I don't understand how convolutional autoencoders achieve dimensionality reduction. For FFNN based autoencoder, the reduction is easy to understand: the input layer has N neurons, and the hidden ones have M neurons, where N is greater than M. Instead, in a convolutional autoencoder, the input image is wide and thin, and it becomes small and thick. It results in an amount of information that is greater than the initial ones.
I report a practical example to explain better what I mean:
# INPUT: 28 x 28 x 1 (wide and thin) conv1 = Conv2D(32, (3, 3), activation='relu', padding='same')(input_img) #28 x 28 x 32 pool1 = MaxPooling2D(pool_size=(2, 2))(conv1) #14 x 14 x 32 conv2 = Conv2D(64, (3, 3), activation='relu', padding='same')(pool1) #14 x 14 x 64 pool2 = MaxPooling2D(pool_size=(2, 2))(conv2) #7 x 7 x 64 conv3 = Conv2D(128, (3, 3), activation='relu', padding='same')(pool2) # OUTPUT: 7 x 7 x 128 (small and thick)
In this example, we start from a 28x28 single-channel image (784), and the encoder output will be 7x7x128 (6272). Is this a dimension reduction?