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Paper details
Number 1 - March 2001
Volume 11 - 2001
Convergence analysis for principal component flows
Shintaro Yoshizawa, Uwe Helmke, Konstantin Starkov
Abstract
A common framework for analyzing the global convergence of several flows for principal component analysis is developed. It is shown that flows proposed by Brockett, Oja, Xu and others are all gradient flows and the global convergence of these flows to single equilibrium points is established. The signature of the Hessian at each critical point is determined.
NOTE: Corrections to the paper were published in 2002, Vol. 12, No. 2.
Keywords
principal component analysis, neural networks, gradient flows, phase portrait, Hessians