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, 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.