The Solution Space for Fisher Discriminant Analysis and the Uniqueness Under Constraints

Weishi Zheng; Jianhuang Lai; Pong Chi Yuen

doi:10.1007/978-3-540-30548-4_36

The Solution Space for Fisher Discriminant Analysis and the Uniqueness Under Constraints

Weishi Zheng, Jianhuang Lai, Pong Chi Yuen

Department of Computer Science

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

Abstract

This paper studies the solution space of Fisher Criteria. The space is large and it is impossible to find the best solution generally. This paper intends to construct an optimal projection, which solves the Fisher criteria and is the unique solution under nonsingular linear transformation if some constraints are0020given. Therefore a theorem is proposed which shows the feasible for constructing the projection, with a simple way to process the construction from the traditional LDA. Experiment result shows the ability and feasible of the proposed solution.

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	313-319
Number of pages	7
Edition	1st
ISBN (Electronic)	9783540305484
ISBN (Print)	9783540240297
DOIs	https://doi.org/10.1007/978-3-540-30548-4_36
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

User-Defined Keywords

Linear Discriminant Analysis
Solution Space
Constraint Qualification
Scatter Matrix
Optimal Projection

Access to Document

10.1007/978-3-540-30548-4_36

Cite this

Zheng, W., Lai, J., & Yuen, P. C. (2004). The Solution Space for Fisher Discriminant Analysis and the Uniqueness Under Constraints. 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. 313-319). (Lecture Notes in Computer Science; Vol. 3338), (SINOBIOMETRICS: Chinese Conference on Biometric Recognition). Springer. https://doi.org/10.1007/978-3-540-30548-4_36

Zheng, Weishi ; Lai, Jianhuang ; Yuen, Pong Chi. / The Solution Space for Fisher Discriminant Analysis and the Uniqueness Under Constraints. 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. 313-319 (Lecture Notes in Computer Science). (SINOBIOMETRICS: Chinese Conference on Biometric Recognition).

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title = "The Solution Space for Fisher Discriminant Analysis and the Uniqueness Under Constraints",

abstract = "This paper studies the solution space of Fisher Criteria. The space is large and it is impossible to find the best solution generally. This paper intends to construct an optimal projection, which solves the Fisher criteria and is the unique solution under nonsingular linear transformation if some constraints are0020given. Therefore a theorem is proposed which shows the feasible for constructing the projection, with a simple way to process the construction from the traditional LDA. Experiment result shows the ability and feasible of the proposed solution.",

keywords = "Linear Discriminant Analysis, Solution Space, Constraint Qualification, Scatter Matrix, Optimal Projection",

author = "Weishi Zheng and Jianhuang Lai and Yuen, {Pong Chi}",

year = "2004",

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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, W, Lai, J & Yuen, PC 2004, The Solution Space for Fisher Discriminant Analysis and the Uniqueness Under Constraints. 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. 313-319, 5th Chinese Conference on Biometric Recognition, SINOBIOMETRICS 2004, Guangzhou, China, 13/12/04. https://doi.org/10.1007/978-3-540-30548-4_36

The Solution Space for Fisher Discriminant Analysis and the Uniqueness Under Constraints. / Zheng, Weishi; Lai, Jianhuang; 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. 313-319 (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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N2 - This paper studies the solution space of Fisher Criteria. The space is large and it is impossible to find the best solution generally. This paper intends to construct an optimal projection, which solves the Fisher criteria and is the unique solution under nonsingular linear transformation if some constraints are0020given. Therefore a theorem is proposed which shows the feasible for constructing the projection, with a simple way to process the construction from the traditional LDA. Experiment result shows the ability and feasible of the proposed solution.

AB - This paper studies the solution space of Fisher Criteria. The space is large and it is impossible to find the best solution generally. This paper intends to construct an optimal projection, which solves the Fisher criteria and is the unique solution under nonsingular linear transformation if some constraints are0020given. Therefore a theorem is proposed which shows the feasible for constructing the projection, with a simple way to process the construction from the traditional LDA. Experiment result shows the ability and feasible of the proposed solution.

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Zheng W, Lai J, Yuen PC. The Solution Space for Fisher Discriminant Analysis and the Uniqueness Under Constraints. 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. 313-319. (Lecture Notes in Computer Science). (SINOBIOMETRICS: Chinese Conference on Biometric Recognition). doi: 10.1007/978-3-540-30548-4_36

The Solution Space for Fisher Discriminant Analysis and the Uniqueness Under Constraints

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