Supervised Dimension Reduction of Intrinsically Low-Dimensional Data
- 1 January 2002
- journal article
- Published by MIT Press in Neural Computation
- Vol. 14 (1) , 191-215
- https://doi.org/10.1162/089976602753284491
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.Keywords
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