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- Title
Local procrustes for manifold embedding: a measure of embedding quality and embedding algorithms.
- Authors
Goldberg, Yair; Ritov, Ya'acov
- 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, ) and Isomap (Tenenbaum et al., Science 290(5500), 2319–2323, ). 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.
- Subjects
ALGORITHMS; EMBEDDINGS (Mathematics); FOUNDATIONS of arithmetic; MACHINE learning; ALGEBRA
- Publication
Machine Learning, 2009, Vol 77, Issue 1, p1
- ISSN
0885-6125
- Publication type
Article
- DOI
10.1007/s10994-009-5107-9