Neural Learning on Grassman/Stiefel Principal/Minor Submanifold

摘要

This paper proposes a generalization of the recently proposed method that transforms known neural network PSA/MSA algorithms, into PCA/MCA algorithms. The method uses two distinct time scales. A given PSA/MSA algorithm is responsible, on a faster time scale, for the "behavior" of all output neurons. At this scale principal/minor subspace is obtained. On a slower time scale, output neurons compete to fulfill their "own interests". On this scale, basis vectors in the principal/minor subspace are rotated toward the principal/minor eigenvectors. Actually, time-oriented hierarchical method is proposed. Some simplified mathematical analysis, as well as simulation results, are presented.