1875/1875 [==============================] - 7s 4ms/step - loss: 0.0102 - accuracy: 0.9970 - val_loss: 0.0346 - val_accuracy: 0.9885\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NAT4cYavbXbY"
      },
      "source": [
        "### Data Augmentation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7KXpqbBjgjnV"
      },
      "source": [
        "Techniques to close the gap between train and validation error are called  `regularization`.\n",
        "\n",
        "Increasing the available train data is the most straight-forward way, but it is often hard to obtain this data. One simple way to increase the available data is to create slightly modified versions of every train image (augmentation). "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EYiSTHwhTEGP"
      },
      "source": [
        "from tensorflow.keras import layers"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BP5Udsg-TETV"
      },
      "source": [
        "data_augmentation = tf.keras.Sequential([\n",
        "  layers.RandomRotation(0.05),\n",
        "  layers.RandomTranslation(height_factor=0.02, width_factor=0.02),\n",
        "  layers.RandomZoom(height_factor=0.02, width_factor=0.02),\n",
        "])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BrOZ491rTEXh"
      },
      "source": [
        "train_dataset = tf.data.Dataset.from_tensor_slices((train_images_ch, train_labels))\n",
        "train_dataset = train_dataset.shuffle(1024).batch(64)\n",
        "train_dataset = train_dataset.map(lambda x, y: (data_augmentation(x, training=True), y), num_parallel_calls=tf.data.experimental.AUTOTUNE)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gtIttZt-TEcC",
        "outputId": "67969eea-f8de-444a-f709-b05a0c869c11"
      },
      "source": [
        "model3.fit(\n",
        "    train_dataset,\n",
        "    validation_data = (test_images_ch, test_labels),\n",
        "    epochs = 20 \n",
        ")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/20\n",
            "938/938 [==============================] - 20s 21ms/step - loss: 0.0387 - accuracy: 0.9877 - val_loss: 0.0327 - val_accuracy: 0.9897\n",
            "Epoch 2/20\n",
            "938/938 [==============================] - 9s 9ms/step - loss: 0.0376 - accuracy: 0.9881 - val_loss: 0.0338 - val_accuracy: 0.9883\n",
            "Epoch 3/20\n",
            "938/938 [==============================] - 8s 9ms/step - loss: 0.0361 - accuracy: 0.9886 - val_loss: 0.0298 - val_accuracy: 0.9896\n",
            "Epoch 4/20\n",
            "938/938 [==============================] - 9s 9ms/step - loss: 0.0364 - accuracy: 0.9883 - val_loss: 0.0302 - val_accuracy: 0.9911\n",
            "Epoch 5/20\n",
            "938/938 [==============================] - 9s 9ms/step - loss: 0.0327 - accuracy: 0.9894 - val_loss: 0.0301 - val_accuracy: 0.9898\n",
            "Epoch 6/20\n",
            "938/938 [==============================] - 8s 9ms/step - loss: 0.0324 - accuracy: 0.9898 - val_loss: 0.0292 - val_accuracy: 0.9910\n",
            "Epoch 7/20\n",
            "938/938 [==============================] - 7s 8ms/step - loss: 0.0312 - accuracy: 0.9898 - val_loss: 0.0291 - val_accuracy: 0.9903\n",
            "Epoch 8/20\n",
            "938/938 [==============================] - 8s 9ms/step - loss: 0.0302 - accuracy: 0.9903 - val_loss: 0.0274 - val_accuracy: 0.9910\n",
            "Epoch 9/20\n",
            "938/938 [==============================] - 8s 8ms/step - loss: 0.0290 - accuracy: 0.9905 - val_loss: 0.0311 - val_accuracy: 0.9895\n",
            "Epoch 10/20\n",
            "938/938 [==============================] - 9s 10ms/step - loss: 0.0290 - accuracy: 0.9913 - val_loss: 0.0315 - val_accuracy: 0.9905\n",
            "Epoch 11/20\n",
            "938/938 [==============================] - 10s 11ms/step - loss: 0.0286 - accuracy: 0.9910 - val_loss: 0.0311 - val_accuracy: 0.9897\n",
            "Epoch 12/20\n",
            "938/938 [==============================] - 8s 9ms/step - loss: 0.0274 - accuracy: 0.9916 - val_loss: 0.0327 - val_accuracy: 0.9899\n",
            "Epoch 13/20\n",
            "938/938 [==============================] - 9s 10ms/step - loss: 0.0253 - accuracy: 0.9923 - val_loss: 0.0323 - val_accuracy: 0.9895\n",
            "Epoch 14/20\n",
            "938/938 [==============================] - 9s 9ms/step - loss: 0.0264 - accuracy: 0.9915 - val_loss: 0.0281 - val_accuracy: 0.9904\n",
            "Epoch 15/20\n",
            "938/938 [==============================] - 9s 10ms/step - loss: 0.0254 - accuracy: 0.9917 - val_loss: 0.0319 - val_accuracy: 0.9900\n",
            "Epoch 16/20\n",
            "938/938 [==============================] - 9s 10ms/step - loss: 0.0231 - accuracy: 0.9929 - val_loss: 0.0305 - val_accuracy: 0.9900\n",
            "Epoch 17/20\n",
            "938/938 [==============================] - 8s 8ms/step - loss: 0.0233 - accuracy: 0.9928 - val_loss: 0.0307 - val_accuracy: 0.9900\n",
            "Epoch 18/20\n",
            "938/938 [==============================] - 8s 8ms/step - loss: 0.0230 - accuracy: 0.9927 - val_loss: 0.0307 - val_accuracy: 0.9901\n",
            "Epoch 19/20\n",
            "938/938 [==============================] - 9s 10ms/step - loss: 0.0228 - accuracy: 0.9928 - val_loss: 0.0298 - val_accuracy: 0.9906\n",
            "Epoch 20/20\n",
            "938/938 [==============================] - 9s 10ms/step - loss: 0.0224 - accuracy: 0.9929 - val_loss: 0.0315 - val_accuracy: 0.9891\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7f7d9cc3a500>"
            ]
          },
          "metadata": {},
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xjfCXlyIEdYg"
      },
      "source": [
        "### Decreasing the learning rate at the end of training"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AYakH1i1hufA",
        "outputId": "fc945098-7394-49a7-be3d-ca001913b764"
      },
      "source": [
        "model3.compile(\n",
        "    loss = 'sparse_categorical_crossentropy',\n",
        "    # a more sophisticated optimizer than SGD\n",
        "    optimizer = tf.keras.optimizers.Adam(learning_rate=1E-5), \n",
        "    metrics = ['accuracy'],                    \n",
        ")\n",
        "\n",
        "model3.fit(\n",
        "    train_dataset,\n",
        "    validation_data = (test_images, test_labels),\n",
        "    epochs = 20 \n",
        ")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/20\n",
            "938/938 [==============================] - 10s 9ms/step - loss: 0.0186 - accuracy: 0.9940 - val_loss: 0.0257 - val_accuracy: 0.9915\n",
            "Epoch 2/20\n",
            "938/938 [==============================] - 9s 9ms/step - loss: 0.0180 - accuracy: 0.9942 - val_loss: 0.0259 - val_accuracy: 0.9920\n",
            "Epoch 3/20\n",
            "938/938 [==============================] - 8s 9ms/step - loss: 0.0182 - accuracy: 0.9943 - val_loss: 0.0264 - val_accuracy: 0.9917\n",
            "Epoch 4/20\n",
            "938/938 [==============================] - 7s 8ms/step - loss: 0.0171 - accuracy: 0.9947 - val_loss: 0.0261 - val_accuracy: 0.9915\n",
            "Epoch 5/20\n",
            "938/938 [==============================] - 9s 9ms/step - loss: 0.0180 - accuracy: 0.9945 - val_loss: 0.0254 - val_accuracy: 0.9918\n",
            "Epoch 6/20\n",
            "938/938 [==============================] - 9s 10ms/step - loss: 0.0180 - accuracy: 0.9944 - val_loss: 0.0259 - val_accuracy: 0.9919\n",
            "Epoch 7/20\n",
            "938/938 [==============================] - 7s 8ms/step - loss: 0.0163 - accuracy: 0.9951 - val_loss: 0.0260 - val_accuracy: 0.9920\n",
            "Epoch 8/20\n",
            "938/938 [==============================] - 8s 9ms/step - loss: 0.0177 - accuracy: 0.9947 - val_loss: 0.0271 - val_accuracy: 0.9916\n",
            "Epoch 9/20\n",
            "938/938 [==============================] - 9s 10ms/step - loss: 0.0168 - accuracy: 0.9949 - val_loss: 0.0263 - val_accuracy: 0.9918\n",
            "Epoch 10/20\n",
            "938/938 [==============================] - 9s 9ms/step - loss: 0.0176 - accuracy: 0.9946 - val_loss: 0.0253 - val_accuracy: 0.9922\n",
            "Epoch 11/20\n",
            "938/938 [==============================] - 9s 10ms/step - loss: 0.0160 - accuracy: 0.9952 - val_loss: 0.0259 - val_accuracy: 0.9921\n",
            "Epoch 12/20\n",
            "938/938 [==============================] - 8s 8ms/step - loss: 0.0172 - accuracy: 0.9949 - val_loss: 0.0265 - val_accuracy: 0.9920\n",
            "Epoch 13/20\n",
            "938/938 [==============================] - 9s 9ms/step - loss: 0.0167 - accuracy: 0.9948 - val_loss: 0.0259 - val_accuracy: 0.9921\n",
            "Epoch 14/20\n",
            "938/938 [==============================] - 9s 9ms/step - loss: 0.0168 - accuracy: 0.9951 - val_loss: 0.0259 - val_accuracy: 0.9919\n",
            "Epoch 15/20\n",
            "938/938 [==============================] - 9s 9ms/step - loss: 0.0158 - accuracy: 0.9952 - val_loss: 0.0264 - val_accuracy: 0.9917\n",
            "Epoch 16/20\n",
            "938/938 [==============================] - 8s 8ms/step - loss: 0.0172 - accuracy: 0.9942 - val_loss: 0.0259 - val_accuracy: 0.9921\n",
            "Epoch 17/20\n",
            "938/938 [==============================] - 8s 8ms/step - loss: 0.0164 - accuracy: 0.9949 - val_loss: 0.0266 - val_accuracy: 0.9916\n",
            "Epoch 18/20\n",
            "938/938 [==============================] - 9s 9ms/step - loss: 0.0158 - accuracy: 0.9950 - val_loss: 0.0270 - val_accuracy: 0.9915\n",
            "Epoch 19/20\n",
            "938/938 [==============================] - 9s 9ms/step - loss: 0.0162 - accuracy: 0.9950 - val_loss: 0.0259 - val_accuracy: 0.9917\n",
            "Epoch 20/20\n",
            "938/938 [==============================] - 9s 9ms/step - loss: 0.0159 - accuracy: 0.9949 - val_loss: 0.0267 - val_accuracy: 0.9913\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7f7db93b2530>"
            ]
          },
          "metadata": {},
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "### Experiments Suggestions\n",
        "Observe the train and validation error. Also take a look at the number of trainable Paramters \n",
        "- add a second convolutional `hidden layer 2` (getting deeper) and change kernel_size to 3 \n"
      ],
      "metadata": {
        "id": "5JO15cWcxYuy"
      }
    }
  ]
}