Constrained projection approximation algorithms for principal component analysis

Abstract

In this paper, we introduce a new error measure, integrated reconstruction error (IRE) and show that the minimization of IRE leads to principal eigenvectors (without rotational ambiguity) of the data covariance matrix. Then, we present iterative algorithms for the IRE minimization, where we use the projection approximation. The proposed algorithm is referred to as COnstrained Projection Approximation (COPA) algorithm and its limiting case is called COPAL. Numerical experiments demonstrate that these algorithms successfully find exact principal eigenvectors of the data covariance matrix.