Distance Metric Learning through Minimization of the Free Energy

TL;DR

This paper introduces a novel distance metric learning method inspired by statistical physics, formulating the problem as free energy minimization and using Monte Carlo techniques, outperforming existing methods in classification tasks.

Contribution

The paper presents a physics-inspired approach to distance metric learning using free energy minimization and Monte Carlo optimization, handling complex constraints effectively.

Findings

Outperforms state-of-the-art metric learning methods in classification accuracy.

Effective on both artificial and real-world datasets.

Handles constraints with spurious local minima efficiently.

Abstract

Distance metric learning has attracted a lot of interest for solving machine learning and pattern recognition problems over the last decades. In this work we present a simple approach based on concepts from statistical physics to learn optimal distance metric for a given problem. We formulate the task as a typical statistical physics problem: distances between patterns represent constituents of a physical system and the objective function corresponds to energy. Then we express the problem as a minimization of the free energy of a complex system, which is equivalent to distance metric learning. Much like for many problems in physics, we propose an approach based on Metropolis Monte Carlo to find the best distance metric. This provides a natural way to learn the distance metric, where the learning process can be intuitively seen as stretching and rotating the metric space until some heuristic is satisfied. Our proposed method can handle a wide variety of constraints including those with spurious local minima. The approach works surprisingly well with stochastic nearest neighbors from neighborhood component analysis (NCA). Experimental results on artificial and real-world data sets reveal a clear superiority over a number of state-of-the-art distance metric learning methods for nearest neighbors classification.