Constrained Projection Approximation Algorithms for Principal Component Analysis

Authors:
Seungjin Choi;Jong-Hoon Ahn;Andrzej Cichocki
Affiliations:
Department of Computer Science, Pohang University of Science and Technology, Nam-gu, Korea 790-784;Department of Physics, Pohang University of Science and Technology, Nam-gu, Korea 790-784;Advanced Brain Signal Processing Lab, Brain Science Institute, RIKEN, Wako-shi, Japan 351-0198
Venue:
Neural Processing Letters
Year:
2006

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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.