ProductClassification/ComputerVisionImageClassification.ipynb

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  "metadata": {
    "colab": {
      "name": "ComputerVisionImageClassification.ipynb",
      "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/MattiaVerticchio/PersonalProjects/blob/master/ProductClassification/ComputerVisionImageClassification.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AXKTEi8vZyEc"
      },
      "source": [
        "# Classifying Product Images via Deep Learning\n",
        "\n",
        "> **Abstract**\n",
        ">\n",
        "> The objective of this notebook is to classify images of the products contained in the Zalando Research Dataset. The dataset contains grayscale images and ten different categories of products. The framework chosen for the task is Auto-Keras, using Keras and TensorFlow as backend. We’ll search for a neural architecture that fits our project and compare it to the official [Zalando Research benchmark](http://fashion-mnist.s3-website.eu-central-1.amazonaws.com). The results are in line with the benchmark, and the accuracy metric is 3% higher."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ihrW7xP1Z8UL"
      },
      "source": [
        "## Framework setup\n",
        "As the central framework for this task, we’ll use [Auto-Keras](https://arxiv.org/abs/1806.10282). It’s an efficient neural architecture search system developed by DATA Lab at Texas A&M University. It leverages a variant of Bayesian Optimization to guide deep neural network morphism and find the optimal architecture for our task and dataset, using Keras and TensorFlow as backend.\n",
        "First, we have to install it with its dependency, [Keras-Tuner](https://keras-team.github.io/keras-tuner/), which is the hyperparameter optimization library used by Auto-Keras."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9CcXH344qh3E"
      },
      "source": [
        "%%bash\n",
        "pip install -q git+https://github.com/keras-team/keras-tuner.git@1.0.2rc1 autokeras"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tyc5sLftaGkr"
      },
      "source": [
        "## Imports\n",
        "Now we can import the TensorFlow dataset loading tool and Auto-Keras, as well as plotting tools to examine the dataset. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EdZi9XY3sUH1"
      },
      "source": [
        "from tensorflow.keras.datasets import fashion_mnist  # Dataset loading tool\n",
        "import autokeras as ak                               # Learning library\n",
        "import matplotlib.pyplot as plt                      # Visualization tools\n",
        "%matplotlib inline                                   # Notebook settings\n",
        "%config InlineBackend.figure_format = 'retina'       # High resolution plots"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MV5SvsqIaIhs"
      },
      "source": [
        "## Loading the data\n",
        "We can now load the dataset into four NumPy arrays."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4KCtGI9zqX6N",
        "outputId": "53ac9f82-5e0d-4784-c642-59c24f6ac13b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 161
        }
      },
      "source": [
        "(x_train, y_train), (x_test, y_test) = fashion_mnist.load_data()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/train-labels-idx1-ubyte.gz\n",
            "32768/29515 [=================================] - 0s 0us/step\n",
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/train-images-idx3-ubyte.gz\n",
            "26427392/26421880 [==============================] - 0s 0us/step\n",
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/t10k-labels-idx1-ubyte.gz\n",
            "8192/5148 [===============================================] - 0s 0us/step\n",
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/t10k-images-idx3-ubyte.gz\n",
            "4423680/4422102 [==============================] - 0s 0us/step\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wfxX80RGhOMe"
      },
      "source": [
        "The arrays `x_train` and `x_test` contain the images as matrixes of grey pixels (in the range 0–255). `y_train` and `y_test` store the class of each image according to the following map."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tVmgxwt6g016"
      },
      "source": [
        "label_map = {\n",
        "    0: 'T-shirt/top',\n",
        "    1: 'Trouser',\n",
        "    2: 'Pullover',\n",
        "    3: 'Dress',\n",
        "    4: 'Coat',\n",
        "    5: 'Sandal',\n",
        "    6: 'Shirt',\n",
        "    7: 'Sneaker',\n",
        "    8: 'Bag',\n",
        "    9: 'Ankle boot'\n",
        "}"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9fyJuIQFgofi"
      },
      "source": [
        "Let’s plot a couple of examples."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n8dyD5qBiZVW"
      },
      "source": [
        "def plot(n):                              # Function to plot\n",
        "    plt.imshow(x_train[n]);               # N-th image\n",
        "    plt.title(label_map.get(y_train[n]))  # Adding the title from dictionary map\n",
        "    plt.colorbar();                       # Adding legend bar"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "acVNKVybfJcy",
        "outputId": "330dc9d6-109e-4c92-f916-46324084061f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 280
        }
      },
      "source": [
        "plot(0)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 305,
              "height": 263
            },
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aQmadxVkfySV",
        "outputId": "39846877-dac8-4357-c543-187e050a80cf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 280
        }
      },
      "source": [
        "plot(1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 305,
              "height": 263
            },
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ERvOnoX0aNkk"
      },
      "source": [
        "## Building the model\n",
        "`ImageClassifier` is the class that initializes the model search. Here I set the number of `trials` to avoid taking too much time for model exploration, but it can be any positive integer. It explores different model architectures by tree-based Bayesian Optimization search. We’ll try only the first one as it’s time-consuming on Google Colab’s GPU, where I’m running this notebook."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ESIL74CvsanY"
      },
      "source": [
        "trials = 1\n",
        "\n",
        "clf = ak.ImageClassifier(             # Initialize the ImageClassifier\n",
        "    num_classes=None,                 # Infer the number of classes\n",
        "    multi_label=False,                # Only one output\n",
        "    loss='categorical_crossentropy',  # Select the loss metric\n",
        "    metrics='accuracy',               # Metric to watch\n",
        "    project_name='image_classifier',  # Name of the folder\n",
        "    max_trials=trials,                # Just try one model\n",
        "    directory=None,                   # Automatic folder creation\n",
        "    objective='val_loss',             # Validation set crossentropy\n",
        "    tuner=None,                       # Automatic hyperparameter tuner selection\n",
        "    overwrite=True,                   # Don't load previous experiments\n",
        "    seed=42                           # Set a seed to replicate the experiment\n",
        ")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "23ad2HOWaSSr"
      },
      "source": [
        "### Neural Architecture Search\n",
        "It’s all ready to start exploring the models."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mnU33Boxsd1-",
        "outputId": "44b7c567-1be5-483f-de14-696202ea3438",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 665
        }
      },
      "source": [
        "clf.fit(                   # Fit the model\n",
        "    x=x_train,             # Training features\n",
        "    y=y_train,             # Training labels\n",
        "    epochs=None,           # Automatic number of epochs\n",
        "    callbacks=None,        # No callbacks\n",
        "    validation_split=0.2,  # Validation data split\n",
        "    validation_data=None   # Use a portion of training data\n",
        ")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Trial 1 Complete [00h 02m 33s]\n",
            "val_loss: 0.2193739414215088\n",
            "\n",
            "Best val_loss So Far: 0.2193739414215088\n",
            "Total elapsed time: 00h 02m 33s\n",
            "INFO:tensorflow:Oracle triggered exit\n",
            "Epoch 1/15\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.4301 - accuracy: 0.8457\n",
            "Epoch 2/15\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.3134 - accuracy: 0.8887\n",
            "Epoch 3/15\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.2775 - accuracy: 0.9012\n",
            "Epoch 4/15\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.2567 - accuracy: 0.9069\n",
            "Epoch 5/15\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.2413 - accuracy: 0.9120\n",
            "Epoch 6/15\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.2318 - accuracy: 0.9145\n",
            "Epoch 7/15\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.2208 - accuracy: 0.9195\n",
            "Epoch 8/15\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.2120 - accuracy: 0.9214\n",
            "Epoch 9/15\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.2082 - accuracy: 0.9232\n",
            "Epoch 10/15\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.2029 - accuracy: 0.9258\n",
            "Epoch 11/15\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.1965 - accuracy: 0.9269\n",
            "Epoch 12/15\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.1954 - accuracy: 0.9275\n",
            "Epoch 13/15\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.1915 - accuracy: 0.9295\n",
            "Epoch 14/15\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.1858 - accuracy: 0.9323\n",
            "Epoch 15/15\n",
            "1875/1875 [==============================] - 6s 3ms/step - loss: 0.1819 - accuracy: 0.9327\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_jLeFe0-jzOg"
      },
      "source": [
        "We can now export the model. It’s a convolutional multi-layer neural network with the following architecture."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rRILCwvjZgwx",
        "outputId": "aa1bba15-996c-4b1d-8bf1-c67ac0cfabff",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521
        }
      },
      "source": [
        "model = clf.export_model()\n",
        "model.summary()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Model: \"functional_1\"\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "input_1 (InputLayer)         [(None, 28, 28, 1)]       0         \n",
            "_________________________________________________________________\n",
            "normalization (Normalization (None, 28, 28, 1)         3         \n",
            "_________________________________________________________________\n",
            "conv2d (Conv2D)              (None, 26, 26, 32)        320       \n",
            "_________________________________________________________________\n",
            "conv2d_1 (Conv2D)            (None, 24, 24, 64)        18496     \n",
            "_________________________________________________________________\n",
            "max_pooling2d (MaxPooling2D) (None, 12, 12, 64)        0         \n",
            "_________________________________________________________________\n",
            "dropout (Dropout)            (None, 12, 12, 64)        0         \n",
            "_________________________________________________________________\n",
            "flatten (Flatten)            (None, 9216)              0         \n",
            "_________________________________________________________________\n",
            "dropout_1 (Dropout)          (None, 9216)              0         \n",
            "_________________________________________________________________\n",
            "dense (Dense)                (None, 10)                92170     \n",
            "_________________________________________________________________\n",
            "classification_head_1 (Softm (None, 10)                0         \n",
            "=================================================================\n",
            "Total params: 110,989\n",
            "Trainable params: 110,986\n",
            "Non-trainable params: 3\n",
            "_________________________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9lLLv3JaagjE"
      },
      "source": [
        "## Testing the model\n",
        "The benchmark chosen for this dataset is the accuracy reported on [the official Zalando Research website](http://fashion-mnist.s3-website.eu-central-1.amazonaws.com). The best accuracy is 0.897, scored by a C-Support Vector Classification model.\n",
        "\n",
        "Let’s now test the model on the holdout test set."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yNPIv3ZLsfch",
        "outputId": "785ee860-05c6-4774-9c6c-7dcf4a779303",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "current = clf.evaluate(x_test, y_test)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "313/313 [==============================] - 1s 2ms/step - loss: 0.2249 - accuracy: 0.9239\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Vmac0sC6akPD",
        "outputId": "f0563549-c2b5-474c-bd9a-5918ec44fc64",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "previous = 0.897\n",
        "improvement = (current[1] - previous) * 100\n",
        "\n",
        "print(f'The accuracy improved by {round(improvement, 1)}%.')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The accuracy improved by 2.7%.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1LjaSRIQnY8i"
      },
      "source": [
        "We scored an accuracy of ~92% with only one model explored, outperforming the benchmark by almost 3%. \n",
        "\n",
        "### [Go back to index >](https://github.com/MattiaVerticchio/PersonalProjects/blob/master/README.md)"
      ]
    }
  ]
}