Constrained principal component analysis via an orthogonal learning network

The regular principal components (PC) analysis of stochastic processes is extended to the so-called constrained principal components (CPC) problem. The CPC analysis involves extracting representative components which contain the most information about the original processes. 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 undesirably noisy or redundant components. A technique for finding optimal CPC solutions via an orthogonal learning network (OLN) is proposed. The underlying numerical analysis for the theoretical proof of the convergency of OLN is discussed. The same numerical analysis provides a useful estimate of optimal learning rates leading to very fast convergence speed. Simulation and application examples are provided.