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

Yair Goldberg; Ya'Acov Ritov

doi:10.1007/s10994-009-5107-9

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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1-25
Number of pages	25
Journal	Machine Learning
Volume	77
Issue number	1
DOIs	https://doi.org/10.1007/s10994-009-5107-9
State	Published - Oct 2009
Externally published	Yes

Bibliographical note

Funding Information:
Acknowledgements We would like to thank S. Kirkpatrick and J. Goldberger for meaningful discussions. We are grateful to the anonymous reviewers of various versions of this manuscript for their helpful suggestions. We thank J. Hamm for providing the database of globe images. This research was supported in part by Israeli Science Foundation grant.

Keywords

Dimension reducing
Local PCA
Manifold learning
Procrustes analysis
Simulated annealing

ASJC Scopus subject areas

Software
Artificial Intelligence

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10.1007/s10994-009-5107-9

Cite this

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N2 - 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.

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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