A maximum correntropy criterion for robust multidimensional scaling

Abstract

Multidimensional Scaling (MDS) refers to a class of dimensionality reduction techniques applied to pairwise dissimilarities between objects, so that the interpoint distances in the space of reduced dimensions approximate the initial pairwise dissimilarities as closely as possible. 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 a multiplicative formulation. The proposed algorithm is coined as Multiplicative Half-Quadratic MDS (MHQMDS). Its performance is assessed for potential functions associated to various M-estimators, because the correntropy criterion is closely related to the Welsch M-estimator. Three state-of-the-art MDS techniques, namely the Scaling by Majorizing a Complicated Function (SMACOF), the Robust Euclidean Embedding (REE), and the Robust MDS (RMDS), are implemented under the same conditions. The experimental results indicate that the MHQMDS, relying on the M-estimators, performs better than the aforementioned state-of-the-art competing techniques.