Deep Learning/Autoencoder.ipynb

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  "metadata": {
    "colab": {
      "name": "Autoencoder.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyMOWkr0EaiKVSpRyVV220p6",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/GustavoHFMO/GrupoSerDisciplinas/blob/master/Autoencoder.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UnlxrRZmy9Na"
      },
      "source": [
        "Código adaptado de: https://www.datatechnotes.com/2020/03/simple-autoencoder-example-with-keras-in-python.html"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t1hJnoucyLOb"
      },
      "source": [
        "# importando as bibliotecas\n",
        "from keras.datasets.mnist import load_data\n",
        "from keras.layers import Input, LeakyReLU\n",
        "from keras.layers import Dense\n",
        "from keras.models import Model\n",
        "import matplotlib.pyplot as plt\n",
        "from numpy import reshape"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gfivLMTwzCbJ",
        "outputId": "60737a58-13c4-4a6e-de6a-c92cf49e4e2f"
      },
      "source": [
        "# importando o conjunto de dados\n",
        "(xtrain, _), (xtest, _) = load_data()"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "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"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eZUf_qTAzMNR"
      },
      "source": [
        "# normalizando os dados para que eles fiquem no intervalo de [0, 1]\n",
        "xtrain = xtrain.astype('float32') / 255.\n",
        "xtest = xtest.astype('float32') / 255."
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PCRxO7OHzRra"
      },
      "source": [
        "# obtendo o tamanho dos dados para ajustar a entrada da rede\n",
        "input_size = xtrain.shape[1] * xtrain.shape[2]\n",
        "latent_size = 16"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "C64dmvYezcuf"
      },
      "source": [
        "# formatando os dados para que a rede consiga ler\n",
        "x_train = xtrain.reshape((len(xtrain), input_size))\n",
        "x_test = xtest.reshape((len(xtest), input_size))"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-wV6L2Xpz7U-",
        "outputId": "8e4bf645-04fc-4e8a-b81d-36c0d757f033"
      },
      "source": [
        "# Encoder - definindo a estrutura da etapa de comprimir os dados\n",
        "enc_input = Input(shape=(input_size,))\n",
        "enc_dense1 = Dense(units=256, activation=\"relu\")(enc_input)\n",
        "enc_activ1 = LeakyReLU()(enc_dense1)\n",
        "enc_dense2 = Dense(units=latent_size)(enc_activ1)\n",
        "enc_output = LeakyReLU()(enc_dense2)\n",
        "encoder = Model(enc_input, enc_output)\n",
        "encoder.summary()\n",
        "\n",
        "# Decoder - definindo a estrutura da etapa de reconstruir os dados\n",
        "dec_input = Input(shape=(latent_size,))\n",
        "dec_dense1 = Dense(units=256, activation=\"relu\")(dec_input)\n",
        "dec_activ1 = LeakyReLU()(dec_dense1)\n",
        "dec_dense2 = Dense(units=input_size, activation='sigmoid')(dec_activ1)\n",
        "dec_output = LeakyReLU()(dec_dense2)\n",
        "decoder = Model(dec_input, dec_output)\n",
        "decoder.summary()\n",
        "\n",
        "# Autoencoder - Agrupando as etapas de codificação e decodificação no modelo\n",
        "aen_input = Input(shape=(input_size,))\n",
        "aen_enc_output = encoder(aen_input)\n",
        "aen_dec_output = decoder(aen_enc_output)\n",
        "aen = Model(aen_input, aen_dec_output)\n",
        "aen.summary()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Model: \"model\"\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "input_1 (InputLayer)         [(None, 784)]             0         \n",
            "_________________________________________________________________\n",
            "dense (Dense)                (None, 256)               200960    \n",
            "_________________________________________________________________\n",
            "leaky_re_lu (LeakyReLU)      (None, 256)               0         \n",
            "_________________________________________________________________\n",
            "dense_1 (Dense)              (None, 16)                4112      \n",
            "_________________________________________________________________\n",
            "leaky_re_lu_1 (LeakyReLU)    (None, 16)                0         \n",
            "=================================================================\n",
            "Total params: 205,072\n",
            "Trainable params: 205,072\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n",
            "Model: \"model_1\"\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "input_2 (InputLayer)         [(None, 16)]              0         \n",
            "_________________________________________________________________\n",
            "dense_2 (Dense)              (None, 256)               4352      \n",
            "_________________________________________________________________\n",
            "leaky_re_lu_2 (LeakyReLU)    (None, 256)               0         \n",
            "_________________________________________________________________\n",
            "dense_3 (Dense)              (None, 784)               201488    \n",
            "_________________________________________________________________\n",
            "leaky_re_lu_3 (LeakyReLU)    (None, 784)               0         \n",
            "=================================================================\n",
            "Total params: 205,840\n",
            "Trainable params: 205,840\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n",
            "Model: \"model_2\"\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "input_3 (InputLayer)         [(None, 784)]             0         \n",
            "_________________________________________________________________\n",
            "model (Functional)           (None, 16)                205072    \n",
            "_________________________________________________________________\n",
            "model_1 (Functional)         (None, 784)               205840    \n",
            "=================================================================\n",
            "Total params: 410,912\n",
            "Trainable params: 410,912\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "itmdkotF0Jj4"
      },
      "source": [
        "# definindo o algoritmo de otimização e a função de custo\n",
        "aen.compile(optimizer=\"rmsprop\", loss=\"binary_crossentropy\")"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "x9M6Qr7o0Meu",
        "outputId": "de2df1e6-8b50-435b-9a9e-db246198e3b5"
      },
      "source": [
        "# iniciando o treinamento do autoencoder\n",
        "aen.fit(x_train, x_train, epochs=20, batch_size=256, shuffle=True)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch 1/20\n",
            "235/235 [==============================] - 6s 23ms/step - loss: 0.1997\n",
            "Epoch 2/20\n",
            "235/235 [==============================] - 5s 23ms/step - loss: 0.1459\n",
            "Epoch 3/20\n",
            "235/235 [==============================] - 5s 23ms/step - loss: 0.1322\n",
            "Epoch 4/20\n",
            "235/235 [==============================] - 5s 23ms/step - loss: 0.1238\n",
            "Epoch 5/20\n",
            "235/235 [==============================] - 5s 23ms/step - loss: 0.1184\n",
            "Epoch 6/20\n",
            "235/235 [==============================] - 5s 23ms/step - loss: 0.1146\n",
            "Epoch 7/20\n",
            "235/235 [==============================] - 5s 23ms/step - loss: 0.1118\n",
            "Epoch 8/20\n",
            "235/235 [==============================] - 5s 23ms/step - loss: 0.1096\n",
            "Epoch 9/20\n",
            "235/235 [==============================] - 5s 23ms/step - loss: 0.1077\n",
            "Epoch 10/20\n",
            "235/235 [==============================] - 5s 23ms/step - loss: 0.1062\n",
            "Epoch 11/20\n",
            "235/235 [==============================] - 5s 23ms/step - loss: 0.1051\n",
            "Epoch 12/20\n",
            "235/235 [==============================] - 5s 23ms/step - loss: 0.1040\n",
            "Epoch 13/20\n",
            "235/235 [==============================] - 5s 23ms/step - loss: 0.1031\n",
            "Epoch 14/20\n",
            "235/235 [==============================] - 5s 23ms/step - loss: 0.1023\n",
            "Epoch 15/20\n",
            "235/235 [==============================] - 5s 23ms/step - loss: 0.1016\n",
            "Epoch 16/20\n",
            "235/235 [==============================] - 5s 23ms/step - loss: 0.1010\n",
            "Epoch 17/20\n",
            "235/235 [==============================] - 5s 23ms/step - loss: 0.1004\n",
            "Epoch 18/20\n",
            "235/235 [==============================] - 5s 23ms/step - loss: 0.0999\n",
            "Epoch 19/20\n",
            "235/235 [==============================] - 5s 23ms/step - loss: 0.0995\n",
            "Epoch 20/20\n",
            "235/235 [==============================] - 5s 23ms/step - loss: 0.0990\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7f2c73ccf690>"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lPMRD60e0Unm"
      },
      "source": [
        "# realizando a previsão do conjunto de teste com o modelo treinado\n",
        "encoded_images = encoder.predict(x_test)\n",
        "decoded_images = decoder.predict(encoded_images)\n",
        "pred_images = reshape(decoded_images, newshape=(decoded_images.shape[0], 28, 28)) "
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 141
        },
        "id": "gQeUDp9v9ewp",
        "outputId": "697a475e-2f98-41b3-b18c-a1f4209dba41"
      },
      "source": [
        "# mostrando visualmente as previsões do modelo \n",
        "n = 10\n",
        "plt.figure(figsize=(10, 2))\n",
        "for i in range(n): \n",
        " ax = plt.subplot(2, n, i + 1)\n",
        " ax.get_xaxis().set_visible(False)\n",
        " ax.get_yaxis().set_visible(False)\n",
        " plt.imshow(xtest[i].reshape(28, 28))\n",
        " plt.gray()\n",
        " \n",
        " ax = plt.subplot(2, n, i + 1 + n)\n",
        " ax.get_xaxis().set_visible(False)\n",
        " ax.get_yaxis().set_visible(False)\n",
        " plt.imshow(pred_images[i].reshape(28, 28))\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x144 with 20 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}