A fast, on-line algorithm for PCA and its convergence characteristics

Abstract

Eigendecompositions play a very important role in a variety of signal processing applications. We derive and study an algorithm for principal component analysis (PCA) which is both online and fast converging and which has been presented earlier as a heuristic alternative to the power method. A rule to extract the maximum eigencomponent is first presented, and then online deflation is applied to estimate the minor components. The algorithm is compared with the traditional Sanger's rule through simulations. The convergence properties of the algorithm are explored thoroughly and we present a complete proof explaining the behavior of the algorithm.