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1D-LDA vs. 2D-LDA: When is vector-based linear discriminant analysis better than matrix-based?
Zheng, Wei-Shi2,3; Lai, J. H.1,3; Li, Stan Z.4,5
2008-07-01
发表期刊PATTERN RECOGNITION
卷号41期号:7页码:2156-2172
文章类型Article
摘要Recent advances have shown that algorithms with (21)) matrix-based representation perform better than the traditional (I D) vector-based ones. In particular, 2D-LDA has been widely reported to outperform 1D-LDA. However, would the matrix-based linear discriminant analysis be always superior and when would 1D-LDA be better! In this paper, we investigate into these questions and have a comprehensive comparison between 1D-LDA and 2D-LDA in theory and in experiments. We analyze the heteroscedastic problem in 2D-LDA and formulate mathematical equalities to explore the relationship between 1D-LDA and 2D-LDA; then we point out potential problems in 2D-LDA. It is shown that 2D-LDA has eliminated the information contained in the covariance, information between different local geometric structures, such as the rows or the columns, which is useful for discriminant feature extraction, whereas 1D-LDA could preserve such information. Interestingly, this new finding indicates that 1D-LDA is able to gain higher Fisher score than 2D-LDA in some extreme case. Furthermore, sufficient conditions on which 2D-LDA would be Bayes optimal for two-class classification problem are derived and comparison with 1D-LDA in this aspect is also analyzed. This could help understand how 2D-LDA is expected to achieve at its best, further discover its relationship with 1D-LDA, and well support other findings. After the theoretical analysis, comprehensive experimental results are reported by fairly and extensively comparing 1D-LDA with 2D-LDA. In contrast to the existing view that some 2D-LDA based algorithms would perform better than 1D-LDA when the number of training samples for each class is small or when the number of discriminant features used is small, we show that it is not always true and show that some standard 1D-LDA based algorithms could perform better in those cases on some challenging data sets. (c) 2007 Elsevier Ltd. All rights reserved.
关键词Fisher's Linear Discriminant Analysis (Lda) Matrix-based Representation Vector-based Representation Pattern Recognition
WOS标题词Science & Technology ; Technology
关键词[WOS]INDEPENDENT COMPONENT ANALYSIS ; FACE-RECOGNITION ; FEATURE-EXTRACTION ; IMAGE MATRIX ; LDA ; PCA ; ALGORITHM ; CRITERION ; REPRESENTATION ; TRANSFORMATION
收录类别SCI
语种英语
WOS研究方向Computer Science ; Engineering
WOS类目Computer Science, Artificial Intelligence ; Engineering, Electrical & Electronic
WOS记录号WOS:000255818900005
引用统计
被引频次:51[WOS]   [WOS记录]     [WOS相关记录]
文献类型期刊论文
条目标识符http://ir.ia.ac.cn/handle/173211/9684
专题09年以前成果
作者单位1.Sun Yat Sen Univ, Dept Elect & Commun Engn, Sch Informat Sci & Technol, Guangzhou, Peoples R China
2.Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou, Peoples R China
3.Guangdong Prov Key Lab Informat Secur, Guangzhou, Guangdong, Peoples R China
4.Chinese Acad Sci, Ctr Biometr & Secur Res, Inst Automat, Beijing, Peoples R China
5.Chinese Acad Sci, Natl Lab Pattern Recognit, Inst Automat, Beijing, Peoples R China
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Zheng, Wei-Shi,Lai, J. H.,Li, Stan Z.. 1D-LDA vs. 2D-LDA: When is vector-based linear discriminant analysis better than matrix-based?[J]. PATTERN RECOGNITION,2008,41(7):2156-2172.
APA Zheng, Wei-Shi,Lai, J. H.,&Li, Stan Z..(2008).1D-LDA vs. 2D-LDA: When is vector-based linear discriminant analysis better than matrix-based?.PATTERN RECOGNITION,41(7),2156-2172.
MLA Zheng, Wei-Shi,et al."1D-LDA vs. 2D-LDA: When is vector-based linear discriminant analysis better than matrix-based?".PATTERN RECOGNITION 41.7(2008):2156-2172.
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