Local Procrustes for Manifold Embedding: A Measure of Embedding Quality and Embedding Algorithms

2008/06/16 by Y. Goldberg, Goldberg, Y., Y. Ritov +1
Mathematics · #FOS: Computer and information sciences #Machine Learning (stat.ML) #stat.ML

paper · pdf · doi:10.48550/arxiv.0806.2669

Submitted to Journal of Machine Learning

arxiv created 2008/06/16 · arxiv updated 2009/12/01

Abstract

We present the Procrustes measure, a novel measure based on Procrustes rotation that enables quantitative comparison of the output of manifold-based embedding algorithms (such as LLE (Roweis and Saul, 2000) and Isomap (Tenenbaum et al, 2000)). The measure also serves as a natural tool when choosing dimension-reduction parameters. We also present two novel dimension-reduction techniques that attempt to minimize the suggested measure, and compare the results of these techniques to the results of existing algorithms. Finally, we suggest a simple iterative method that can be used to improve the output of existing algorithms.

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