Geometric Mean Metric Learning

TL;DR

This paper introduces a simple, closed-form solution for learning Euclidean metrics from data, leveraging Riemannian geometry, which outperforms existing methods in speed and accuracy on benchmark datasets.

Contribution

It presents a novel, geometrically motivated formulation of metric learning that admits a closed-form solution, enhancing interpretability and computational efficiency.

Findings

Achieves higher classification accuracy than LMNN and ITML.

Significantly faster computation than existing metric learning methods.

Provides a geometrically appealing and interpretable solution.

Abstract

We revisit the task of learning a Euclidean metric from data. We approach this problem from first principles and formulate it as a surprisingly simple optimization problem. Indeed, our formulation even admits a closed form solution. This solution possesses several very attractive properties: (i) an innate geometric appeal through the Riemannian geometry of positive definite matrices; (ii) ease of interpretability; and (iii) computational speed several orders of magnitude faster than the widely used LMNN and ITML methods. Furthermore, on standard benchmark datasets, our closed-form solution consistently attains higher classification accuracy.