Local procrustes for manifold embedding: a measure of embedding quality and embedding algorithms
Copyright policy )Local procrustes for manifold embedding: a measure of embedding quality and embedding algorithms
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.
Submitted to Journal of Machine Learning
- The Hebrew University Israel
- Hebrew University of Jerusalem Israel
FOS: Computer and information sciences, Procrustes analysis, Statistics - Machine Learning, manifold learning, local PCA, Learning and adaptive systems in artificial intelligence, Machine Learning (stat.ML), simulated annealing, Factor analysis and principal components; correspondence analysis, dimension reducing, Statistics on manifolds
FOS: Computer and information sciences, Procrustes analysis, Statistics - Machine Learning, manifold learning, local PCA, Learning and adaptive systems in artificial intelligence, Machine Learning (stat.ML), simulated annealing, Factor analysis and principal components; correspondence analysis, dimension reducing, Statistics on manifolds
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