Vanilla_AutoEncoder.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Vanilla_AutoEncoder.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "7XmXo3zqq4cW"
      },
      "source": [
        "from tensorflow.keras.layers import Input, Dense, LeakyReLU\n",
        "from tensorflow.keras.models import Model\n",
        "from tensorflow.keras.utils import plot_model\n",
        "from tensorflow.keras.optimizers import Adam #since we want to modify our leaning rate for our optimizer so functional API call"
      ],
      "execution_count": 31,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jCr_8lSsq6g3"
      },
      "source": [
        "#ENCODER MODEL"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y-vRe1p-rWH9"
      },
      "source": [
        "# The input is 784 instead of 28x28 because we are using dense layers instead of CNN. So a vector is expected instead of a matrix\n",
        "encoder_input = Input(shape=(784), name=\"encoder_input\")"
      ],
      "execution_count": 76,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "evDbQl9DrliA"
      },
      "source": [
        "#The encoder\n",
        "encoder_dense_layer1 = Dense(units=500, name=\"encoder_dense_1\")(encoder_input)\n",
        "encoder_activ_layer1 = LeakyReLU(name=\"encoder_leakyrelu_1\")(encoder_dense_layer1)\n",
        "\n",
        "encoder_dense_layer2 = Dense(units=2, name=\"encoder_dense_2\")(encoder_activ_layer1)\n",
        "encoder_output = LeakyReLU(name=\"encoder_output\")(encoder_dense_layer2)"
      ],
      "execution_count": 77,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XMar6iq5sB5f"
      },
      "source": [
        "encoder = Model(encoder_input, encoder_output, name=\"encoder_model\")"
      ],
      "execution_count": 78,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tranvrZ1sVQl",
        "outputId": "311ae488-f51d-4be7-ed9b-ca9b325bf294"
      },
      "source": [
        "#The parameters in the encoder model\n",
        "encoder.summary()"
      ],
      "execution_count": 79,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Model: \"encoder_model\"\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "encoder_input (InputLayer)   [(None, 784)]             0         \n",
            "_________________________________________________________________\n",
            "encoder_dense_1 (Dense)      (None, 500)               392500    \n",
            "_________________________________________________________________\n",
            "encoder_leakyrelu_1 (LeakyRe (None, 500)               0         \n",
            "_________________________________________________________________\n",
            "encoder_dense_2 (Dense)      (None, 2)                 1002      \n",
            "_________________________________________________________________\n",
            "encoder_output (LeakyReLU)   (None, 2)                 0         \n",
            "=================================================================\n",
            "Total params: 393,502\n",
            "Trainable params: 393,502\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 465
        },
        "id": "MC2TVQLrskuj",
        "outputId": "1e65ba9b-36bd-4d1a-ee45-8dd0c53060cf"
      },
      "source": [
        "#Model structure\n",
        "plot_model(encoder)"
      ],
      "execution_count": 80,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 80
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "12V9lDEfs68r"
      },
      "source": [
        "#DECODER MODEL"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SGIbZHt-tJzx"
      },
      "source": [
        "#Decoder Input\n",
        "decoder_input = Input(shape=(2,),name=\"decoder_input\")"
      ],
      "execution_count": 81,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bY8gPXJos6oh"
      },
      "source": [
        "#The decoder\n",
        "decoder_dense_layer1 = Dense(units=500, name=\"decoder_dense_1\")(decoder_input)\n",
        "decoder_activ_layer1 = LeakyReLU(name=\"decoder_leakyrelu_1\")(decoder_dense_layer1)\n",
        "\n",
        "decoder_dense_layer2 = Dense(units=784, name=\"decoder_dense_2\")(decoder_activ_layer1) #We want to get the orginal vector back\n",
        "decoder_output = LeakyReLU(name=\"decoder_output\")(decoder_dense_layer2)"
      ],
      "execution_count": 82,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sCllREI8uCDV"
      },
      "source": [
        "decoder = Model(decoder_input,decoder_output,name=\"Decoder\")"
      ],
      "execution_count": 83,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mG4_JTzysoE7",
        "outputId": "3ba37659-1fb8-46e2-fe9e-31068eecf639"
      },
      "source": [
        "#The decoder model parameters\n",
        "decoder.summary()"
      ],
      "execution_count": 84,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Model: \"Decoder\"\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "decoder_input (InputLayer)   [(None, 2)]               0         \n",
            "_________________________________________________________________\n",
            "decoder_dense_1 (Dense)      (None, 500)               1500      \n",
            "_________________________________________________________________\n",
            "decoder_leakyrelu_1 (LeakyRe (None, 500)               0         \n",
            "_________________________________________________________________\n",
            "decoder_dense_2 (Dense)      (None, 784)               392784    \n",
            "_________________________________________________________________\n",
            "decoder_output (LeakyReLU)   (None, 784)               0         \n",
            "=================================================================\n",
            "Total params: 394,284\n",
            "Trainable params: 394,284\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 465
        },
        "id": "XEClhaN1uNd7",
        "outputId": "e8f9eb85-ecc6-48e7-dfb7-69fd67501625"
      },
      "source": [
        "#Decoder model\n",
        "plot_model(decoder)"
      ],
      "execution_count": 85,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 85
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lEbAkzSguep6"
      },
      "source": [
        "#The Complete AutoEncoder Model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TFK-t0kfuSuE"
      },
      "source": [
        "AutoEncoder_output = decoder(encoder(encoder_input))"
      ],
      "execution_count": 86,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tDICIqJFvSm3"
      },
      "source": [
        "#The autoencoder model\n",
        "AutoEncoder = Model(encoder_input,AutoEncoder_output,name=\"Autoencoder\")"
      ],
      "execution_count": 87,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TumywvdDvevU",
        "outputId": "231fd91d-cf11-43cc-8e1e-3624b50cc442"
      },
      "source": [
        "#Autoencoder parameters\n",
        "AutoEncoder.summary()"
      ],
      "execution_count": 88,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Model: \"Autoencoder\"\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "encoder_input (InputLayer)   [(None, 784)]             0         \n",
            "_________________________________________________________________\n",
            "encoder_model (Functional)   (None, 2)                 393502    \n",
            "_________________________________________________________________\n",
            "Decoder (Functional)         (None, 784)               394284    \n",
            "=================================================================\n",
            "Total params: 787,786\n",
            "Trainable params: 787,786\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 272
        },
        "id": "1u8A8Zn9vji9",
        "outputId": "3e548c9c-6b55-4c6b-a73c-814d58cce87e"
      },
      "source": [
        "#Autoencoder layers\n",
        "plot_model(AutoEncoder)"
      ],
      "execution_count": 89,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 89
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wsMj21vRwB8Z"
      },
      "source": [
        "### Compiling the autoencoder model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZWWxf8x4vs_6"
      },
      "source": [
        "AutoEncoder.compile(optimizer=Adam(learning_rate=0.0005),loss='mse')"
      ],
      "execution_count": 90,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tShj_K1awrDO"
      },
      "source": [
        "# Loading the data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "41q2OIZywi9w"
      },
      "source": [
        "from tensorflow.keras.datasets.mnist import load_data #we used the mnist dataset\n",
        "import numpy as np"
      ],
      "execution_count": 91,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5DjMI9XMxFQc"
      },
      "source": [
        "(x_train_orig,y_train),(x_test_orig,y_test) = load_data() #downloading the data"
      ],
      "execution_count": 92,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pLuJGUDJxNO0",
        "outputId": "8b2dda0b-2498-44a6-d434-aaddfd7084e8"
      },
      "source": [
        "x_train_orig.shape, x_test_orig.shape"
      ],
      "execution_count": 93,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((60000, 28, 28), (10000, 28, 28))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 93
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wJVR2q7wxTLL"
      },
      "source": [
        "#Normalising the pixels of the images\n",
        "x_train_orig = x_train_orig.astype('float32')/255.0\n",
        "x_test_orig = x_test_orig.astype('float32')/255.0"
      ],
      "execution_count": 94,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OoJL850-xiaK"
      },
      "source": [
        "#Since the images are in a matrix so converting them into a vector\n",
        "x_train = x_train_orig.reshape((x_train_orig.shape[0],np.prod(x_train_orig.shape[1:])))\n",
        "x_test = x_test_orig.reshape((x_test_orig.shape[0],np.prod(x_test_orig.shape[1:])))"
      ],
      "execution_count": 95,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SBQjyEVZx0f7",
        "outputId": "ceb984ae-be25-46bc-a970-0f9f4406f31f"
      },
      "source": [
        "#new shapes\n",
        "x_train.shape, x_test.shape"
      ],
      "execution_count": 96,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((60000, 784), (10000, 784))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 96
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6Y0-8pyByHBe",
        "outputId": "4a694159-fcad-4288-cb38-f88254fece0f"
      },
      "source": [
        "#Now that our data is in vector order, we provide it as an input and train our model\n",
        "\n",
        "#The labels y have not been given because we don't need that\n",
        "AutoEncoder.fit(x_train,x_train,batch_size=256,epochs=20,shuffle=True,validation_data=(x_test,x_test),verbose = 1)"
      ],
      "execution_count": 97,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch 1/20\n",
            "235/235 [==============================] - 2s 6ms/step - loss: 0.0596 - val_loss: 0.0551\n",
            "Epoch 2/20\n",
            "235/235 [==============================] - 1s 6ms/step - loss: 0.0544 - val_loss: 0.0533\n",
            "Epoch 3/20\n",
            "235/235 [==============================] - 1s 6ms/step - loss: 0.0530 - val_loss: 0.0520\n",
            "Epoch 4/20\n",
            "235/235 [==============================] - 1s 6ms/step - loss: 0.0518 - val_loss: 0.0509\n",
            "Epoch 5/20\n",
            "235/235 [==============================] - 1s 6ms/step - loss: 0.0508 - val_loss: 0.0502\n",
            "Epoch 6/20\n",
            "235/235 [==============================] - 1s 6ms/step - loss: 0.0500 - val_loss: 0.0494\n",
            "Epoch 7/20\n",
            "235/235 [==============================] - 1s 6ms/step - loss: 0.0493 - val_loss: 0.0489\n",
            "Epoch 8/20\n",
            "235/235 [==============================] - 2s 7ms/step - loss: 0.0488 - val_loss: 0.0486\n",
            "Epoch 9/20\n",
            "235/235 [==============================] - 1s 6ms/step - loss: 0.0483 - val_loss: 0.0480\n",
            "Epoch 10/20\n",
            "235/235 [==============================] - 1s 6ms/step - loss: 0.0480 - val_loss: 0.0478\n",
            "Epoch 11/20\n",
            "235/235 [==============================] - 1s 5ms/step - loss: 0.0477 - val_loss: 0.0478\n",
            "Epoch 12/20\n",
            "235/235 [==============================] - 1s 6ms/step - loss: 0.0474 - val_loss: 0.0472\n",
            "Epoch 13/20\n",
            "235/235 [==============================] - 1s 6ms/step - loss: 0.0472 - val_loss: 0.0471\n",
            "Epoch 14/20\n",
            "235/235 [==============================] - 1s 6ms/step - loss: 0.0470 - val_loss: 0.0469\n",
            "Epoch 15/20\n",
            "235/235 [==============================] - 1s 6ms/step - loss: 0.0467 - val_loss: 0.0466\n",
            "Epoch 16/20\n",
            "235/235 [==============================] - 1s 6ms/step - loss: 0.0465 - val_loss: 0.0464\n",
            "Epoch 17/20\n",
            "235/235 [==============================] - 1s 6ms/step - loss: 0.0464 - val_loss: 0.0463\n",
            "Epoch 18/20\n",
            "235/235 [==============================] - 1s 6ms/step - loss: 0.0462 - val_loss: 0.0462\n",
            "Epoch 19/20\n",
            "235/235 [==============================] - 1s 6ms/step - loss: 0.0460 - val_loss: 0.0461\n",
            "Epoch 20/20\n",
            "235/235 [==============================] - 1s 6ms/step - loss: 0.0459 - val_loss: 0.0458\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tensorflow.python.keras.callbacks.History at 0x7f9b53515310>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 97
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wb4sNGFs29uY"
      },
      "source": [
        "## Predicting using Encoder and Decoder independently"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wlbsPXMTzjln"
      },
      "source": [
        "#Now we predict first using the encoder model to get a vector of 2 latent features\n",
        "encoder_prediction = encoder.predict(x_train)"
      ],
      "execution_count": 98,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nQAGZMWXz1X2"
      },
      "source": [
        "#Predciting the decoder output using the output of the encoder which generates an image vector of 784 \n",
        "decoder_prediction = decoder.predict(encoder_prediction)"
      ],
      "execution_count": 99,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0AVxzErv0MzM"
      },
      "source": [
        "#Converting the image vector to a matrix\n",
        "decoder_images =  decoder_prediction.reshape((decoder_prediction.shape[0],28,28))"
      ],
      "execution_count": 100,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AyjS0HGM02ES"
      },
      "source": [
        "import matplotlib"
      ],
      "execution_count": 101,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        },
        "id": "ynw37X0-0sGp",
        "outputId": "422e21db-5e31-4381-a0ca-2ff67759fda7"
      },
      "source": [
        "#Plotting the output\n",
        "num_images_to_show = 5\n",
        "for im_ind in range(num_images_to_show):\n",
        "    plot_ind = im_ind*2 + 1\n",
        "    rand_ind = np.random.randint(low=0, high=x_train.shape[0])\n",
        "    matplotlib.pyplot.subplot(num_images_to_show, 2, plot_ind)\n",
        "    matplotlib.pyplot.imshow(x_train_orig[rand_ind, :, :], cmap=\"gray\")\n",
        "    matplotlib.pyplot.subplot(num_images_to_show, 2, plot_ind+1)\n",
        "    matplotlib.pyplot.imshow(decoder_images[rand_ind, :, :], cmap=\"gray\")"
      ],
      "execution_count": 102,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 10 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "P5bI-Mcj2c-F"
      },
      "source": [
        "### Note: The quality of images can be improved by using more neurons and by using CNNs"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SLk3Hvu533bR"
      },
      "source": [
        "### Encoder Model cluster based output"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "id": "YaMdsVcz37YI",
        "outputId": "3441f030-70d2-446c-943e-c4b4471345f7"
      },
      "source": [
        "matplotlib.pyplot.figure()\n",
        "matplotlib.pyplot.scatter(encoder_prediction[:, 0], encoder_prediction[:, 1], c=y_train) \n",
        "matplotlib.pyplot.colorbar()"
      ],
      "execution_count": 107,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.colorbar.Colorbar at 0x7f9b4f048ed0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 107
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JHdM-Jr3243v"
      },
      "source": [
        "## Predicting using complete Model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pJK6WT0UyxnH"
      },
      "source": [
        "#Predicitng using the Overall Model\n",
        "#Since we want to generate the images themselevs, so we predict on x_train again\n",
        "autoencoder_output_vector = AutoEncoder.predict(x_train)"
      ],
      "execution_count": 104,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vyRJm7wizbdw"
      },
      "source": [
        "#Converting vector to matrix\n",
        "autoencoder_images = autoencoder_output_vector.reshape((autoencoder_output_vector.shape[0],28,28))"
      ],
      "execution_count": 105,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        },
        "id": "l8iEp1V32uDw",
        "outputId": "08d49cb9-a744-4871-9cfe-8ebba5b00c8b"
      },
      "source": [
        "#Plotting these images\n",
        "num_images_to_show = 5\n",
        "for im_ind in range(num_images_to_show):\n",
        "    plot_ind = im_ind*2 + 1\n",
        "    rand_ind = np.random.randint(low=0, high=x_train.shape[0])\n",
        "    matplotlib.pyplot.subplot(num_images_to_show, 2, plot_ind)\n",
        "    matplotlib.pyplot.imshow(x_train_orig[rand_ind, :, :], cmap=\"gray\")\n",
        "    matplotlib.pyplot.subplot(num_images_to_show, 2, plot_ind+1)\n",
        "    matplotlib.pyplot.imshow(autoencoder_images[rand_ind, :, :], cmap=\"gray\")"
      ],
      "execution_count": 106,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 10 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Zdz7t1f94QiW"
      },
      "source": [
        ""
      ]
    }
  ]
}