UNIT: A unified metric learning framework based on maximum entropy regularization

doi:10.1007/s10489-023-04831-x

2023-07-26

PRE

邓惠元 (Huiyuan Deng)

Fengxia Deng

Lin Feng *

DOI：10.1007/s10489-023-04831-x

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摘要

En 中文

Metric learning has emerged as a critical tool for analyzing the semantic similarities between objects. However, numerous existing methods are incapable of simultaneously maximizing the proximity of similar pairs and the separability between dissimilar ones to achieve the largest margin principle. Additionally, most graph Laplacian-based semi-supervised approaches fail to consider the valuable dissimilar information of unlabeled data, and they treat neighborhood graph construction and metric learning as separate procedures, thereby breaking the unified relationship between these two components. To overcome these challenges, this paper proposes a scalable and efficient metric learning framework called Unified metric learNing based on maxIum enTropy (UNIT). UNIT attempts to unify supervised and semi-supervised metric learning into a framework by introducing the maximum entropy regularizer of the eigenvalues of the learned matrix. With the novel regularizer, UNIT can maximize the closeness of similar instances and the separability of dissimilar ones without encountering the trivial solution problem. Furthermore, the adaptive graph Laplacian, formulated by a similar graph as well as a dissimilar graph, is constructed to mine the rich discriminant information of the unlabeled data. We demonstrate that UNIT can be solved efficiently with the alternating direction method, with each sub-problem being solvable using a closed-form solution. To account for nonlinear data distribution, a kernelized version of UNIT is also provided. The effectiveness of the proposed methods is validated through extensive supervised and semi-supervised experiments on various datasets.

Keyword:

Metric learning

Kernel learning

Nearest-neighbors classification

Semi-supervised learning

Maximum entropy principle