A power-based adaptive method for eigenanalysis without square-root operations

Abstract

This paper describes an adaptive eigenanalysis algorithm for estimating the eigenstructure of a sample covariance matrix. A minimization nonquadratic criterion is formulated by exploring the relationship of eigenvalues between the covariance matrix and its inverse matrix. A quasi-Newton approach is proposed to perform the task of minimization. It is shown that the new algorithm can be acted as another power method but without square-root operation. This approach is well-suited to parallel implementation when it is used for iterative estimation of multiple principal components by a deflation method. A unified modular architecture is developed for the analysis of both principal and minor components. Simulation experiments are carried out with both stationary and nonstationary data. The results show that the proposed method is capable of extracting multiple principal components in parallel with fast convergence speed and high tracking accuracy.