Supervised Dimension Reduction of Intrinsically Low-Dimensional Data
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.
Cite
Text
Vlassis et al. "Supervised Dimension Reduction of Intrinsically Low-Dimensional Data." Neural Computation, 2002. doi:10.1162/089976602753284491Markdown
[Vlassis et al. "Supervised Dimension Reduction of Intrinsically Low-Dimensional Data." Neural Computation, 2002.](https://mlanthology.org/neco/2002/vlassis2002neco-supervised/) doi:10.1162/089976602753284491BibTeX
@article{vlassis2002neco-supervised,
title = {{Supervised Dimension Reduction of Intrinsically Low-Dimensional Data}},
author = {Vlassis, Nikos and Motomura, Yoichi and Kröse, Ben J. A.},
journal = {Neural Computation},
year = {2002},
pages = {191-215},
doi = {10.1162/089976602753284491},
volume = {14},
url = {https://mlanthology.org/neco/2002/vlassis2002neco-supervised/}
}