A Unified Scheme for Distance Metric Learning and Clustering via Rank-Reduced Regression

Abstract

Distance metric learning aims to learn a positive semidefinite matrix such that similar samples are preserved with small distances while dissimilar ones are mapped with big values above a predefined margin. It can facilitate to improve the performance of certain learning tasks. In this article, distance metric learning and clustering are integrated into an unified framework via rank-reduced regression. First, distance metric learning is proved to be consistent with rank-reduced regression, which provides a new perspective to learn structured regularization matrices. Second, orthogonal and non-negative rank-reduced regression problems are addressed individually for clustering, and the corresponding algorithms with proved convergence are proposed. Finally, both distance metric learning and clustering are addressed simultaneously in the problem formulation, which may trigger some new insights for learning an effective clustering oriented low-dimensional embedding. To show the superior performance of the proposed method, we compare it with several state-of-the-art clustering approaches. And, extensive experiments on the test datasets demonstrate the superiority of the proposed method.