OPML: A One-Pass Closed-Form Solution for Online Metric Learning

TL;DR

This paper introduces OPML, a low-cost online metric learning method with a one-pass closed-form solution, and an extension COPML for improved robustness, validated across various large-scale tasks with promising results.

Contribution

The paper proposes OPML, a novel one-pass closed-form solution for online metric learning, and COPML, an extension enhancing robustness in cold start scenarios.

Findings

OPML achieves low computational complexity in large-scale data.

COPML improves robustness during cold start conditions.

Both methods perform well across classification, verification, and detection tasks.

Abstract

To achieve a low computational cost when performing online metric learning for large-scale data, we present a one-pass closed-form solution namely OPML in this paper. Typically, the proposed OPML first adopts a one-pass triplet construction strategy, which aims to use only a very small number of triplets to approximate the representation ability of whole original triplets obtained by batch-manner methods. Then, OPML employs a closed-form solution to update the metric for new coming samples, which leads to a low space (i.e., $O(d)$) and time (i.e., $O(d^2)$) complexity, where $d$ is the feature dimensionality. In addition, an extension of OPML (namely COPML) is further proposed to enhance the robustness when in real case the first several samples come from the same class (i.e., cold start problem). In the experiments, we have systematically evaluated our methods (OPML and COPML) on three typical tasks, including UCI data classification, face verification, and abnormal event detection in videos, which aims to fully evaluate the proposed methods on different sample number, different feature dimensionalities and different feature extraction ways (i.e., hand-crafted and deeply-learned). The results show that OPML and COPML can obtain the promising performance with a very low computational cost. Also, the effectiveness of COPML under the cold start setting is experimentally verified.