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

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