Classification with mixtures of curved mahalanobis metrics

We study the classification with respect to the class of curved Mahalanobis metrics that extend the celebrated flat Mahalanobis distances to constant curvature spaces. We prove that these curved Mahalanobis k-NN classifiers define piecewise linear decision boundaries, and report the performance of learning those metrics within the framework of the Large Margin Nearest Neighbor (LMNN). Finally, we show experimentally that a mixture of curved Mahalanobis metrics define a composite metric distance that improves the classification performance.