An empirical study on the performance of spectral manifold learning techniques

Authors:
Peter Mysling;Søren Hauberg;Kim Steenstrup Pedersen
Affiliations:
The eScience Center, Dept. of Computer Science, University of Copenhagen, Copenhagen Ø, Denmark;The eScience Center, Dept. of Computer Science, University of Copenhagen, Copenhagen Ø, Denmark;The eScience Center, Dept. of Computer Science, University of Copenhagen, Copenhagen Ø, Denmark
Venue:
ICANN'11 Proceedings of the 21th international conference on Artificial neural networks - Volume Part I
Year:
2011

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Abstract

In recent years, there has been a surge of interest in spectral manifold learning techniques. Despite the interest, only little work has focused on the empirical behavior of these techniques. We construct synthetic data of variable complexity and observe the performance of the techniques as they are subjected to increasingly difficult problems. We evaluate performance in terms of both a classification and a regression task. Our study includes Isomap, LLE, Laplacian eigenmaps, and diffusion maps. Among others, our results indicate that the techniques are highly dependent on data density, sensitive to scaling, and greatly influenced by intrinsic dimensionality.