Supervised dimension reduction of intrinsically low-dimensional data

Authors:
Nikos Vlassis;Yoichi Motomura;Ben Kröse
Affiliations:
RWCP, Autonomous Learning Functions SNN, University of Amsterdam, The Netherlands;Electrotechnical Laboratory, Tsukuba Ibaraki 305-8568, Umezono 1-1-4, Japan;RWCP, Autonomous Learning Functions SNN, University of Amsterdam, The Netherlands
Venue:
Neural Computation
Year:
2002

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Abstract

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.