The Bilipschitz criterion for dimension reduction mapping design

Authors:
Markus Anderle;Douglas R. Hundley;Michael J. Kirby
Affiliations:
Department of Mathematics, Colorado State University, Fort Collins, CO 80523, USA;Department of Mathematics, Whitman College, Walla Walla, WA 99362, USA;Department of Mathematics, Whitman College, Walla Walla, WA 99362, USA
Venue:
Intelligent Data Analysis
Year:
2002

Citing 6
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Abstract

We present a graphical method for evaluating the quality of a feature extraction mapping. Based on the Bilipschitz criterion, this Bilipschitz Criterion Plot (BCP) can be used to evaluate dimension reducing mappings for relative quality and to estimate the injectivity of the reduction map (as well as the associated reconstruction map). It can also be used to survey regions where the map is locally an expansion or contraction map. The plot is easy and fast to construct, and gives much more insight than any single value can, such as the distance preservation error. We demonstrate the value of such a mapping when examining the quality of the Sammon map, Neuroscale, the autoassociative map, and a recent technique that is designed to optimize the BCP in a linear fashion, the adaptive secant basis algorithm.