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Supervised Dimension Reduction of Intrinsically Low-Dimensional Data

vlassis{at}science.uva.nl, RWCP, Autonomous Learning Functions SNN, University of Amsterdam, The Netherlands

Yoichi Motomura

motomura{at}etl.go.jp, Electrotechnical Laboratory, Tsukuba Ibaraki 305-8568, Umezono 1-1-4, Japan

Ben Kröse

krose{at}science.uva.nl, RWCP, Autonomous Learning Functions SNN, University of Amsterdam, The Netherlands

High-dimensional data generated by a system with limited degrees of freedom are often constrained in low-dimensional manifolds in the original space. In this article, we investigate dimension-reduction methods for such intrinsically low-dimensional data through linear projections that preserve the manifold structure of the data. For intrinsically one-dimensional data, this implies projecting to a curve on the plane with as few intersections as possible. We are proposing a supervised projection pursuit method that can be regarded as an extension of the single-index model for nonparametric regression. We show results from a toy and two robotic applications.

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				S. Vijayakumar, A. D'Souza, and S. Schaal Incremental Online Learning in High Dimensions Neural Comput., December 1, 2005; 17(12): 2602 - 2634. [Abstract] [Full Text] [PDF]