{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"provenance": [],
"gpuType": "T4"
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
},
"accelerator": "GPU"
},
"cells": [
{
"cell_type": "markdown",
"source": [
"# AutoEncoder"
],
"metadata": {
"id": "yG5hlKoPyzw2"
}
},
{
"cell_type": "markdown",
"source": [
"We'll start off by building a simple autoencoder to compress the MNIST dataset. With autoencoders, we pass input data through an encoder that makes a compressed representation of the input. Then, this representation is passed through a decoder to reconstruct the input data. Generally the encoder and decoder will be built with neural networks, then trained on example data."
],
"metadata": {
"id": "PLXjw5n0-fpC"
}
},
{
"cell_type": "markdown",
"source": [
""
],
"metadata": {
"id": "je-RN-8D-qh4"
}
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"id": "qF4qZQN7vMB_",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "8eb4d6bf-33c1-4a55-eaef-fb3097d52454"
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n",
"\u001b[1m11490434/11490434\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m0s\u001b[0m 0us/step\n"
]
}
],
"source": [
"from tensorflow.keras.datasets import mnist\n",
"import numpy as np\n",
"import torch\n",
"import matplotlib.pyplot as plt\n",
"# Load the MNIST dataset\n",
"(X_train, y_train), (X_test, y_test) = mnist.load_data()\n",
"\n",
"# Normalize the pixel values to be in the range [0, 1]\n",
"X_train = X_train.astype(np.float32) / 255.0\n",
"X_test = X_test.astype(np.float32) / 255.0\n",
"\n",
"num_workers = 0\n",
"# how many samples per batch to load\n",
"batch_size = 20\n",
"\n",
"# prepare data loaders\n",
"train_loader = torch.utils.data.DataLoader(X_train, batch_size=batch_size, num_workers=num_workers)\n",
"test_loader = torch.utils.data.DataLoader(X_test, batch_size=batch_size, num_workers=num_workers)\n"
]
},
{
"cell_type": "markdown",
"source": [
"## Visualization"
],
"metadata": {
"id": "koPWqX1mypCE"
}
},
{
"cell_type": "code",
"source": [
"def show_images(images, labels):\n",
" \"\"\"\n",
" Display a set of images and their labels using matplotlib.\n",
" The first column of `images` should contain the image indices,\n",
" and the second column should contain the flattened image pixels\n",
" reshaped into 28x28 arrays.\n",
" \"\"\"\n",
" # Extract the image indices and reshaped pixels\n",
" pixels = images.reshape(-1, 28, 28)\n",
"\n",
" # Create a figure with subplots for each image\n",
" fig, axs = plt.subplots(\n",
" ncols=min(len(images),10), nrows=1, figsize=(10, 3 * min(10,len(images)))\n",
" )\n",
"\n",
" # Loop over the images and display them with their labels\n",
" for i in range(min(len(images),10)):\n",
" # Display the image and its label\n",
" axs[i].imshow(pixels[i], cmap=\"gray\")\n",
" axs[i].set_title(\"Label: {}\".format(labels[i]))\n",
"\n",
" # Remove the tick marks and axis labels\n",
" axs[i].set_xticks([])\n",
" axs[i].set_yticks([])\n",
" axs[i].set_xlabel(\"Index: {}\".format(i))\n",
"\n",
" # Adjust the spacing between subplots\n",
" fig.subplots_adjust(hspace=0.5)\n",
"\n",
" # Show the figure\n",
" plt.show()"
],
"metadata": {
"id": "2eQoChrNvVh5"
},
"execution_count": 2,
"outputs": []
},
{
"cell_type": "code",
"source": [
"show_images(X_train, y_train)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 138
},
"id": "21C6Ul4c1oOK",
"outputId": "c607b809-cc6b-403b-b3e6-b79f3482f51a"
},
"execution_count": 3,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 1000x3000 with 10 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"## Architecture"
],
"metadata": {
"id": "J344tO6PyseE"
}
},
{
"cell_type": "code",
"source": [
"import torch.nn as nn\n",
"import torch.nn.functional as F\n",
"\n",
"# define the NN architecture\n",
"class Autoencoder(nn.Module):\n",
" def __init__(self, encoding_dim):\n",
" super(Autoencoder, self).__init__()\n",
" ## encoder ##\n",
" self.fc1 = nn.Linear(28*28, encoding_dim)\n",
" self.fc2 = nn.Linear(encoding_dim, 28*28)\n",
" ## decoder ##\n",
"\n",
"\n",
" def forward(self, x):\n",
" # define feedforward behavior\n",
" # and scale the *output* layer with a sigmoid activation function\n",
" x = F.relu(self.fc1(x))\n",
" x = F.sigmoid(self.fc2(x))\n",
" return x\n"
],
"metadata": {
"id": "jIlrduzDvYTH"
},
"execution_count": 24,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"## Train"
],
"metadata": {
"id": "48Oy2E_9yvfO"
}
},
{
"cell_type": "code",
"source": [
"# Create the autoencoder model and optimizer\n",
"encoding_dim = 4\n",
"model = Autoencoder(encoding_dim)\n",
"\n",
"optimizer = torch.optim.Adam(model.parameters(), lr=0.001)\n",
"\n",
"# Define the loss function\n",
"criterion = nn.MSELoss()\n",
"\n",
"# Set the device to GPU if available, otherwise use CPU\n",
"device='cuda'\n",
"model.to(device)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "vr33jaCevczo",
"outputId": "ffbe5dc0-245f-4946-d851-2092841d0f2f"
},
"execution_count": 28,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Autoencoder(\n",
" (fc1): Linear(in_features=784, out_features=4, bias=True)\n",
" (fc2): Linear(in_features=4, out_features=784, bias=True)\n",
")"
]
},
"metadata": {},
"execution_count": 28
}
]
},
{
"cell_type": "code",
"source": [
"# number of epochs to train the model\n",
"n_epochs = 20\n",
"\n",
"for epoch in range(1, n_epochs+1):\n",
" # monitor training loss\n",
" train_loss = 0.0\n",
"\n",
" ###################\n",
" # train the model #\n",
" ###################\n",
" for images in train_loader:\n",
"\n",
" ### training code ###\n",
" images = images.to(device)\n",
" images = images.view(images.shape[0], -1)\n",
" optimizer.zero_grad()\n",
" outputs = model(images)\n",
" loss = criterion(outputs, images)\n",
" loss.backward()\n",
" optimizer.step()\n",
" # update running training loss\n",
" train_loss += loss.item()*images.size(0)\n",
"\n",
" # print avg training statistics\n",
" train_loss = train_loss/len(train_loader)\n",
" print('Epoch: {} \\tTraining Loss: {:.6f}'.format(\n",
" epoch,\n",
" train_loss\n",
" ))"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "jubr913gxWbu",
"outputId": "f4349d8e-35f5-4af9-a7ed-c7818e7eec31"
},
"execution_count": 29,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Epoch: 1 \tTraining Loss: 1.490595\n",
"Epoch: 2 \tTraining Loss: 1.215091\n",
"Epoch: 3 \tTraining Loss: 1.154939\n",
"Epoch: 4 \tTraining Loss: 1.132552\n",
"Epoch: 5 \tTraining Loss: 1.121539\n",
"Epoch: 6 \tTraining Loss: 1.116499\n",
"Epoch: 7 \tTraining Loss: 1.114284\n",
"Epoch: 8 \tTraining Loss: 1.113049\n",
"Epoch: 9 \tTraining Loss: 1.112245\n",
"Epoch: 10 \tTraining Loss: 1.111732\n",
"Epoch: 11 \tTraining Loss: 1.111336\n",
"Epoch: 12 \tTraining Loss: 1.111043\n",
"Epoch: 13 \tTraining Loss: 1.110823\n",
"Epoch: 14 \tTraining Loss: 1.110647\n",
"Epoch: 15 \tTraining Loss: 1.110504\n",
"Epoch: 16 \tTraining Loss: 1.110394\n",
"Epoch: 17 \tTraining Loss: 1.110300\n",
"Epoch: 18 \tTraining Loss: 1.110222\n",
"Epoch: 19 \tTraining Loss: 1.110153\n",
"Epoch: 20 \tTraining Loss: 1.110083\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"## Evaluation"
],
"metadata": {
"id": "bUwECCKs-wZA"
}
},
{
"cell_type": "markdown",
"source": [
"encoding_dim = 4"
],
"metadata": {
"id": "Y7AGvPSsXut3"
}
},
{
"cell_type": "code",
"source": [
"import matplotlib.pyplot as plt\n",
"\n",
"# obtain one batch of test images\n",
"dataiter = iter(test_loader)\n",
"images = next(dataiter).to(device)\n",
"\n",
"images_flatten = images.view(images.size(0), -1)\n",
"# get sample outputs\n",
"output = model(images_flatten)\n",
"# prep images for display\n",
"images = images.cpu().numpy()\n",
"\n",
"# output is resized into a batch of images\n",
"output = output.view(batch_size, 1, 28, 28)\n",
"# use detach when it's an output that requires_grad\n",
"output = output.cpu().detach().numpy()\n",
"\n",
"# plot the first ten input images and then reconstructed images\n",
"fig, axes = plt.subplots(nrows=2, ncols=10, sharex=True, sharey=True, figsize=(25,4))\n",
"\n",
"# input images on top row, reconstructions on bottom\n",
"for images, row in zip([images, output], axes):\n",
" for img, ax in zip(images, row):\n",
" ax.imshow(np.squeeze(img), cmap='gray')\n",
" ax.get_xaxis().set_visible(False)\n",
" ax.get_yaxis().set_visible(False)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 145
},
"id": "2rnx9Kx9d-os",
"outputId": "867cd8c9-4b58-4f32-ad33-c1233c7b7c3d"
},
"execution_count": 27,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 2500x400 with 20 Axes>"
],
"image/png": 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},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"encoding_dim = 8"
],
"metadata": {
"id": "gqKF82bVXyl-"
}
},
{
"cell_type": "code",
"source": [
"import matplotlib.pyplot as plt\n",
"\n",
"# obtain one batch of test images\n",
"dataiter = iter(test_loader)\n",
"images = next(dataiter).to(device)\n",
"\n",
"images_flatten = images.view(images.size(0), -1)\n",
"# get sample outputs\n",
"output = model(images_flatten)\n",
"# prep images for display\n",
"images = images.cpu().numpy()\n",
"\n",
"# output is resized into a batch of images\n",
"output = output.view(batch_size, 1, 28, 28)\n",
"# use detach when it's an output that requires_grad\n",
"output = output.cpu().detach().numpy()\n",
"\n",
"# plot the first ten input images and then reconstructed images\n",
"fig, axes = plt.subplots(nrows=2, ncols=10, sharex=True, sharey=True, figsize=(25,4))\n",
"\n",
"# input images on top row, reconstructions on bottom\n",
"for images, row in zip([images, output], axes):\n",
" for img, ax in zip(images, row):\n",
" ax.imshow(np.squeeze(img), cmap='gray')\n",
" ax.get_xaxis().set_visible(False)\n",
" ax.get_yaxis().set_visible(False)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 145
},
"id": "bH5JK__Mc-WS",
"outputId": "82c93a0f-0cb6-475e-e509-d99c11f39416"
},
"execution_count": 18,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 2500x400 with 20 Axes>"
],
"image/png": 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},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"encoding_dim = 16"
],
"metadata": {
"id": "ftq0FB2gX0GW"
}
},
{
"cell_type": "code",
"source": [
"import matplotlib.pyplot as plt\n",
"\n",
"# obtain one batch of test images\n",
"dataiter = iter(test_loader)\n",
"images = next(dataiter).to(device)\n",
"\n",
"images_flatten = images.view(images.size(0), -1)\n",
"# get sample outputs\n",
"output = model(images_flatten)\n",
"# prep images for display\n",
"images = images.cpu().numpy()\n",
"\n",
"# output is resized into a batch of images\n",
"output = output.view(batch_size, 1, 28, 28)\n",
"# use detach when it's an output that requires_grad\n",
"output = output.cpu().detach().numpy()\n",
"\n",
"# plot the first ten input images and then reconstructed images\n",
"fig, axes = plt.subplots(nrows=2, ncols=10, sharex=True, sharey=True, figsize=(25,4))\n",
"\n",
"# input images on top row, reconstructions on bottom\n",
"for images, row in zip([images, output], axes):\n",
" for img, ax in zip(images, row):\n",
" ax.imshow(np.squeeze(img), cmap='gray')\n",
" ax.get_xaxis().set_visible(False)\n",
" ax.get_yaxis().set_visible(False)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 145
},
"id": "sdUGpNvtcnXi",
"outputId": "49a8f912-9111-4049-83a8-3bf1d7b2d209"
},
"execution_count": 15,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 2500x400 with 20 Axes>"
],
"image/png": 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},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"encoding_dim = 32"
],
"metadata": {
"id": "sDGNrdiLX2ZH"
}
},
{
"cell_type": "code",
"source": [
"import matplotlib.pyplot as plt\n",
"\n",
"# obtain one batch of test images\n",
"dataiter = iter(test_loader)\n",
"images = next(dataiter).to(device)\n",
"\n",
"images_flatten = images.view(images.size(0), -1)\n",
"# get sample outputs\n",
"output = model(images_flatten)\n",
"# prep images for display\n",
"images = images.cpu().numpy()\n",
"\n",
"# output is resized into a batch of images\n",
"output = output.view(batch_size, 1, 28, 28)\n",
"# use detach when it's an output that requires_grad\n",
"output = output.cpu().detach().numpy()\n",
"\n",
"# plot the first ten input images and then reconstructed images\n",
"fig, axes = plt.subplots(nrows=2, ncols=10, sharex=True, sharey=True, figsize=(25,4))\n",
"\n",
"# input images on top row, reconstructions on bottom\n",
"for images, row in zip([images, output], axes):\n",
" for img, ax in zip(images, row):\n",
" ax.imshow(np.squeeze(img), cmap='gray')\n",
" ax.get_xaxis().set_visible(False)\n",
" ax.get_yaxis().set_visible(False)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 145
},
"id": "K3btcCl78rNa",
"outputId": "e199517f-5298-41f9-ff11-3183114c2334"
},
"execution_count": 12,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 2500x400 with 20 Axes>"
],
"image/png": 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