Autoencoders are trained using a local unsupervised criterion (Vincent et al., 2010;Hinton and Salakhutdinov, 2006;Vincent et al., 2008).
the basic autoencoder in Figure 1(a) locally optimizes the hidden representation h of its input x such that h can be used to accurately reconstruct x, wherex is the reconstruction of x, the learning parameters W ∈ R d ×d and W ∈ R d×d are weight matrices, b h ∈ R d and bx ∈ R d are bias vectors for the hidden and output layers respectively, and g is a nonlinear function such as tanh(.).