Generalized subspace rules for on-line PCA and their application in signal and image compression

Weighted subspace (WS) algorithms developed by Oja and Xu for PCA are unified into generalized forms and theoretically analyzed. It is then proved that the generalized rules are stable at only the fixed point where the principal components are extracted. We moreover find the optimal parameter in terms of the preservation of orthogonality of estimated principal components during tracking. To understand the theoretical behavior, then, toy numerical examples are shown. Moreover, a possibility for the application of adaptive data compression is discussed, by showing examples of backward adaptation image coding.