Nonrigid Embeddings for Dimensionality Reduction

Spectral methods for embedding graphs and immersing data manifolds in low-dimensional speaces are notoriously unstable due to insufficient and/or numberically ill-conditioned constraint sets. Why show shy this is endemic to spectral methods, and develop low-complexity solutions for stiffening ill-conditioned problems and regulatizing ill-posed problems, with proofs of correctness. The regularization exploits sparse but complementary constraints on affine rigidity and edge lengths to obtain isometric embeddings. Am implemented algorithm is fast, accurate and industrial-strength: Experiments with problem sizes spanning four orders of magnitude show O (N) scaling. We demonstrate with speech data. European Conference on Machine Learning (ECML) This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or par...

• Type: Conference
• Year: 2005
• Where: ECML
• Authors: Matthew Brand
• Keywords: ECML 2005, Electric Research Laboratories, Mitsubishi Electric Research, Spectral Methods