Autoencoders
Autoencoders are a class of neural network that attempt to recreate the input as their target using back-propagation. An autoencoder consists of two parts; an encoder and a decoder. The encoder will read the input and compress it to a compact representation, and the decoder will read the compact representation and recreate the input from it. In other words, the autoencoder tries to learn the identity function by minimizing the reconstruction error. They have an inherent capability to learn a compact representation of data. They are at the center of deep belief networks and find applications in image reconstruction, clustering, machine translation, and much more.
This exercise aims to test your understanding of autoencoder architecture, and how it can be used to denoise an image. We will build a convolutional autoencoder. Combining your knowledge of a Vanilla/Denoising Autoencoder and Convolutional Networks.
Here five Practice Exercises are given below:
#@title Import Modules
import numpy as np
import tensorflow as tf
import tensorflow.keras as K
import matplotlib.pyplot as plt
from tensorflow.keras.layers import Dense, Conv2D, MaxPooling2D, UpSampling2D
np.random.seed(11)
tf.random.set_seed(11)AutoEncoder Architecture The number of hidden units in the autoencoder is typically less than the number of input (and output) units. This forces the encoder to learn a compressed representation of the input, which the decoder reconstructs. If there is a structure in the input data in the form of correlations between input features, then the autoencoder will discover some of these correlations, and end up learning a low-dimensional representation of the data similar to that learned using principal component analysis (PCA). Once trained
We can discard decoder and use Encoder to optain a compact representation of input.
We can cascade Encoder to a classifier.
The encoder and decoder components of an autoencoder can be implemented using either dense, convolutional, or recurrent networks, depending on the kind of data that is being modeled.
Below we define an encoder and a decoder using Convolutional layers. Both consist of three convolutional layers. Each layer in Encoder has a corresponding layer in decoder, thus in this case it is like three autoencoders stacked over each other. This is also called Stacked Autoencoders
#@title Encoder
class Encoder(K.layers.Layer):
def __init__(self, filters):
super(Encoder, self).__init__()
self.conv1 = Conv2D(filters=filters[0], kernel_size=3, strides=1, activation='relu', padding='same')
self.conv2 = Conv2D(filters=filters[1], kernel_size=3, strides=1, activation='relu', padding='same')
self.conv3 = Conv2D(filters=filters[2], kernel_size=3, strides=1, activation='relu', padding='same')
self.pool = MaxPooling2D((2, 2), padding='same')
def call(self, input_features):
x = self.conv1(input_features)
#print("Ex1", x.shape)
x = self.pool(x)
#print("Ex2", x.shape)
x = self.conv2(x)
x = self.pool(x)
x = self.conv3(x)
x = self.pool(x)
return x #@title Decoder
class Decoder(K.layers.Layer):
def __init__(self, filters):
super(Decoder, self).__init__()
self.conv1 = Conv2D(filters=filters[2], kernel_size=3, strides=1, activation='relu', padding='same')
self.conv2 = Conv2D(filters=filters[1], kernel_size=3, strides=1, activation='relu', padding='same')
self.conv3 = Conv2D(filters=filters[0], kernel_size=3, strides=1, activation='relu', padding='valid')
self.conv4 = Conv2D(1, 3, 1, activation='sigmoid', padding='same')
self.upsample = UpSampling2D((2, 2))
def call(self, encoded):
x = self.conv1(encoded)
#print("dx1", x.shape)
x = self.upsample(x)
#print("dx2", x.shape)
x = self.conv2(x)
x = self.upsample(x)
x = self.conv3(x)
x = self.upsample(x)
return self.conv4(x)Denoising Autoencoder When we train the autoencoder, we can train it directly on the raw images or we can add noise to the input images while training. When the autoencoder is trained on noisy data, it gets an even interesting property--it can reconstruct noisy images. In other words--you give it an image with noise and it will remove the noise from it.
Exercise 1:
In this exercise we will train the stacked autoencoder in four steps:
In Step 1 choose the noise = 0
Complete the Step 2
In the Step 3 choose filters as [16, 32, 64] for Encoder and [64, 32, 16] for Decoder.
Perform Step 4 for batch size of 64 and 10 epochs
Reflect on the plotted images what do you see?
Answer 1 Step 1: Read the dataset, process it for noise = 0
#@title Dataset Reading and Processing
Noise = 1 #@param {type:"slider", min:0, max:1, step:0.1}
(x_train, _), (x_test, _) = K.datasets.mnist.load_data()
x_train = x_train / 255.
x_test = x_test / 255.
x_train = np.reshape(x_train, (len(x_train),28, 28, 1))
x_test = np.reshape(x_test, (len(x_test), 28, 28, 1))
noise = Noise
x_train_noisy = x_train + noise * np.random.normal(loc=0.0, scale=1.0, size=x_train.shape)
x_test_noisy = x_test + noise * np.random.normal(loc=0.0, scale=1.0, size=x_test.shape)
x_train_noisy = np.clip(x_train_noisy, 0, 1)
x_test_noisy = np.clip(x_test_noisy, 0, 1)
x_train_noisy = x_train_noisy.astype('float32')
x_test_noisy = x_test_noisy.astype('float32')
Step 2 You need to complete the code below. We will be using the Encoder and Decoder architectures that we have defined above to build an autoencoder. In the code below replace ... with right code.
class Autoencoder(K.Model):
def __init__(self, filters_encoder, filters_decoder):
super(Autoencoder, self).__init__()
self.loss = []
self.encoder = Encoder(...)
self.decoder = Decoder(...)
def call(self, input_features):
#print(input_features.shape)
encoded = self.encoder(...)
#print(encoded.shape)
reconstructed = self.decoder(...)
#print(reconstructed.shape)
return reconstructed
Exercise 2: In this exercise we will make only one change, in step 3 choose filters as: [16, 32, 64] for both Encoder and Decoder. Try training the Autoencoder. What happens? Why do you think it is so?
Answer 2: Write Your Answer Here
Exercise 3: Now we will introduce noise of 0.2 in the training dataset. Train an autoencoder with filters [64,32,16] for encoder and [16,32,64] for decoder and observe the reconstrucred images. What do you find? Is the autoencoder able to recognize noisy digits?
Answer 3: Write your answer here
Exercise 4: Let us be more adventurous with the same Encoder-Decoder architecture, we increase the noise and observe the reconstrucred images. What do you find? Till what noise value is the autoencoder able to reconstruct images? Till what noise level you (human) can recognize the digits in the noisy image.
Answer 4: Write your answer here
Step 3: We have built Convolutional Autoencoder. That is both Encoder and Decoder are buit using Convolutional layers. Below you need to select
#@title Select Filters for Encoder & Decoder
filter_encoder_0 = 16 #@param {type:"slider", min:8, max:256, step:2}
filter_encoder_1 = 32 #@param {type:"slider", min:8, max:256, step:2}
filter_encoder_2 = 64 #@param {type:"slider", min:8, max:256, step:2}
filters_en = [filter_encoder_0,filter_encoder_1,filter_encoder_2]
filter_decoder_0 = 16 #@param {type:"slider", min:8, max:256, step:2}
filter_decoder_1 = 32 #@param {type:"slider", min:8, max:256, step:2}
filter_decoder_2 = 64 #@param {type:"slider", min:8, max:256, step:2}
filters_de = [filter_decoder_0,filter_decoder_1,filter_decoder_2]
model = Autoencoder(filters_en, filters_de)
model.compile(loss='binary_crossentropy', optimizer='adam')Step 4: Choose the appropriate batch_size and epochs
#@title Train the model
BATCH_SIZE = 132 #@param {type:"slider", min:32, max:2000, step:10}
EPOCHS = 13 #@param {type:"slider", min:1, max:100, step:1}
batch_size = BATCH_SIZE
max_epochs = EPOCHS
loss = model.fit(x_train_noisy,
x_train,
validation_data=(x_test_noisy, x_test),
epochs=max_epochs,
batch_size=batch_size)Output:
Epoch 1/7
1875/1875 [==============================] - 136s 73ms/step - loss: 0.1829 - val_loss: 0.1531
Epoch 2/7
1875/1875 [==============================] - 135s 72ms/step - loss: 0.1505 - val_loss: 0.1459
Epoch 3/7
1875/1875 [==============================] - 135s 72ms/step - loss: 0.1452 - val_loss: 0.1424
Epoch 4/7
1875/1875 [==============================] - 134s 72ms/step - loss: 0.1423 - val_loss: 0.1409
Epoch 5/7
1875/1875 [==============================] - 135s 72ms/step - loss: 0.1405 - val_loss: 0.1394
Epoch 6/7
1875/1875 [==============================] - 135s 72ms/step - loss: 0.1393 - val_loss: 0.1381
Epoch 7/7
1875/1875 [==============================] - 136s 72ms/step - loss: 0.1383 - val_loss: 0.1377
...
...#@title Reconstructed images
number = 10 # how many digits we will display
plt.figure(figsize=(20, 4))
for index in range(number):
# display original
ax = plt.subplot(2, number, index + 1)
plt.imshow(x_test_noisy[index].reshape(28, 28), cmap='gray')
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
# display reconstruction
ax = plt.subplot(2, number, index + 1 + number)
plt.imshow(tf.reshape(model(x_test_noisy)[index], (28, 28)), cmap='gray')
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
plt.show()Optional Exercise Construct a Sparse Autoencoder with Dense layer/s, train it on noisy images as before. See how the hidden dimensions influence the reconstruction. Which is one is better for denoising, the convolution Encoder/Decoder or Dense Encoder/Decoder, why?
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