Neural networks for extracting Unsymmetric Principal Components

In this paper we introduce two forms of Unsymmetric Principal Component Analysis (UPCA), namely the cross-correlation UPCA and the linear approximation UPCA problem. Both are concerned with the SVD of the input-teacher crosscorrelation matrix itself (first problem) or after prewhitening (second problem). The second problem is also equivalent to reduced-rank Wiener filtering. For the former problem, we propose an unsymmetric linear model for extracting one or more components using lateral inhibition connections in the hidden layer. The numerical convergence properties of the model are theoretically established. For the linear approximation UPCA problem, we can apply Back-Propagation extended either using a straightforward deflation procedure or with the use of lateral orthogonalizing connections in the hidden layer. All proposed models were tested and the simulation results confirm the theoretical expectations.