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Intro to Autoencoders

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This tutorial introduces autoencoders with three examples: the basics, image denoising, and anomaly detection.

An autoencoder is a special type of neural network that is trained to copy its input to its output. For example, given an image of a handwritten digit, an autoencoder first encodes the image into a lower dimensional latent representation, then decodes the latent representation back to an image. An autoencoder learns to compress the data while minimizing the reconstruction error.

To learn more about autoencoders, please consider reading chapter 14 from Deep Learning by Ian Goodfellow, Yoshua Bengio, and Aaron Courville.

Import TensorFlow and other libraries

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import tensorflow as tf

from sklearn.metrics import accuracy_score, precision_score, recall_score
from sklearn.model_selection import train_test_split
from tensorflow.keras import layers, losses
from tensorflow.keras.datasets import fashion_mnist
from tensorflow.keras.models import Model

Load the dataset

To start, you will train the basic autoencoder using the Fashion MNIST dataset. Each image in this dataset is 28x28 pixels.

(x_train, _), (x_test, _) = fashion_mnist.load_data()

x_train = x_train.astype('float32') / 255.
x_test = x_test.astype('float32') / 255.

print (x_train.shape)
print (x_test.shape)
Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/train-labels-idx1-ubyte.gz
32768/29515 [=================================] - 0s 0us/step
40960/29515 [=========================================] - 0s 0us/step
Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/train-images-idx3-ubyte.gz
26427392/26421880 [==============================] - 0s 0us/step
26435584/26421880 [==============================] - 0s 0us/step
Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/t10k-labels-idx1-ubyte.gz
16384/5148 [===============================================================================================] - 0s 0us/step
Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/t10k-images-idx3-ubyte.gz
4423680/4422102 [==============================] - 0s 0us/step
4431872/4422102 [==============================] - 0s 0us/step
(60000, 28, 28)
(10000, 28, 28)

First example: Basic autoencoder

Basic autoencoder results

Define an autoencoder with two Dense layers: an encoder, which compresses the images into a 64 dimensional latent vector, and a decoder, that reconstructs the original image from the latent space.

To define your model, use the Keras Model Subclassing API.

latent_dim = 64 

class Autoencoder(Model):
  def __init__(self, latent_dim):
    super(Autoencoder, self).__init__()
    self.latent_dim = latent_dim   
    self.encoder = tf.keras.Sequential([
      layers.Flatten(),
      layers.Dense(latent_dim, activation='relu'),
    ])
    self.decoder = tf.keras.Sequential([
      layers.Dense(784, activation='sigmoid'),
      layers.Reshape((28, 28))
    ])

  def call(self, x):
    encoded = self.encoder(x)
    decoded = self.decoder(encoded)
    return decoded

autoencoder = Autoencoder(latent_dim)
autoencoder.compile(optimizer='adam', loss=losses.MeanSquaredError())

Train the model using x_train as both the input and the target. The encoder will learn to compress the dataset from 784 dimensions to the latent space, and the decoder will learn to reconstruct the original images. .

autoencoder.fit(x_train, x_train,
                epochs=10,
                shuffle=True,
                validation_data=(x_test, x_test))
Epoch 1/10
1875/1875 [==============================] - 5s 2ms/step - loss: 0.0240 - val_loss: 0.0133
Epoch 2/10
1875/1875 [==============================] - 4s 2ms/step - loss: 0.0116 - val_loss: 0.0109
Epoch 3/10
1875/1875 [==============================] - 4s 2ms/step - loss: 0.0101 - val_loss: 0.0098
Epoch 4/10
1875/1875 [==============================] - 4s 2ms/step - loss: 0.0095 - val_loss: 0.0095
Epoch 5/10
1875/1875 [==============================] - 4s 2ms/step - loss: 0.0092 - val_loss: 0.0092
Epoch 6/10
1875/1875 [==============================] - 4s 2ms/step - loss: 0.0091 - val_loss: 0.0091
Epoch 7/10
1875/1875 [==============================] - 4s 2ms/step - loss: 0.0090 - val_loss: 0.0090
Epoch 8/10
1875/1875 [==============================] - 4s 2ms/step - loss: 0.0089 - val_loss: 0.0090
Epoch 9/10
1875/1875 [==============================] - 4s 2ms/step - loss: 0.0088 - val_loss: 0.0089
Epoch 10/10
1875/1875 [==============================] - 4s 2ms/step - loss: 0.0088 - val_loss: 0.0089
<keras.callbacks.History at 0x7f1a23134d90>

Now that the model is trained, let's test it by encoding and decoding images from the test set.

encoded_imgs = autoencoder.encoder(x_test).numpy()
decoded_imgs = autoencoder.decoder(encoded_imgs).numpy()
n = 10
plt.figure(figsize=(20, 4))
for i in range(n):
  # display original
  ax = plt.subplot(2, n, i + 1)
  plt.imshow(x_test[i])
  plt.title("original")
  plt.gray()
  ax.get_xaxis().set_visible(False)
  ax.get_yaxis().set_visible(False)

  # display reconstruction
  ax = plt.subplot(2, n, i + 1 + n)
  plt.imshow(decoded_imgs[i])
  plt.title("reconstructed")
  plt.gray()
  ax.get_xaxis().set_visible(False)
  ax.get_yaxis().set_visible(False)
plt.show()

png

Second example: Image denoising

Image denoising results

An autoencoder can also be trained to remove noise from images. In the following section, you will create a noisy version of the Fashion MNIST dataset by applying random noise to each image. You will then train an autoencoder using the noisy image as input, and the original image as the target.

Let's reimport the dataset to omit the modifications made earlier.

(x_train, _), (x_test, _) = fashion_mnist.load_data()
x_train = x_train.astype('float32') / 255.
x_test = x_test.astype('float32') / 255.

x_train = x_train[..., tf.newaxis]
x_test = x_test[..., tf.newaxis]

print(x_train.shape)
(60000, 28, 28, 1)

Adding random noise to the images

noise_factor = 0.2
x_train_noisy = x_train + noise_factor * tf.random.normal(shape=x_train.shape) 
x_test_noisy = x_test + noise_factor * tf.random.normal(shape=x_test.shape) 

x_train_noisy = tf.clip_by_value(x_train_noisy, clip_value_min=0., clip_value_max=1.)
x_test_noisy = tf.clip_by_value(x_test_noisy, clip_value_min=0., clip_value_max=1.)

Plot the noisy images.

n = 10
plt.figure(figsize=(20, 2))
for i in range(n):
    ax = plt.subplot(1, n, i + 1)
    plt.title("original + noise")
    plt.imshow(tf.squeeze(x_test_noisy[i]))
    plt.gray()
plt.show()

png

Define a convolutional autoencoder

In this example, you will train a convolutional autoencoder using Conv2D layers in the encoder, and Conv2DTranspose layers in the decoder.

class Denoise(Model):
  def __init__(self):
    super(Denoise, self).__init__()
    self.encoder = tf.keras.Sequential([
      layers.Input(shape=(28, 28, 1)),
      layers.Conv2D(16, (3, 3), activation='relu', padding='same', strides=2),
      layers.Conv2D(8, (3, 3), activation='relu', padding='same', strides=2)])

    self.decoder = tf.keras.Sequential([
      layers.Conv2DTranspose(8, kernel_size=3, strides=2, activation='relu', padding='same'),
      layers.Conv2DTranspose(16, kernel_size=3, strides=2, activation='relu', padding='same'),
      layers.Conv2D(1, kernel_size=(3, 3), activation='sigmoid', padding='same')])

  def call(self, x):
    encoded = self.encoder(x)
    decoded = self.decoder(encoded)
    return decoded

autoencoder = Denoise()
autoencoder.compile(optimizer='adam', loss=losses.MeanSquaredError())
autoencoder.fit(x_train_noisy, x_train,
                epochs=10,
                shuffle=True,
                validation_data=(x_test_noisy, x_test))
Epoch 1/10
1875/1875 [==============================] - 15s 3ms/step - loss: 0.0181 - val_loss: 0.0100
Epoch 2/10
1875/1875 [==============================] - 6s 3ms/step - loss: 0.0089 - val_loss: 0.0084
Epoch 3/10
1875/1875 [==============================] - 6s 3ms/step - loss: 0.0078 - val_loss: 0.0076
Epoch 4/10
1875/1875 [==============================] - 6s 3ms/step - loss: 0.0074 - val_loss: 0.0074
Epoch 5/10
1875/1875 [==============================] - 6s 3ms/step - loss: 0.0073 - val_loss: 0.0073
Epoch 6/10
1875/1875 [==============================] - 6s 3ms/step - loss: 0.0072 - val_loss: 0.0071
Epoch 7/10
1875/1875 [==============================] - 6s 3ms/step - loss: 0.0071 - val_loss: 0.0071
Epoch 8/10
1875/1875 [==============================] - 6s 3ms/step - loss: 0.0071 - val_loss: 0.0070
Epoch 9/10
1875/1875 [==============================] - 6s 3ms/step - loss: 0.0070 - val_loss: 0.0070
Epoch 10/10
1875/1875 [==============================] - 6s 3ms/step - loss: 0.0070 - val_loss: 0.0070
<keras.callbacks.History at 0x7f19ac2ab490>

Let's take a look at a summary of the encoder. Notice how the images are downsampled from 28x28 to 7x7.

autoencoder.encoder.summary()
Model: "sequential_2"
_________________________________________________________________
 Layer (type)                Output Shape              Param #   
=================================================================
 conv2d (Conv2D)             (None, 14, 14, 16)        160       
                                                                 
 conv2d_1 (Conv2D)           (None, 7, 7, 8)           1160      
                                                                 
=================================================================
Total params: 1,320
Trainable params: 1,320
Non-trainable params: 0
_________________________________________________________________

The decoder upsamples the images back from 7x7 to 28x28.

autoencoder.decoder.summary()
Model: "sequential_3"
_________________________________________________________________
 Layer (type)                Output Shape              Param #   
=================================================================
 conv2d_transpose (Conv2DTra  (None, 14, 14, 8)        584       
 nspose)                                                         
                                                                 
 conv2d_transpose_1 (Conv2DT  (None, 28, 28, 16)       1168      
 ranspose)                                                       
                                                                 
 conv2d_2 (Conv2D)           (None, 28, 28, 1)         145       
                                                                 
=================================================================
Total params: 1,897
Trainable params: 1,897
Non-trainable params: 0
_________________________________________________________________

Plotting both the noisy images and the denoised images produced by the autoencoder.

encoded_imgs = autoencoder.encoder(x_test).numpy()
decoded_imgs = autoencoder.decoder(encoded_imgs).numpy()
n = 10
plt.figure(figsize=(20, 4))
for i in range(n):

    # display original + noise
    ax = plt.subplot(2, n, i + 1)
    plt.title("original + noise")
    plt.imshow(tf.squeeze(x_test_noisy[i]))
    plt.gray()
    ax.get_xaxis().set_visible(False)
    ax.get_yaxis().set_visible(False)

    # display reconstruction
    bx = plt.subplot(2, n, i + n + 1)
    plt.title("reconstructed")
    plt.imshow(tf.squeeze(decoded_imgs[i]))
    plt.gray()
    bx.get_xaxis().set_visible(False)
    bx.get_yaxis().set_visible(False)
plt.show()

png

Third example: Anomaly detection

Overview

In this example, you will train an autoencoder to detect anomalies on the ECG5000 dataset. This dataset contains 5,000 Electrocardiograms, each with 140 data points. You will use a simplified version of the dataset, where each example has been labeled either 0 (corresponding to an abnormal rhythm), or 1 (corresponding to a normal rhythm). You are interested in identifying the abnormal rhythms.

How will you detect anomalies using an autoencoder? Recall that an autoencoder is trained to minimize reconstruction error. You will train an autoencoder on the normal rhythms only, then use it to reconstruct all the data. Our hypothesis is that the abnormal rhythms will have higher reconstruction error. You will then classify a rhythm as an anomaly if the reconstruction error surpasses a fixed threshold.

Load ECG data

The dataset you will use is based on one from timeseriesclassification.com.

# Download the dataset
dataframe = pd.read_csv('http://storage.googleapis.com/download.tensorflow.org/data/ecg.csv', header=None)
raw_data = dataframe.values
dataframe.head()
# The last element contains the labels
labels = raw_data[:, -1]

# The other data points are the electrocadriogram data
data = raw_data[:, 0:-1]

train_data, test_data, train_labels, test_labels = train_test_split(
    data, labels, test_size=0.2, random_state=21
)

Normalize the data to [0,1].

min_val = tf.reduce_min(train_data)
max_val = tf.reduce_max(train_data)

train_data = (train_data - min_val) / (max_val - min_val)
test_data = (test_data - min_val) / (max_val - min_val)

train_data = tf.cast(train_data, tf.float32)
test_data = tf.cast(test_data, tf.float32)

You will train the autoencoder using only the normal rhythms, which are labeled in this dataset as 1. Separate the normal rhythms from the abnormal rhythms.

train_labels = train_labels.astype(bool)
test_labels = test_labels.astype(bool)

normal_train_data = train_data[train_labels]
normal_test_data = test_data[test_labels]

anomalous_train_data = train_data[~train_labels]
anomalous_test_data = test_data[~test_labels]

Plot a normal ECG.

plt.grid()
plt.plot(np.arange(140), normal_train_data[0])
plt.title("A Normal ECG")
plt.show()

png

Plot an anomalous ECG.

plt.grid()
plt.plot(np.arange(140), anomalous_train_data[0])
plt.title("An Anomalous ECG")
plt.show()

png

Build the model

class AnomalyDetector(Model):
  def __init__(self):
    super(AnomalyDetector, self).__init__()
    self.encoder = tf.keras.Sequential([
      layers.Dense(32, activation="relu"),
      layers.Dense(16, activation="relu"),
      layers.Dense(8, activation="relu")])

    self.decoder = tf.keras.Sequential([
      layers.Dense(16, activation="relu"),
      layers.Dense(32, activation="relu"),
      layers.Dense(140, activation="sigmoid")])

  def call(self, x):
    encoded = self.encoder(x)
    decoded = self.decoder(encoded)
    return decoded

autoencoder = AnomalyDetector()
autoencoder.compile(optimizer='adam', loss='mae')

Notice that the autoencoder is trained using only the normal ECGs, but is evaluated using the full test set.

history = autoencoder.fit(normal_train_data, normal_train_data, 
          epochs=20, 
          batch_size=512,
          validation_data=(test_data, test_data),
          shuffle=True)
Epoch 1/20
5/5 [==============================] - 1s 36ms/step - loss: 0.0578 - val_loss: 0.0532
Epoch 2/20
5/5 [==============================] - 0s 9ms/step - loss: 0.0557 - val_loss: 0.0516
Epoch 3/20
5/5 [==============================] - 0s 9ms/step - loss: 0.0529 - val_loss: 0.0501
Epoch 4/20
5/5 [==============================] - 0s 9ms/step - loss: 0.0495 - val_loss: 0.0487
Epoch 5/20
5/5 [==============================] - 0s 8ms/step - loss: 0.0458 - val_loss: 0.0463
Epoch 6/20
5/5 [==============================] - 0s 9ms/step - loss: 0.0425 - val_loss: 0.0444
Epoch 7/20
5/5 [==============================] - 0s 9ms/step - loss: 0.0394 - val_loss: 0.0428
Epoch 8/20
5/5 [==============================] - 0s 9ms/step - loss: 0.0365 - val_loss: 0.0414
Epoch 9/20
5/5 [==============================] - 0s 8ms/step - loss: 0.0339 - val_loss: 0.0402
Epoch 10/20
5/5 [==============================] - 0s 8ms/step - loss: 0.0317 - val_loss: 0.0393
Epoch 11/20
5/5 [==============================] - 0s 9ms/step - loss: 0.0298 - val_loss: 0.0383
Epoch 12/20
5/5 [==============================] - 0s 8ms/step - loss: 0.0282 - val_loss: 0.0375
Epoch 13/20
5/5 [==============================] - 0s 8ms/step - loss: 0.0269 - val_loss: 0.0367
Epoch 14/20
5/5 [==============================] - 0s 8ms/step - loss: 0.0258 - val_loss: 0.0360
Epoch 15/20
5/5 [==============================] - 0s 8ms/step - loss: 0.0249 - val_loss: 0.0352
Epoch 16/20
5/5 [==============================] - 0s 9ms/step - loss: 0.0241 - val_loss: 0.0346
Epoch 17/20
5/5 [==============================] - 0s 9ms/step - loss: 0.0234 - val_loss: 0.0342
Epoch 18/20
5/5 [==============================] - 0s 9ms/step - loss: 0.0228 - val_loss: 0.0337
Epoch 19/20
5/5 [==============================] - 0s 9ms/step - loss: 0.0223 - val_loss: 0.0334
Epoch 20/20
5/5 [==============================] - 0s 8ms/step - loss: 0.0218 - val_loss: 0.0331
plt.plot(history.history["loss"], label="Training Loss")
plt.plot(history.history["val_loss"], label="Validation Loss")
plt.legend()
<matplotlib.legend.Legend at 0x7f1a25b27950>

png

You will soon classify an ECG as anomalous if the reconstruction error is greater than one standard deviation from the normal training examples. First, let's plot a normal ECG from the training set, the reconstruction after it's encoded and decoded by the autoencoder, and the reconstruction error.

encoded_data = autoencoder.encoder(normal_test_data).numpy()
decoded_data = autoencoder.decoder(encoded_data).numpy()

plt.plot(normal_test_data[0], 'b')
plt.plot(decoded_data[0], 'r')
plt.fill_between(np.arange(140), decoded_data[0], normal_test_data[0], color='lightcoral')
plt.legend(labels=["Input", "Reconstruction", "Error"])
plt.show()

png

Create a similar plot, this time for an anomalous test example.

encoded_data = autoencoder.encoder(anomalous_test_data).numpy()
decoded_data = autoencoder.decoder(encoded_data).numpy()

plt.plot(anomalous_test_data[0], 'b')
plt.plot(decoded_data[0], 'r')
plt.fill_between(np.arange(140), decoded_data[0], anomalous_test_data[0], color='lightcoral')
plt.legend(labels=["Input", "Reconstruction", "Error"])
plt.show()

png

Detect anomalies

Detect anomalies by calculating whether the reconstruction loss is greater than a fixed threshold. In this tutorial, you will calculate the mean average error for normal examples from the training set, then classify future examples as anomalous if the reconstruction error is higher than one standard deviation from the training set.

Plot the reconstruction error on normal ECGs from the training set

reconstructions = autoencoder.predict(normal_train_data)
train_loss = tf.keras.losses.mae(reconstructions, normal_train_data)

plt.hist(train_loss[None,:], bins=50)
plt.xlabel("Train loss")
plt.ylabel("No of examples")
plt.show()

png

Choose a threshold value that is one standard deviations above the mean.

threshold = np.mean(train_loss) + np.std(train_loss)
print("Threshold: ", threshold)
Threshold:  0.0330268

If you examine the reconstruction error for the anomalous examples in the test set, you'll notice most have greater reconstruction error than the threshold. By varing the threshold, you can adjust the precision and recall of your classifier.

reconstructions = autoencoder.predict(anomalous_test_data)
test_loss = tf.keras.losses.mae(reconstructions, anomalous_test_data)

plt.hist(test_loss[None, :], bins=50)
plt.xlabel("Test loss")
plt.ylabel("No of examples")
plt.show()

png

Classify an ECG as an anomaly if the reconstruction error is greater than the threshold.

def predict(model, data, threshold):
  reconstructions = model(data)
  loss = tf.keras.losses.mae(reconstructions, data)
  return tf.math.less(loss, threshold)

def print_stats(predictions, labels):
  print("Accuracy = {}".format(accuracy_score(labels, predictions)))
  print("Precision = {}".format(precision_score(labels, predictions)))
  print("Recall = {}".format(recall_score(labels, predictions)))
preds = predict(autoencoder, test_data, threshold)
print_stats(preds, test_labels)
Accuracy = 0.944
Precision = 0.9941176470588236
Recall = 0.9053571428571429

Next steps

To learn more about anomaly detection with autoencoders, check out this excellent interactive example built with TensorFlow.js by Victor Dibia. For a real-world use case, you can learn how Airbus Detects Anomalies in ISS Telemetry Data using TensorFlow. To learn more about the basics, consider reading this blog post by François Chollet. For more details, check out chapter 14 from Deep Learning by Ian Goodfellow, Yoshua Bengio, and Aaron Courville.