Robust Multidimensional Scaling Using a Maximum Correntropy Criterion

Abstract

Multidimensional scaling (MDS) refers to a class of dimensionality reduction techniques, which represent entities as points in a low-dimensional space so that the interpoint distances approximate the initial pairwise dissimilarities between entities as closely as possible. The traditional methods for solving MDS are susceptible to outliers. Here, a unified framework is proposed, where the MDS is treated as maximization of a correntropy criterion, which is solved by half-quadratic optimization in either multiplicative or additive forms. By doing so, MDS can cope with an initial dissimilarity matrix contaminated with outliers because the correntropy criterion is closely related to $M$ -estimators. Three novel algorithms are derived. Their performances are assessed experimentally against three state-of-the-art MDS techniques, namely the scaling by majorizing a complicated function, the robust Euclidean embedding, and the robust MDS under the same conditions. The experimental results indicate that the proposed algorithms perform substantially better than the aforementioned competing techniques.