Autoencoder.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/Autoencoder.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IKgoIQgiDQ0G",
        "outputId": "a1a5e2f2-4a71-4cf8-fa45-7494877a9e29",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "import tensorflow as tf\n",
        "# Es lohnt sich zu überprüfen, ob man auch wirklich eine GPU bekommen hat.\n",
        "print(\"Anzahl der zugewiesenen GPUs:\", len(tf.config.list_physical_devices('GPU')))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Anzahl der zugewiesenen GPUs: 1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Kc79VlOAOM9B"
      },
      "source": [
        "# Autoencoder\n",
        "\n",
        "Der [Autoencoder](https://de.wikipedia.org/wiki/Autoencoder) besteht aus zwei Teilen: einem *Encoder* und einem *Decoder*. Der Encoder bekommt als Input ein Bild und generiert als Output einen *Code* oder *Embedding* der eine kompakte Repräsentation wichtiger Merkmale des Inputs darstellt. Dieses *Embedding* wird dann dem *Decoder* als Input übergeben. Die Aufgabe des Decoders besteht darin, aus dem Code wieder das ursprüngliche Inputbild möglichst gut zu rekonstruieren. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B_z4cD2qSKAY"
      },
      "source": [
        "![](data:image/png;base64,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)\n",
        "(Quelle:https://upload.wikimedia.org/wikipedia/commons/3/37/Autoencoder_schema.png)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sw6-CcDZit1_"
      },
      "source": [
        "Der ursprüngliche Zweck eines Autoencoders ist die Kompression mithilfe einer geeigneten Kodierung. Dieser Code (also die kompakte Repräsentation des Inputs) hat zumeist eine deutlich niedrigere Dimensionalität als das Inputbild. Schafft man es, das Bild aus dem Code zu rekonstruieren, hat man also die im Bild enthaltene relevante Information in einem kompakteren Format gespeichert. Da die Suche nach einer möglichst guten Kodierung dank maschinellen Lernens automatisch passiert, wurde das ganze Autoencoder getauft.\n",
        "\n",
        "Trainiert werden Autoencoder so, dass man für Input und gewünschte Ausgabe jeweils dasselbe Bild präsentiert. Wird der Autoencoder auf einer großen Anzahl von Bildern trainiert, lernt er die in den Bildern enhaltene Struktur und deren Statistik. \n",
        "\n",
        "Wie Ihnen vielleicht schon aufgefallen ist, haben wir es hier mit einem Beispiel von *self-supervised learning* zu tun. Es werden also nicht, wie beim Training von Klassifikationsnetzwerken, annotierte Daten benötigt sondern einfach nur die Bilder, die gleichzeitig Input und gewünschte Ausgabe (Teacher-Signal) sind.\n",
        "\n",
        "Neben der Komprimierung ergibt sich aus der Art wie Autoencoder trainiert werden auch die Möglichkeit, den Decoder getrennt zu verwenden. Ebenso wie der Encoder muss der Decoder die inhärente Struktur der Daten lernen, um die Bilder möglichst gut rekonstruieren zu können. Wir können den Decoder also dazu benutzen, neue Bilder zu generieren. \n",
        "\n",
        "Im Folgenden nehmen wir uns wieder den guten alten MNIST-Datensatz vor, um die Funktionsweise des Autoencoders kennenzulernen."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LOH3x1tXljGx"
      },
      "source": [
        "### Laden des MNIST-Datensatzes\n",
        "\n",
        "Viele der folgenden Schritte kennen Sie bereits. Wir importieren einige Bibliotheken und laden mit Hilfe von `Keras` den MNIST-Datensatz herunter."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c6sSUrDuDXkX"
      },
      "source": [
        "import time\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from tensorflow.keras import layers\n",
        "from IPython import display"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5qZ4SAPRDacS",
        "outputId": "31515b73-3df3-4f8a-e6c5-74ee924e28b9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "# Herunterladen des Datensatzes\n",
        "(train_images, train_labels), (test_images, test_labels) = tf.keras.datasets.mnist.load_data()\n",
        "train_images.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n",
            "11493376/11490434 [==============================] - 0s 0us/step\n",
            "11501568/11490434 [==============================] - 0s 0us/step\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6UX1eYAnDeic",
        "outputId": "48c38fe6-6667-4bd5-94f4-769b578f3502",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "# Hinzufügen einer weiteren Dimension damit der Tensor alle erforderlichen Dimensionen für\n",
        "# Bilddaten in Keras hat (sample, width, height, channel)\n",
        "train_images = train_images[:,:,:,np.newaxis].astype('float32')\n",
        "# Und Skalierung auf den Bereich [0,1]\n",
        "train_images_01 = train_images / 255.\n",
        "\n",
        "test_images = test_images[:,:,:,np.newaxis]\n",
        "test_images_01 = test_images / 255.\n",
        "\n",
        "train_images_01.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000, 28, 28, 1)"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_Q38R8YSm39j"
      },
      "source": [
        "### Encoder und Decoder\n",
        "\n",
        "Wie bereits erwähnt, besteht der Autoencoder aus einem *Encoder* und einem *Decoder*, die wir hier als getrennte Netzwerkteile implementieren. Das *Embedding*, also die Schicht, die die Ausgabe der Encoders und die Eingabe des Decoders darstellt, wird im Fachjargon oft *latente Variable* genannt, da sie *unter der Oberfläche* liegt und nicht direkt einsehbar ist. \n",
        "\n",
        "Wir müssen für unsere *latente Variable* eine Dimensionalität festlegen, also die Anzahl der Elemente/units, aus der das Embedding bestehen soll. Die MNIST-Ziffern haben eine Auflösung von 28x28 Pixel. Die in den Bildern enthaltene Information beschränkt sich aber auf eine von zehn Ziffern. Es ist also davon auszugehen, dass die Information sehr stark komprimiert werden kann. Wir wählen entsprechend ein Embedding mit acht Kanälen."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xh0jExCRNysK"
      },
      "source": [
        "latent_dim = 8\n",
        "\n",
        "encoder = tf.keras.Sequential(\n",
        "    name='encoder',\n",
        "    layers = [\n",
        "        layers.InputLayer(input_shape=(28, 28, 1)),\n",
        "        layers.Conv2D(filters=32, kernel_size=3, strides=2, activation='relu'),\n",
        "        layers.Conv2D(filters=64, kernel_size=3, strides=2, activation='relu'),\n",
        "        layers.Flatten(),\n",
        "        layers.Dense(latent_dim),\n",
        "        ]\n",
        "    )"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yWjTrgZLo28K"
      },
      "source": [
        "Der Decoder soll nun die acht Kanäle der Ausgabeschicht des Encoders wieder in ein 28x28-Pixelbild umwandeln. Wir können uns den Decoder also als eine Art *umgedrehten* Encoder vorstellen. Hierfür bietet sich die in `Keras` implementierte Klasse `Conv2DTranspose` an, die die entsprechende Umkehroperation einer `Conv2D`-Schicht umsetzt."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sPxcbAdVhj2-"
      },
      "source": [
        "decoder = tf.keras.Sequential(\n",
        "    name = 'decoder', \n",
        "    layers = [\n",
        "        layers.InputLayer(input_shape=(latent_dim,)),\n",
        "        layers.Dense(units=7*7*32, activation=tf.nn.relu),\n",
        "        layers.Reshape(target_shape=(7, 7, 32)),\n",
        "        layers.Conv2DTranspose(filters=64, kernel_size=3, strides=2, padding=\"same\", activation='relu'),\n",
        "        layers.Conv2DTranspose(filters=32, kernel_size=3, strides=2, padding=\"same\", activation='relu'),\n",
        "        layers.Conv2DTranspose(filters=1,  kernel_size=3, strides=1, padding=\"same\", activation='sigmoid'),\n",
        "        ]\n",
        "    )"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q-jWvPYjpjcA"
      },
      "source": [
        "Wir können die beiden Netzwerke jetzt verbinden, indem wir ein Modell generieren, dessen *Input* der input des *Encoders* ist, während der *Output* der Output des *Decoders* ist,  dem zuvor der *Output* des Encoders (also das *Embedding*) als *Input* gegeben wurde. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ib91KPB3hkJj"
      },
      "source": [
        "# autoencoder = tf.keras.Sequential([encoder, decoder])\n",
        "# autoencoder = tf.keras.Model(inputs=encoder.input, outputs=decoder(encoder.output))\n",
        "encoder_model = encoder(encoder.input)  # kleiner Hack, um einen besseren Graphen zu bekommen\n",
        "autoencoder = tf.keras.Model(inputs=encoder.input, outputs=decoder(encoder_model))\n",
        "autoencoder.compile(optimizer='adam', loss='binary_crossentropy')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vUk1ExpILaca",
        "outputId": "6870e712-5050-459e-c57f-495aad89a060",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 942
        }
      },
      "source": [
        "tf.keras.utils.plot_model(autoencoder, show_shapes=True, dpi=70, expand_nested=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": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "y1zzu08sqXF2"
      },
      "source": [
        "Unser untrainiertes Modell ist bislang lediglich mit Zufallszahlen gefüllt und generiert daher aus den Inputbildern einen Ameisenkrieg der Größe 28x28."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xO6mkohB7dci",
        "outputId": "1403ed43-6a0c-4af9-9426-aaa5dc334bf0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        }
      },
      "source": [
        "decoded_imgs = autoencoder.predict(test_images_01)\n",
        "\n",
        "n_plot = 10\n",
        "plt.figure(figsize=(20, 4))\n",
        "for i in range(n_plot):\n",
        "    # display original\n",
        "    ax = plt.subplot(2, n_plot, i+1)\n",
        "    plt.imshow(test_images_01[i].reshape(28, 28))\n",
        "    plt.gray()\n",
        "    ax.get_xaxis().set_visible(False)\n",
        "    ax.get_yaxis().set_visible(False)\n",
        "\n",
        "    # display reconstruction\n",
        "    ax = plt.subplot(2, n_plot, i+n_plot+1)\n",
        "    plt.imshow(decoded_imgs[i].reshape(28, 28))\n",
        "    plt.gray()\n",
        "    ax.get_xaxis().set_visible(False)\n",
        "    ax.get_yaxis().set_visible(False)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1440x288 with 20 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mVAQoyg-quxV"
      },
      "source": [
        "### Trainieren des Modells\n",
        "\n",
        "Wir trainieren jetzt den Autoencoder anhand der Ziffernbilder. Beachten Sie, dass `x` und `y` in der `fit`-Funktion als Trainingsdaten *und* gewünschte Ausgabe *dieselbe* Variable sind, da der Autoencoder diese rekonstrukieren soll."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gYuQOgY5hkFB",
        "outputId": "127f908d-ad32-4ab6-c7b0-7af7e2def5b4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "autoencoder.fit(\n",
        "    x = train_images_01, \n",
        "    y = train_images_01,\n",
        "    epochs=40,\n",
        "    batch_size=256,\n",
        "    shuffle=True,\n",
        "    validation_data=(test_images_01, test_images_01)\n",
        ")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/40\n",
            "235/235 [==============================] - 5s 15ms/step - loss: 0.2759 - val_loss: 0.1624\n",
            "Epoch 2/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1454 - val_loss: 0.1349\n",
            "Epoch 3/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1324 - val_loss: 0.1281\n",
            "Epoch 4/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1272 - val_loss: 0.1245\n",
            "Epoch 5/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1240 - val_loss: 0.1218\n",
            "Epoch 6/40\n",
            "235/235 [==============================] - 3s 14ms/step - loss: 0.1219 - val_loss: 0.1200\n",
            "Epoch 7/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1203 - val_loss: 0.1192\n",
            "Epoch 8/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1191 - val_loss: 0.1180\n",
            "Epoch 9/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1182 - val_loss: 0.1169\n",
            "Epoch 10/40\n",
            "235/235 [==============================] - 3s 14ms/step - loss: 0.1172 - val_loss: 0.1167\n",
            "Epoch 11/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1166 - val_loss: 0.1157\n",
            "Epoch 12/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1160 - val_loss: 0.1151\n",
            "Epoch 13/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1154 - val_loss: 0.1146\n",
            "Epoch 14/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1149 - val_loss: 0.1153\n",
            "Epoch 15/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1145 - val_loss: 0.1140\n",
            "Epoch 16/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1141 - val_loss: 0.1137\n",
            "Epoch 17/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1138 - val_loss: 0.1134\n",
            "Epoch 18/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1133 - val_loss: 0.1132\n",
            "Epoch 19/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1131 - val_loss: 0.1133\n",
            "Epoch 20/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1128 - val_loss: 0.1125\n",
            "Epoch 21/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1125 - val_loss: 0.1130\n",
            "Epoch 22/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1123 - val_loss: 0.1124\n",
            "Epoch 23/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1120 - val_loss: 0.1120\n",
            "Epoch 24/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1118 - val_loss: 0.1120\n",
            "Epoch 25/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1116 - val_loss: 0.1117\n",
            "Epoch 26/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1114 - val_loss: 0.1115\n",
            "Epoch 27/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1112 - val_loss: 0.1116\n",
            "Epoch 28/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1111 - val_loss: 0.1111\n",
            "Epoch 29/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1108 - val_loss: 0.1110\n",
            "Epoch 30/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1107 - val_loss: 0.1109\n",
            "Epoch 31/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1106 - val_loss: 0.1106\n",
            "Epoch 32/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1103 - val_loss: 0.1107\n",
            "Epoch 33/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1102 - val_loss: 0.1110\n",
            "Epoch 34/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1101 - val_loss: 0.1109\n",
            "Epoch 35/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1099 - val_loss: 0.1106\n",
            "Epoch 36/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1099 - val_loss: 0.1107\n",
            "Epoch 37/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1097 - val_loss: 0.1101\n",
            "Epoch 38/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1096 - val_loss: 0.1100\n",
            "Epoch 39/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1095 - val_loss: 0.1099\n",
            "Epoch 40/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1092 - val_loss: 0.1100\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7f1dc0211f90>"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j3gKYjYVs1CH"
      },
      "source": [
        "Jetzt können wir das Netzwerk erneut Output zu den Testdaten erzeugen lassen."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LNdJQV7uhj_7",
        "outputId": "bab6e90c-cea2-4c99-acf3-10cd62314c5f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 326
        }
      },
      "source": [
        "encoded_imgs = encoder.predict(test_images_01)\n",
        "de_encoded_imgs = decoder.predict(encoded_imgs)\n",
        "\n",
        "n = 10\n",
        "plt.figure(figsize=(30, 8))\n",
        "for i in range(n):\n",
        "\n",
        "    # display original\n",
        "    ax = plt.subplot(3, n, i+1)\n",
        "    plt.imshow(test_images_01[i].reshape(28, 28))\n",
        "    plt.axis('off')\n",
        "\n",
        "    # encodint original\n",
        "    ax = plt.subplot(3, n, n+i+1)\n",
        "    plt.imshow(encoded_imgs[i].reshape(-1, 2), cmap=plt.cm.Spectral, vmin=-10, vmax=10)\n",
        "    plt.xlim((-5, 9))\n",
        "    plt.ylim((-5, 9))\n",
        "    plt.axis('off')\n",
        "\n",
        "    # display reconstruction\n",
        "    ax = plt.subplot(3, n, 2*n+i+1)\n",
        "    plt.imshow(de_encoded_imgs[i].reshape(28, 28))\n",
        "    plt.axis('off')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 2160x576 with 30 Axes>"
            ],
            "image/png": 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          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K2MkL6Lyo9ZP"
      },
      "source": [
        "Wie wir sehen, erzeugt das Modell Ziffern, die dem Input sehr ähnlich sind. In der Mitte der Darstellung sehen sie den jeweils zugehörigen *Code*. Es ist wichtig sich vor Augen zu führen, dass sämtliche Information im Autoencoder durch diesen *Flaschenhals* fließen muss. Das heisst, die Outputbilder werden aus dem achtstelligen Code generiert und nicht aus dem Inputbild."
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Aufgabe**: Embedding Größe\n",
        "Experimentieren Sie mit der Größe des Embedding. Was beobachten Sie, wenn z.B. es nur 2-dimensional ist?"
      ],
      "metadata": {
        "id": "cDUp7D5tE0hN"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "OTKexjPTMNwB"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tqsso7dFtkfr"
      },
      "source": [
        "### Der Decoder als generatives Modell\n",
        "\n",
        "Da der Decoder nur auf Basis der *latent variable* arbeitet, können wir ihn auch isoliert benutzen. Wir können auf Basis von *Embeddings* mit beliebigen Werten zugehörige Bilder generieren lassen. \n",
        "\n",
        "Versuchen wir zunächst einen zufälligen Embedding:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "572Eq8JKBnY3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 574
        },
        "outputId": "ce49c751-7f7e-4cf1-a3e0-8e5c1448111f"
      },
      "source": [
        "#np.random.seed(44)\n",
        "random_encoding = (np.random.rand(latent_dim)-0.5)*10\n",
        "random_img = decoder.predict(random_encoding[np.newaxis]).reshape((28,28))\n",
        "\n",
        "plt.figure(figsize=(5,10))\n",
        "plt.subplot(2,1,1)\n",
        "plt.imshow(random_encoding.reshape((4,2)),  cmap=plt.cm.Spectral, vmin=-10, vmax=10)\n",
        "plt.axis('off')\n",
        "plt.subplot(2,1,2)\n",
        "plt.imshow(random_img)\n",
        "_ = plt.axis('off')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 360x720 with 2 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q3KZU7CrwGxj"
      },
      "source": [
        "Der *latente Raum*, also alle möglichen Kombinationen von Zahlen, die das Embedding abdecken kann, ist riesig, und nur in bestimmten Bereichen haben sich durch das Training *Cluster* gebildet, in denen die einzelnen Ziffern abgebildet sind. Wir sehen aber, dass auch ein zufällig gewählter Code ein Gebilde hervorbringt, dass die gundlegende Struktur einer handgeschriebenen Ziffer besitzt. \n",
        "\n",
        "Wir können auch gezielt einen Punkt im Embedding-Raum aussuchen, indem wir bei dem Embedding einer echten Zahl starten. Wählen wir anschließend eine zufällige Veränderungsrichtung, und addieren diese mit immer größer werdenden Gewichtungen auf den Code, so sieht das dekodierte Bild zunächst noch aus wie die ursprüngliche Zahl. Doch je mehr wir uns vom ursprünglichen Code entfernen, desto mehr verschwindet unsere Zahl."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sTmeIWPvxFHE",
        "outputId": "f48476bb-0c6b-40e8-f271-4381f259567d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 132
        }
      },
      "source": [
        "code = encoder.predict(test_images_01[0][None,:,:,:])\n",
        "direction = np.random.randn(*code.shape)\n",
        "displacements = [0,.5,1,1.5,2, 2.5, 3]\n",
        "plt.figure(figsize=(12,10))\n",
        "for i,d in enumerate(displacements):\n",
        "    plt.subplot(1,len(displacements),i+1)\n",
        "    img = decoder.predict(code+direction*d)\n",
        "    _ = plt.imshow(img.squeeze())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x720 with 7 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cC2biQM3zVNh"
      },
      "source": [
        "Wir haben es bei unserem Code also mit einem *kontinuierlichen* Raum zu tun, in dem jeder Punkt uns ein Ergebnis gibt und nahe beieinanderliegende Punkte ähnliche Bilder hervorbringen. \n",
        "\n",
        "Wir können zum Beispiel auch ein *Morphing* zwischen zwei Zahlen generieren, in dem wir uns im Code-Raum von einer Zahl zur nächsten bewegen und unterwegs einige Bilder generieren:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mVrcjdeV0R7c"
      },
      "source": [
        "### **Aufgabe**: Morphen von Codes\n",
        "- Starten sie mit 2 unterschiedlichen Bildern und bilden Sie die Embeddings\n",
        "- bilden Sie jeweils das gewichtete Mittel dieser Embeddings `morphed = (1-alpha) * encoded_imgs[start_img_number] + alpha * encoded_imgs[end_img_number]` für verschiedene Werte von `alpha = 0 bis 1`\n",
        "- visualiseren sie das Ergebniss wenn Sie diese \"neuen\" Embeddings dekodieren "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DGfQIep0QrSW"
      },
      "source": [],
      "execution_count": null,
      "outputs": []
    }
  ]
}