引用本文:高云龙,王志豪,丁柳,等.动态加权非参数判别分析[J].控制与决策,2020,35(8):1866-1872
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动态加权非参数判别分析
高云龙1, 王志豪1, 丁柳1, 潘金艳2, 王德鑫1
(1. 厦门大学航空航天学院,福建厦门361102;2. 集美大学信息工程学院,福建厦门361021)
摘要:
线性判别分析(LDA)是最经典的子空间学习和有监督判别特征提取方法之一.受到流形学习的启发,近年来众多基于LDA的改进方法被提出.尽管出发点不同,但这些算法本质上都是基于欧氏距离来度量样本的空间散布度.欧氏距离的非线性特性带来了如下两个问题:1)算法对噪声和异常样本点敏感;2)算法对流形或者是多模态数据集中局部散布度较大的样本点过度强调,导致特征提取过程中数据的本质结构特征被破坏.为了解决这些问题,提出一种新的基于非参数判别分析(NDA)的维数约减方法,称作动态加权非参数判别分析(DWNDA).DWNDA采用动态加权距离来计算类间散布度和类内散布度,不仅能够保留多模态数据集的本质结构特征,还能有效地利用边界样本点对之间的判别信息.因此,DWNDA在噪声实验中展现出对噪声和异常样本的强鲁棒性.此外,在人脸和手写体数据库上进行实验,DWNDA方法均取得了优异的实验结果.
关键词:  非参数判别分析  特征提取  动态加权距离  局部散布度  判别信息  鲁棒性
DOI:10.13195/j.kzyjc.2018.1716
分类号:TP181
基金项目:国家自然科学基金项目(61203176);福建省自然科学基金项目(2013J05098,2016J01756).
Dynamic weighted nonparametric discriminant analysis
GAO Yun-long1,WANG Zhi-hao1,DING Liu1,PAN Jin-yan2,WANG De-xin1
(1. College of Aeronautics and Astronautics,Xiamen University,Xiamen361102,China;2. College of Information Engineering,Jimei University,Xiamen361021,China)
Abstract:
Linea discriminant analysis(LDA) is one of the most classical subspace learning and supervised learning methods. Inspired by manifold learning, many improved methods based on LDA have been proposed in recent years. Although the motivations of these methods are different, they are all based on the Euclidean distance to measure the spatial dispersion of the samples. The non-linear characteristic of Eucilidean distance brings about two problems: 1) these methods are too sensitive to noise and outlier; 2) the essential structure would be destructed, due to the overemphasis of the points which has a large local dispersion in manifold or multimodal datasets. To solve these problems, a new dimension reduction method based on nonparametric discriminant analysis (NDA) is proposed, called a dynamic weighted nonparametric discriminant analysis (DWNDA).Then DWNDA uses the dynamic weighted distance to caluculate the within-class and between-class scatters. It can not only retain the essential geometrical structure of multimodal datasets, but also make better use of the discriminant information between marginal point pairs. Hence, the DWNDA shows better robustness to noise and outlier than other methods, which is also demonstrated in experiments. Besides, the DWNDA also shows excellent performance for face and handwrting classification.
Key words:  nonparametric discriminant analysis  feature extraction  dynamic weighted distance  local dispersion  discriminative information  robustness

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