高维数据正定核与不定核的KPCA变换阵比较

山东大学学报(工学版) ›› 2011, Vol. 41 ›› Issue (1): 17-23.

高维数据正定核与不定核的KPCA变换阵比较

崔燕,范丽亚

聊城大学数学科学学院, 山东聊城 252059

收稿日期:2010-04-20 出版日期:2011-02-16 发布日期:2010-04-20
作者简介:崔燕(1985- ), 女, 山东东明人, 硕士研究生, 主要研究方向为模式识别. E-mail:cuiyan899@163.com
基金资助:
国家自然科学基金资助项目(10871226); 山东省自然科学基金资助项目(ZR2009AL006)

Comparison of KPCA transformation matrices with definite and indefinite kernels for high-dimensional data

CUI Yan, FAN Li-ya

School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China

Received:2010-04-20 Online:2011-02-16 Published:2010-04-20

摘要/Abstract

摘要：

两步降维的核主成份分析(kernel principal component analysis,KPCA)+线性判别式分析(linear discriminant analysis,LDA)法中,第一步KPCA变换阵的选取影响数据的分类结果。对线性不可分问题首先研究了正定核KPCA+LDA中KPCA变换阵的选取对分类结果的影响;其次,将正定核推广到不定核,研究了不定核KPCA+LDA中KPCA变换阵的选取对分类结果的影响;最后通过实验加以分析和验证。

关键词: 主成份分析, 线性判别式分析, 正定核, 不定核, 降维变换阵

Abstract:

The transformation matrices in the first stage of two-stage dimension reduction KPCA (kernel principal component analysis)+LDA (linear discriminant analysis) influenced the classification results of data. For linear non-separated problems, the influence of the transformation matrices in the first stage of KPCA+LDA to the classification results with definite kernels and then with indefinite kernels was first studied. In addition, experiments were provided for analyzing and illustrating the results.

Key words: principal component analysis, linear discriminant analysis, definite kernel, indefinite kernel, dimension reduction transformation matrix

崔燕,范丽亚. 高维数据正定核与不定核的KPCA变换阵比较[J]. 山东大学学报(工学版), 2011, 41(1): 17-23.

CUI Yan, FAN Li-ya. Comparison of KPCA transformation matrices with definite and indefinite kernels for high-dimensional data[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2011, 41(1): 17-23.

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