Fast Calculation for Fisher Criteria in Small Sample Size Problem

Wei Shi Zheng; Jian Huang Lai; Pong Chi Yuen

doi:10.1007/978-3-540-30548-4_38

Fast Calculation for Fisher Criteria in Small Sample Size Problem

Wei Shi Zheng, Jian Huang Lai, Pong Chi Yuen

Department of Computer Science

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

Abstract

LDA is popularly used in the pattern recognition field. Unfortunately LDA always confronts the small sample size problem (S3), which leads the within-class scatter matrix to be singular. In this case, PCA is always used for dimensional reduction to solve the problem in practice. This paper analyzes that when the small sample size problem happens, the PCA processing is not only to play the role of solving the S3 problem but also can be used to induce a fast calculation algorithm for solving the fisher criteria. This paper will show that calculating the eigenvectors of within-class scatter matrix after dimensional reduction can solve the optimal projection for fisher criteria.

Original language	English
Title of host publication	Advances in Biometric Person Authentication
Subtitle of host publication	5th Chinese Conference on Biometric Recognition, SINOBIOMETRICS 2004, Guangzhou, China, December 13-14, 2004, Proceedings
Editors	Stan Z. Li, Jianhuang Lai, Tieniu Tan, Guocan Feng, Yunhong Wang
Place of Publication	Berlin, Heidelberg
Publisher	Springer
Pages	330-338
Number of pages	9
Edition	1st
ISBN (Electronic)	9783540305484
ISBN (Print)	9783540240297
DOIs	https://doi.org/10.1007/978-3-540-30548-4_38
Publication status	Published - 29 Nov 2004
Event	5th Chinese Conference on Biometric Recognition, SINOBIOMETRICS 2004 - Guangzhou, China Duration: 13 Dec 2004 → 14 Dec 2004 https://link.springer.com/book/10.1007/b104239

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	3338
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Name	SINOBIOMETRICS: Chinese Conference on Biometric Recognition

Conference

Conference	5th Chinese Conference on Biometric Recognition, SINOBIOMETRICS 2004
Country/Territory	China
City	Guangzhou
Period	13/12/04 → 14/12/04
Internet address	https://link.springer.com/book/10.1007/b104239

Scopus Subject Areas

Theoretical Computer Science
General Computer Science

User-Defined Keywords

Face Recognition
Linear Discriminant Analysis
Scatter Matrix
Optimal Projection
Fisher Criterion

Access to Document

10.1007/978-3-540-30548-4_38

Cite this

Zheng, W. S., Lai, J. H., & Yuen, P. C. (2004). Fast Calculation for Fisher Criteria in Small Sample Size Problem. In S. Z. Li, J. Lai, T. Tan, G. Feng, & Y. Wang (Eds.), Advances in Biometric Person Authentication: 5th Chinese Conference on Biometric Recognition, SINOBIOMETRICS 2004, Guangzhou, China, December 13-14, 2004, Proceedings (1st ed., pp. 330-338). (Lecture Notes in Computer Science; Vol. 3338), (SINOBIOMETRICS: Chinese Conference on Biometric Recognition). Springer. https://doi.org/10.1007/978-3-540-30548-4_38

Zheng, Wei Shi ; Lai, Jian Huang ; Yuen, Pong Chi. / Fast Calculation for Fisher Criteria in Small Sample Size Problem. Advances in Biometric Person Authentication: 5th Chinese Conference on Biometric Recognition, SINOBIOMETRICS 2004, Guangzhou, China, December 13-14, 2004, Proceedings. editor / Stan Z. Li ; Jianhuang Lai ; Tieniu Tan ; Guocan Feng ; Yunhong Wang. 1st. ed. Berlin, Heidelberg : Springer, 2004. pp. 330-338 (Lecture Notes in Computer Science). (SINOBIOMETRICS: Chinese Conference on Biometric Recognition).

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title = "Fast Calculation for Fisher Criteria in Small Sample Size Problem",

abstract = "LDA is popularly used in the pattern recognition field. Unfortunately LDA always confronts the small sample size problem (S3), which leads the within-class scatter matrix to be singular. In this case, PCA is always used for dimensional reduction to solve the problem in practice. This paper analyzes that when the small sample size problem happens, the PCA processing is not only to play the role of solving the S3 problem but also can be used to induce a fast calculation algorithm for solving the fisher criteria. This paper will show that calculating the eigenvectors of within-class scatter matrix after dimensional reduction can solve the optimal projection for fisher criteria.",

keywords = "Face Recognition, Linear Discriminant Analysis, Scatter Matrix, Optimal Projection, Fisher Criterion",

author = "Zheng, {Wei Shi} and Lai, {Jian Huang} and Yuen, {Pong Chi}",

year = "2004",

month = nov,

day = "29",

doi = "10.1007/978-3-540-30548-4_38",

language = "English",

isbn = "9783540240297",

series = "Lecture Notes in Computer Science",

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editor = "Li, {Stan Z.} and Jianhuang Lai and Tieniu Tan and Guocan Feng and Yunhong Wang",

booktitle = "Advances in Biometric Person Authentication",

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}

Zheng, WS, Lai, JH & Yuen, PC 2004, Fast Calculation for Fisher Criteria in Small Sample Size Problem. in SZ Li, J Lai, T Tan, G Feng & Y Wang (eds), Advances in Biometric Person Authentication: 5th Chinese Conference on Biometric Recognition, SINOBIOMETRICS 2004, Guangzhou, China, December 13-14, 2004, Proceedings. 1st edn, Lecture Notes in Computer Science, vol. 3338, SINOBIOMETRICS: Chinese Conference on Biometric Recognition, Springer, Berlin, Heidelberg, pp. 330-338, 5th Chinese Conference on Biometric Recognition, SINOBIOMETRICS 2004, Guangzhou, China, 13/12/04. https://doi.org/10.1007/978-3-540-30548-4_38

Fast Calculation for Fisher Criteria in Small Sample Size Problem. / Zheng, Wei Shi; Lai, Jian Huang; Yuen, Pong Chi.
Advances in Biometric Person Authentication: 5th Chinese Conference on Biometric Recognition, SINOBIOMETRICS 2004, Guangzhou, China, December 13-14, 2004, Proceedings. ed. / Stan Z. Li; Jianhuang Lai; Tieniu Tan; Guocan Feng; Yunhong Wang. 1st. ed. Berlin, Heidelberg: Springer, 2004. p. 330-338 (Lecture Notes in Computer Science; Vol. 3338), (SINOBIOMETRICS: Chinese Conference on Biometric Recognition).

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

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AU - Zheng, Wei Shi

AU - Lai, Jian Huang

AU - Yuen, Pong Chi

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N2 - LDA is popularly used in the pattern recognition field. Unfortunately LDA always confronts the small sample size problem (S3), which leads the within-class scatter matrix to be singular. In this case, PCA is always used for dimensional reduction to solve the problem in practice. This paper analyzes that when the small sample size problem happens, the PCA processing is not only to play the role of solving the S3 problem but also can be used to induce a fast calculation algorithm for solving the fisher criteria. This paper will show that calculating the eigenvectors of within-class scatter matrix after dimensional reduction can solve the optimal projection for fisher criteria.

AB - LDA is popularly used in the pattern recognition field. Unfortunately LDA always confronts the small sample size problem (S3), which leads the within-class scatter matrix to be singular. In this case, PCA is always used for dimensional reduction to solve the problem in practice. This paper analyzes that when the small sample size problem happens, the PCA processing is not only to play the role of solving the S3 problem but also can be used to induce a fast calculation algorithm for solving the fisher criteria. This paper will show that calculating the eigenvectors of within-class scatter matrix after dimensional reduction can solve the optimal projection for fisher criteria.

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KW - Linear Discriminant Analysis

KW - Scatter Matrix

KW - Optimal Projection

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Zheng WS, Lai JH, Yuen PC. Fast Calculation for Fisher Criteria in Small Sample Size Problem. In Li SZ, Lai J, Tan T, Feng G, Wang Y, editors, Advances in Biometric Person Authentication: 5th Chinese Conference on Biometric Recognition, SINOBIOMETRICS 2004, Guangzhou, China, December 13-14, 2004, Proceedings. 1st ed. Berlin, Heidelberg: Springer. 2004. p. 330-338. (Lecture Notes in Computer Science). (SINOBIOMETRICS: Chinese Conference on Biometric Recognition). doi: 10.1007/978-3-540-30548-4_38

Fast Calculation for Fisher Criteria in Small Sample Size Problem

Abstract

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Scopus Subject Areas

User-Defined Keywords

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