Mixture correntropy-based robust distance metric learning for classification

Metric learning is a branch of machine learning that aims to learn from the given training data a valid distance metric, with which the similarity between samples can be more effectively evaluated for classification. Metric learning has attracted significant attention, and a large number of models have been proposed in the past few years. However, the traditional methods adopt hinge loss which easily leads to noise sensitivity and instability. In this paper, to improve the robustness performance, we develop a mixture correntropy criterion where two Laplacian kernel functions are combined as the kernel function and induce a more general nonconvex robust loss function by the mixture correntropy. The properties related to the loss function are analysed and presented. The induced loss amalgamates the superiors of the state-of-the-art robust loss functions and is more effective. With this induced loss, we establish a robust metric learning model (called MCML) and design an effective iterative algorithm to optimize the nonconvex challenging problem. The computational complexity and convergence of algorithm are discussed in theory. Furthermore, a boosting version of MCML (BMCML) is derived, where the low -rank basis learning is jointly optimized with the metric to better uncover the data structure. Finally, extensive experiments are conducted on artificial datasets, UCI benchmark datasets and image datasets. The experimental results verify the robustness and effectiveness of the proposed methods.