J Austral Math Soc Ser B 37 pp430--450, 1996.

Gradient algorithms for principal component analysis

R. E. Mahony, U. Helmke and J. B. Moore

Abstract

The problem of principal component analysis of a symmetric matrix (finding a p-dimensional eigenspace associated with the largest p eigenvalues) can be viewed as a smooth optimization problem on a homogeneous space. A solution in terms of the limiting value of a continuous-time dynamical system is presented. A discretization of the dynamical system is proposed that exploits the geometry of the homogeneous space. The relationship between the proposed algorithm and classical methods are investigated.

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Authors

R. E. Mahony

J. B. Moore

Dept of Systems Eng, Research School of Phys. Sciences and Eng, ANU, Canberra ACT 0200.

U. Helmke

Dept of Mathematics, University of Regensburg, 8400 Regensburg, F.R.G.