 
Summary: Proceedings of MTNS 2004, Leuven, Belgium
Continuoustime flows on quotient spaces
for principal component analysis
P.A. Absil
Abstract
A novel matrix flow for principal or minor component analysis is
constructed. The development is based on decompositions of the
set of fullrank n × p matrices into orbits of Lie group actions.
Key words. Principal component analysis, principal subspace analysis, minor component
analysis, continuoustime matrix flows, quotient spaces, Lie group actions, semidefinite Lya
punov functions, leftmost and rightmost eigenspaces.
1 Introduction
Given a symmetric matrix A, a flow on Rn×p
is said to have principal subspace analysis (PSA)
properties if the column space of the solution converges to the pdimensional eigenspace of
A associated with the largest eigenvalues. If moreover the columns of the solution converge
to the p principal eigenvectors of A, i.e. those corresponding to the largest eigenvalues, then
the flow is said to achieve principal component analysis (PCA).
Several continuoustime dynamical systems on matrix spaces (also called matrix flows)
have been proposed in the literature that achieve PSA or even PCA. Interest for study
