Iterative Projection Approximation Algorithms for PCA

In this paper we introduce a new error measure, integrated reconstruction error (IRE), the minimization of which leads to principal eigenvectors (without rotational ambiguity) of the data covariance matrix. Then we present iterative algorithms for the IRE minimization, through the projection approximation. The proposed algorithm is referred to as constrained projection approximation (COPA) algorithm and its limiting case is called COPAL. We also discuss regularized algorithms, referred to as R-COPA and R-COPAL. Numerical experiments demonstrate that these algorithms successfully find exact principal eigenvectors of the data covariance matrix