Scalable Large-Margin Mahalanobis Distance Metric Learning

TL;DR

This paper introduces a fast, scalable algorithm for learning Mahalanobis distance metrics that maximizes margin, improving efficiency and scalability while maintaining competitive classification accuracy.

Contribution

It presents a convex optimization-based, margin maximization approach with a specialized gradient descent method for scalable Mahalanobis metric learning.

Findings

Achieves comparable accuracy to state-of-the-art methods.

Significantly improves computational efficiency and scalability.

Effective on benchmark datasets.

Abstract

For many machine learning algorithms such as $k$-Nearest Neighbor ($k$-NN) classifiers and $ k $-means clustering, often their success heavily depends on the metric used to calculate distances between different data points. An effective solution for defining such a metric is to learn it from a set of labeled training samples. In this work, we propose a fast and scalable algorithm to learn a Mahalanobis distance metric. By employing the principle of margin maximization to achieve better generalization performances, this algorithm formulates the metric learning as a convex optimization problem and a positive semidefinite (psd) matrix is the unknown variable. a specialized gradient descent method is proposed. our algorithm is much more efficient and has a better performance in scalability compared with existing methods. Experiments on benchmark data sets suggest that, compared with state-of-the-art metric learning algorithms, our algorithm can achieve a comparable classification accuracy with reduced computational complexity.