Parametric Local Metric Learning for Nearest Neighbor Classification

TL;DR

This paper introduces a parametric local metric learning method that learns smooth, data manifold-aware metrics for improved nearest neighbor classification, demonstrating superior performance on large-scale datasets.

Contribution

It proposes a novel parametric approach to local metric learning using basis metrics and manifold regularization, reducing overfitting and enhancing scalability.

Findings

Outperforms state-of-the-art metric learning methods on large datasets

Achieves high predictive accuracy and scalability

Effectively models smooth metric variations along data manifolds

Abstract

We study the problem of learning local metrics for nearest neighbor classification. Most previous works on local metric learning learn a number of local unrelated metrics. While this "independence" approach delivers an increased flexibility its downside is the considerable risk of overfitting. We present a new parametric local metric learning method in which we learn a smooth metric matrix function over the data manifold. Using an approximation error bound of the metric matrix function we learn local metrics as linear combinations of basis metrics defined on anchor points over different regions of the instance space. We constrain the metric matrix function by imposing on the linear combinations manifold regularization which makes the learned metric matrix function vary smoothly along the geodesics of the data manifold. Our metric learning method has excellent performance both in terms of predictive power and scalability. We experimented with several large-scale classification problems, tens of thousands of instances, and compared it with several state of the art metric learning methods, both global and local, as well as to SVM with automatic kernel selection, all of which it outperforms in a significant manner.