Local Procrustes for Manifold Embedding: A Measure of Embedding Quality and Embedding Algorithms
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.
Cite
Text
Goldberg and Ritov. "Local Procrustes for Manifold Embedding: A Measure of Embedding Quality and Embedding Algorithms." Machine Learning, 2009. doi:10.1007/S10994-009-5107-9Markdown
[Goldberg and Ritov. "Local Procrustes for Manifold Embedding: A Measure of Embedding Quality and Embedding Algorithms." Machine Learning, 2009.](https://mlanthology.org/mlj/2009/goldberg2009mlj-local/) doi:10.1007/S10994-009-5107-9BibTeX
@article{goldberg2009mlj-local,
title = {{Local Procrustes for Manifold Embedding: A Measure of Embedding Quality and Embedding Algorithms}},
author = {Goldberg, Yair and Ritov, Yaacov},
journal = {Machine Learning},
year = {2009},
pages = {1-25},
doi = {10.1007/S10994-009-5107-9},
volume = {77},
url = {https://mlanthology.org/mlj/2009/goldberg2009mlj-local/}
}