Dimensionality Reduction on the Cartesian Product of Embeddings of Multiple Dissimilarity Matrices

We consider the problem of combining multiple dissimilarity representations via the Cartesian product of their embeddings. For concreteness, we choose the inferential task at hand to be classification. The high dimensionality of this Cartesian product space implies the necessity of dimensionality reduction before training a classifier. We propose a supervised dimensionality reduction method, which utilizes the class label information, to help achieve a favorable combination. The simulation and real data results show that our approach can improve classification accuracy compared to the alternatives of principal components analysis and no dimensionality reduction at all.