Local procrustes for manifold embedding: a measure of embedding quality and embedding algorithms

Authors:
Yair Goldberg;Ya'Acov Ritov
Affiliations:
Department of Statistics and The Center for the Study of Rationality, The Hebrew University, Jerusalem, Israel 91905;Department of Statistics and The Center for the Study of Rationality, The Hebrew University, Jerusalem, Israel 91905
Venue:
Machine Learning
Year:
2009

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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, Science 290(5500), 2323---2326, 2000) and Isomap (Tenenbaum et al., Science 290(5500), 2319---2323, 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.