Simultaneous extraction of Principal Components using givens rotations and output variances

Abstract

Principal Components Analysis (PCA) is an invaluable statistical tool in signal processing. In many cases, an on-line algorithm to adapt the PCA network to determine the principal projections in the input space is desired. Algorithms proposed until now use the traditional deflation or the inflation procedure to determine the intermediate components sequentially, after the convergence of the principal or minor component is achieved. In this paper, we propose a constrained linear network and a robust cost function to determine any number of principal components simultaneously. The topology exploits the fact that the eigenvector matrix sought is orthonormal. A gradient-based algorithm named SIPEX-G is also presented.