Deep learning recently becomes such a hot topic across both academic and industry area. Guess the best way to learn some stuff is to implement them. So I checked the recent tutorial posted at
ACL 2012 + NAACL 2013 Tutorial: Deep Learning for NLP (without Magic)
There are two main parts for an autoencoder: feedforward and backpropagation. The essential thing needs to be calculated is the “error term”, because it is going to decide the partial derivatives for parameters including both W and the bias term b.
You can think of autoencoder as an unsupervised learning algorithm, that sets the target value to be equal to the inputs. But why so, or that is, then why bother to reconstruct the signal? The trick is actually in the hidden layers, where small number of nodes are used (smaller than the dimension of the input data — the sparsity enforced to the hidden layer). So you may see autoencoder has this ‘vase’ shape.
Thus, the network will be forced to learn a compressed representation of the input. You can think it of learning some intrinsic structures of the data, that is concise, analog to the PCA representation, where data can be represented by few axis. To enforce such sparsity, the average activation value ( averaged across all training samples) for each node in the hidden layer is forced to equal to a small value close to zero (called sparsity parameters) . For every node, a KL divergence between the ‘expected value of activation’ and the ‘activation from training data’ is computed, and adding to both cost function and derivatives which helps to update the parameters (W & b).
After learning completed, the weights represent the signals ( think of certain abstraction or atoms) that unsupervised learned from the data, like below: