Autoencoder_Keras.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Autoencoder.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "IKgoIQgiDQ0G",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "85ba34a0-9752-46bc-b3e4-5235b1c8cc79"
      },
      "source": [
        "import tensorflow as tf\n",
        "# Es lohnt sich zu überprüfen, ob man auch wirklich eine GPU bekommen hat.\n",
        "tf.config.list_physical_devices('GPU')"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[PhysicalDevice(name='/physical_device:GPU:0', device_type='GPU')]"
            ]
          },
          "metadata": {},
          "execution_count": 1
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Kc79VlOAOM9B"
      },
      "source": [
        "# Autoencoder\n"
      ]
    },
    {
      "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": "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": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5qZ4SAPRDacS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "392ee8d3-9b05-48d7-8605-6ec626ee75cc"
      },
      "source": [
        "(train_images, train_labels), (test_images, test_labels) = tf.keras.datasets.mnist.load_data()\n",
        "train_images.shape"
      ],
      "execution_count": 3,
      "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"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6UX1eYAnDeic",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5eff499b-88a7-47d5-9b4d-00a185881a0e"
      },
      "source": [
        "# adding a color channel\n",
        "train_images = train_images[:,:,:,np.newaxis].astype('float32')\n",
        "# and scale to 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": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000, 28, 28, 1)"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4nrlvl19S2pt"
      },
      "source": [
        "## Encoder\n",
        "\n",
        "The Encoder is similar to a classification network. Only there is no final classification head at the end."
      ]
    },
    {
      "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": 5,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Myd9p0dJTxXK"
      },
      "source": [
        "## Decoder"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yWjTrgZLo28K"
      },
      "source": [
        "The Decoder is taking an input and reconstructing an image from this"
      ]
    },
    {
      "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": 6,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q-jWvPYjpjcA"
      },
      "source": [
        "## Autoencoder\n",
        "\n",
        "Combining Encoder-Autoencoder\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ib91KPB3hkJj"
      },
      "source": [
        "# Posibility 1\n",
        "autoencoder = tf.keras.Model(inputs=encoder.input, outputs=decoder(encoder.output))\n",
        "autoencoder.compile(optimizer='adam', loss='binary_crossentropy')"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vUk1ExpILaca",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 896
        },
        "outputId": "406f7caf-a272-4e36-fadf-d2be0559c2e5"
      },
      "source": [
        "tf.keras.utils.plot_model(autoencoder, show_shapes=True, dpi=70, expand_nested=True)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "y1zzu08sqXF2"
      },
      "source": [
        "initial model predictions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xO6mkohB7dci",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 246
        },
        "outputId": "aa32828a-ffba-4407-fedf-94e79e2e8c17"
      },
      "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": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "313/313 [==============================] - 9s 3ms/step\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 2000x400 with 20 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mVAQoyg-quxV"
      },
      "source": [
        "### Training\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gYuQOgY5hkFB",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "652e9640-63ff-4655-c85b-19be32ebebf5"
      },
      "source": [
        "autoencoder.fit(\n",
        "    x = train_images_01,\n",
        "    y = train_images_01, # input and output are the same (i.e. autoencoder)\n",
        "    epochs=40,\n",
        "    batch_size=256,\n",
        "    shuffle=True,\n",
        "    validation_data=(test_images_01, test_images_01)\n",
        ")"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/40\n",
            "235/235 [==============================] - 7s 17ms/step - loss: 0.2711 - val_loss: 0.1675\n",
            "Epoch 2/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1453 - val_loss: 0.1339\n",
            "Epoch 3/40\n",
            "235/235 [==============================] - 3s 12ms/step - loss: 0.1315 - val_loss: 0.1272\n",
            "Epoch 4/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1266 - val_loss: 0.1239\n",
            "Epoch 5/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1235 - val_loss: 0.1212\n",
            "Epoch 6/40\n",
            "235/235 [==============================] - 4s 16ms/step - loss: 0.1213 - val_loss: 0.1195\n",
            "Epoch 7/40\n",
            "235/235 [==============================] - 3s 14ms/step - loss: 0.1198 - val_loss: 0.1185\n",
            "Epoch 8/40\n",
            "235/235 [==============================] - 3s 12ms/step - loss: 0.1186 - val_loss: 0.1175\n",
            "Epoch 9/40\n",
            "235/235 [==============================] - 3s 12ms/step - loss: 0.1177 - val_loss: 0.1167\n",
            "Epoch 10/40\n",
            "235/235 [==============================] - 4s 18ms/step - loss: 0.1169 - val_loss: 0.1163\n",
            "Epoch 11/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1163 - val_loss: 0.1155\n",
            "Epoch 12/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1157 - val_loss: 0.1152\n",
            "Epoch 13/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1152 - val_loss: 0.1146\n",
            "Epoch 14/40\n",
            "235/235 [==============================] - 3s 14ms/step - loss: 0.1148 - val_loss: 0.1146\n",
            "Epoch 15/40\n",
            "235/235 [==============================] - 3s 14ms/step - loss: 0.1144 - val_loss: 0.1139\n",
            "Epoch 16/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1140 - val_loss: 0.1134\n",
            "Epoch 17/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1136 - val_loss: 0.1130\n",
            "Epoch 18/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1134 - val_loss: 0.1129\n",
            "Epoch 19/40\n",
            "235/235 [==============================] - 3s 14ms/step - loss: 0.1131 - val_loss: 0.1128\n",
            "Epoch 20/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1128 - val_loss: 0.1126\n",
            "Epoch 21/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1125 - val_loss: 0.1124\n",
            "Epoch 22/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1123 - val_loss: 0.1121\n",
            "Epoch 23/40\n",
            "235/235 [==============================] - 3s 14ms/step - loss: 0.1121 - val_loss: 0.1120\n",
            "Epoch 24/40\n",
            "235/235 [==============================] - 3s 14ms/step - loss: 0.1119 - val_loss: 0.1118\n",
            "Epoch 25/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1117 - val_loss: 0.1115\n",
            "Epoch 26/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1115 - val_loss: 0.1114\n",
            "Epoch 27/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1113 - val_loss: 0.1118\n",
            "Epoch 28/40\n",
            "235/235 [==============================] - 3s 15ms/step - loss: 0.1111 - val_loss: 0.1112\n",
            "Epoch 29/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1110 - val_loss: 0.1113\n",
            "Epoch 30/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1108 - val_loss: 0.1108\n",
            "Epoch 31/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1106 - val_loss: 0.1113\n",
            "Epoch 32/40\n",
            "235/235 [==============================] - 3s 14ms/step - loss: 0.1105 - val_loss: 0.1111\n",
            "Epoch 33/40\n",
            "235/235 [==============================] - 3s 14ms/step - loss: 0.1104 - val_loss: 0.1110\n",
            "Epoch 34/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1102 - val_loss: 0.1106\n",
            "Epoch 35/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1102 - val_loss: 0.1109\n",
            "Epoch 36/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1100 - val_loss: 0.1105\n",
            "Epoch 37/40\n",
            "235/235 [==============================] - 3s 14ms/step - loss: 0.1099 - val_loss: 0.1103\n",
            "Epoch 38/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1098 - val_loss: 0.1103\n",
            "Epoch 39/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1097 - val_loss: 0.1100\n",
            "Epoch 40/40\n",
            "235/235 [==============================] - 3s 13ms/step - loss: 0.1096 - val_loss: 0.1100\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.src.callbacks.History at 0x7c5873ba28f0>"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j3gKYjYVs1CH"
      },
      "source": [
        "ouput after the training"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LNdJQV7uhj_7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 337
        },
        "outputId": "05e5dfbf-8008-4f86-9f7e-39d99efe9633"
      },
      "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), cmap='gray')\n",
        "    plt.axis('off')\n",
        "\n",
        "    # encodint original\n",
        "    ax = plt.subplot(3, n, n+i+1)\n",
        "    plt.imshow(encoded_imgs[i].reshape(4, 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), cmap='gray')\n",
        "    plt.axis('off')"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "313/313 [==============================] - 1s 2ms/step\n",
            "313/313 [==============================] - 1s 2ms/step\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 3000x800 with 30 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tqsso7dFtkfr"
      },
      "source": [
        "# Exploring the latent Space\n",
        "\n",
        "We can feed the decoder any input"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "572Eq8JKBnY3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 824
        },
        "outputId": "976ce4c0-cac7-44a6-8d1b-6b4c8ac60d20"
      },
      "source": [
        "#np.random.seed(44)\n",
        "random_encoding = (np.random.rand(latent_dim)-0.5)*10\n",
        "\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, cmap='gray')\n",
        "_ = plt.axis('off')"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1/1 [==============================] - 0s 17ms/step\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x1000 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q3KZU7CrwGxj"
      },
      "source": [
        "## Shifts in latent space"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sTmeIWPvxFHE",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 316
        },
        "outputId": "4ac0c84e-e913-44cd-bb22-aeb920159edd"
      },
      "source": [
        "code = encoder.predict(test_images_01[4][None,:,:,:])\n",
        "direction = np.random.randn(*code.shape)\n",
        "displacements = [0,1,2,4,8,16, 32]\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(), cmap='gray')"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1/1 [==============================] - 0s 25ms/step\n",
            "1/1 [==============================] - 0s 27ms/step\n",
            "1/1 [==============================] - 0s 30ms/step\n",
            "1/1 [==============================] - 0s 30ms/step\n",
            "1/1 [==============================] - 0s 30ms/step\n",
            "1/1 [==============================] - 0s 30ms/step\n",
            "1/1 [==============================] - 0s 26ms/step\n",
            "1/1 [==============================] - 0s 22ms/step\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x1000 with 7 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mVrcjdeV0R7c"
      },
      "source": [
        "### Aufgaben\n",
        "1. Dimension des latenten Raumes\n",
        "  - Verlgleichen Sie die Resultate für unterschiedlich große latente Räumen\n",
        "    - Wieviele Dimensionen muss der latente Raum mindestens haben?\n",
        "\n",
        "2. Rechnen im latenten Raum\n",
        "  - Berechnen Sie die latente Darstellung für 2 Testbilder (encoded images)\n",
        "  -  Erstellen Sie ein gewichtetes Mittel der beiden Embeddings  $\\alpha \\vec{e_1} + (1-\\alpha) \\vec{e_2}$ für verschiedene Werte von $\\alpha$ zwischen 0 und 1\n",
        "  - Dekodieren Sie nun wieder den gemittelten Code\n",
        "  - Bonus: Wie sieht das Ergebniss aus, wenn man dieses gewichtete Mittel direkt im Pixelraum ausführt?"
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "HKm8l5UDe7vv"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}