Information-theoretic metric learning

In this paper, we present an information-theoretic approach to learning a Mahalanobis distance function. We formulate the problem as that of minimizing the differential relative entropy between two multivariate Gaussians under constraints on the distance function. We express this problem as a particular Bregman optimization problem--that of minimizing the LogDet divergence subject to linear constraints. Our resulting algorithm has several advantages over existing methods. First, our method can handle a wide variety of constraints and can optionally incorporate a prior on the distance function. Second, it is fast and scalable. Unlike most existing methods, no eigenvalue computations or semi-definite programming are required. We also present an online version and derive regret bounds for the resulting algorithm. Finally, we evaluate our method on a recent error reporting system for software called Clarify, in the context of metric learning for nearest neighbor classification, as well as...

• Type: Conference
• Year: 2007
• Where: ICML
• Authors: Jason V. Davis, Brian Kulis, Prateek Jain, Suvrit Sra, Inderjit S. Dhillon
• Keywords: ICML 2007, Machine Learning, Mahalanobis Distance Function, Nearest Neighbor Classification, Particular Bregman Optimization