Correntropy based robust multidimensional scaling applied to faces

Here, we are interested in obtaining a two-dimensional embedding of face-pose images that preserves their local structure captured by the pair-wise distances among them by using multidimensional scaling (MDS). The MDS problem is formulated as maximization of a correntropy criterion, which is solved by half-quadratic optimization in a multiplicative formulation. By doing so, theMDS copes with an initial dissimilarity matrix contaminated with outliers, because the correntropy criterion is closely related to the Welsch M-estimator. The proposed algorithm is coined as Multiplicative Half-Quadratic MDS (MHQMDS). Its performance is assessed for potential functions associated to various M-estimators have been tested. 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, outperforms the aforementioned state-of-the-art competing techniques.