A Local-to-Global Metric Learning Framework From the Geometric Insight

Abstract

Metric plays a key role in the description of similarity between samples. An appropriate metric for data can well represent their distribution and further promote the performance of learning tasks. In this paper, to better describe the heterogeneous distributions of data, we propose a semi-supervised local-to-global metric learning framework from the geometric insight. Our contributions can be summarized as: Firstly, to enlarge the application scope of local metric learning, we introduce the unsupervised information as the regularization term into our smoothly glued nonlinear metric model. Secondly, we propose two different nonlinear semi-supervised metric learning models with two different loss terms, and find that the smooth loss performs better than the hinge loss by comparison results. Thirdly, we have established not only two metric learning models, but also a nonlinear metric learning framework based on local metrics, which includes supervised and semi-supervised as well as linear and nonlinear metric learning. Moreover, we present an intrinsic steepest descent algorithm on the positive definite manifold for implementation of our semi-supervised nonlinear metric learning models with smooth triplet constrain loss. Finally, we compare our approaches with several state-of-the-art methods on a variety of datasets. The results validate that the robustness and accuracy of classification are both improved under our metrics.

Keywords

• Local metric learning
• semi-supervised method
• partition of unity
• intrinsic steep descent method