Recursive PCA and the structure of time series

A recurrent linear network can be trained with Oja´s constrained Hebbian learning rule. As a result, the network learns to represent the temporal context associated to its input sequence. The operation performed by the network is a generalization of principal components analysis (PCA) to time-series, called recursive PCA. During learning, the weights of the network are adapted to the temporal statistics of its input, in a way that maximizes the information retained by the network. Sequences stored in the network may be retrieved in the reverse order of presentation, thus providing a straight-forward implementation of a logical stack.