Computational and theoretical analysis of supervised dimensionality reduction(监督降维算法的计算和理论分析)

ZHAOWu-feng(赵武锋); SHENHai-bin(沈海斌); YANXiao-lang(严晓浪)

doi:10.3785/j.issn.1008-9497.2009.06.015

Zhejiang Daxue xuebao. Lixue ban (Nov 2009)

Computational and theoretical analysis of supervised dimensionality reduction(监督降维算法的计算和理论分析)

ZHAOWu-feng(赵武锋),
SHENHai-bin(沈海斌),
YANXiao-lang(严晓浪)

Affiliations

ZHAOWu-feng(赵武锋): 1.Institute of VLSI Design, Zhejiang University,Hangzhou 310027, China( 1.浙江大学超大规模集成电路设计研究所，浙江杭州 310027)
SHENHai-bin(沈海斌): 1.Institute of VLSI Design, Zhejiang University,Hangzhou 310027, China( 1.浙江大学超大规模集成电路设计研究所，浙江杭州 310027)
YANXiao-lang(严晓浪): 1.Institute of VLSI Design, Zhejiang University,Hangzhou 310027, China( 1.浙江大学超大规模集成电路设计研究所，浙江杭州 310027)

DOI: https://doi.org/10.3785/j.issn.1008-9497.2009.06.015
Journal volume & issue: Vol. 36, no. 6
pp. 670 – 674

Abstract

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在小样本条件下,由于离散矩阵的奇异性,作为监督降维的传统线性鉴别分析(LDA)并不能直接计算.许多扩展算法被提出以克服此问题,一般可分为3类：基于类内离散矩阵零空间的方法、基于总体离散矩阵列空间的方法和基于其它子空间的方法.为了深入了解前2类算法的特性,作了计算和理论分析,并得出结论：在满足一定条件下（小样本高维数据一般都满足）,基于类内离散矩阵零空间和基于总体离散矩阵列空间的方法具有等价关系,仅最优矢量集的约束条件和实现途径有所区别.在人脸数据库ORL和YALE上的比较实验结果亦证实了上述结论.

Published in Zhejiang Daxue xuebao. Lixue ban

ISSN: 1008-9497 (Print)
Publisher: Zhejiang University Press
Country of publisher: China
LCC subjects: Science: Mathematics: Instruments and machines: Electronic computers. Computer science; Science: Physics
Website: https://www.zjujournals.com/sci/EN/1008-9497/home.shtml

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