基于约束分层加权的多度量学习算法

doi:10.6040/j.issn.1671-9352.7.2021.149

摘要/Abstract

摘要： 为解决经典的多度量学习算法从预先获得的样本划分中学习度量时,样本划分不精确所导致局部度量拟合能力不足的问题,基于约束分层加权的思想,提出了为约束逐层分配度量并使其度量尽可能满足当前所有约束的优化模型,同时添加正则项使得不同度量对应的约束应该尽可能不同。由于单个样本所形成的不同约束可能对应不同的局部度量,相比于传统的多度量学习方法,提出的算法能够获得更精细的局部度量且更具有灵活性,使得度量的拟合能力更强。实验结果表明,提出的算法在真实数据集上对比代表性的单度量学习算法和多度量学习算法具有明显的优势。

关键词: 度量学习, 约束加权, 马氏距离, 三元约束, 多度量学习

Abstract: In order to solve the problem of insufficient local metric fitting ability caused by inaccurate sample partitioning when the classic multi-metric learning algorithm learns metrics from sample partitions obtained in advance, based on the idea of constraint stratification weighting, this paper proposes to assign metrics to constraints layer by layer and makes the measurement as far as possible to meet the optimization model of all constraints, while adding regular terms to make the constraints corresponding to different metrics should be as different as possible. Since different constraints formed by a single sample may correspond to different local metrics, compared with traditional multi-metric learning methods, the proposed algorithm can obtain finer local metrics and is more flexible, making the metric's fitting ability stronger. Experimental results show that the proposed algorithm has obvious advantages compared with representative single-metric learning algorithms and multi-metric learning algorithms on real data sets.

Key words: metric learning, constraint weighting, Mahalanobis distance, triplet constraint, multi-metric learning

中图分类号:

TP181

韩露,郭鑫垚,魏巍,梁吉业. 基于约束分层加权的多度量学习算法[J]. 《山东大学学报(理学版)》, 2022, 57(4): 12-20.

HAN Lu, GUO Xin-yao, WEI Wei, LIANG Ji-ye. Multi-metric learning algorithm based on constraint hierarchical weighting[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(4): 12-20.

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