Orthogonal learning network for constrained principal component problem

The regular principal components (PC) analysis of stochastic processes is extended to the constrained principal components (CPC) problem. As in the PC analysis, the CPC analysis involves extracting representative components which contain the most information about the original processes. In contrast to the PC problem, the CPC solution has to be extracted from a given constraint subspace. Therefore, the CPC solution may be adopted to best recover the original signal and simultaneously avoid the undesirable noisy or redundant components. This is very appealing in many practical applications, e.g., motion or still-image data compression, high-resolution (antijamming) spectrum analysis, NMR, etc. A technique is proposed for finding optimal CPC solutions with an orthogonal learning network (OLN). The underlying numerical analysis for the theoretical proof of the convergency of OLN is discussed. As a byproduct, the same numerical analysis also provides a useful estimate of optimal learning rates, leading to very fast convergence speed. Simulation and application examples are provided.