An outer product neural network for extracting principal components from a time series

Abstract

An outer product neural network architecture has been developed based on subspace concepts. The network is trained by auto-encoding the input exemplars, and will represent the input signal by k-principal components, k being the number of neurons or processing elements in the network. The network is essentially a single linear layer. The weight matrix columns orthonormalize during training. The output signal converges to the projection of the input onto a k-principal component subspace, while the residual signal represents the novelty of the input. An application to extracting sinusoids from a noisy time series is given.<>