Active Metric Learning for Supervised Classification

TL;DR

This paper introduces mixed-integer optimization techniques to learn optimal distance metrics for classification, removing reliance on predefined pairs, and enabling active learning to improve efficiency and accuracy.

Contribution

It develops a novel optimization-based framework for metric learning that generalizes existing Mahalanobis methods and incorporates active learning strategies.

Findings

Effective metric learning demonstrated on image and medical datasets.

Active learning reduces data collection costs and improves classification accuracy.

Method outperforms traditional approaches in computational efficiency.

Abstract

Clustering and classification critically rely on distance metrics that provide meaningful comparisons between data points. We present mixed-integer optimization approaches to find optimal distance metrics that generalize the Mahalanobis metric extensively studied in the literature. Additionally, we generalize and improve upon leading methods by removing reliance on pre-designated "target neighbors," "triplets," and "similarity pairs." Another salient feature of our method is its ability to enable active learning by recommending precise regions to sample after an optimal metric is computed to improve classification performance. This targeted acquisition can significantly reduce computational burden by ensuring training data completeness, representativeness, and economy. We demonstrate classification and computational performance of the algorithms through several simple and intuitive examples, followed by results on real image and medical datasets.