Positive Semidefinite Metric Learning with Boosting

TL;DR

This paper introduces oostmetric, a scalable boosting-based method for learning Mahalanobis distance metrics that maintains positive semidefiniteness efficiently, improving classification accuracy and computational speed.

Contribution

It proposes a novel boosting approach using rank-one positive semidefinite matrices as weak learners for metric learning, avoiding complex semidefinite programming.

Findings

Outperforms state-of-the-art methods in accuracy

Runs faster than existing approaches

Easily accommodates various constraints

Abstract

The learning of appropriate distance metrics is a critical problem in image classification and retrieval. In this work, we propose a boosting-based technique, termed \BoostMetric, for learning a Mahalanobis distance metric. One of the primary difficulties in learning such a metric is to ensure that the Mahalanobis matrix remains positive semidefinite. Semidefinite programming is sometimes used to enforce this constraint, but does not scale well. \BoostMetric is instead based on a key observation that any positive semidefinite matrix can be decomposed into a linear positive combination of trace-one rank-one matrices. \BoostMetric thus uses rank-one positive semidefinite matrices as weak learners within an efficient and scalable boosting-based learning process. The resulting method is easy to implement, does not require tuning, and can accommodate various types of constraints. Experiments on various datasets show that the proposed algorithm compares favorably to those state-of-the-art methods in terms of classification accuracy and running time.