Robust Euclidean embedding

We derive a robust Euclidean embedding procedure based on semidefinite programming that may be used in place of the popular classical multidimensional scaling (cMDS) algorithm. We motivate this algorithm by arguing that cMDS is not particularly robust and has several other deficiencies. Generalpurpose semidefinite programming solvers are too memory intensive for medium to large sized applications, so we also describe a fast subgradient-based implementation of the robust algorithm. Additionally, since cMDS is often used for dimensionality reduction, we provide an in-depth look at reducing dimensionality with embedding procedures. In particular, we show that it is NP-hard to find optimal low-dimensional embeddings under a variety of cost functions.

• Type: Conference
• Year: 2006
• Where: ICML
• Authors: Lawrence Cayton, Sanjoy Dasgupta
• Keywords: Euclidean Embedding Procedure, ICML 2006, Machine Learning, Robust Algorithm, Semidefinite Programming Solvers