Indefinite Kernel Fisher discriminant

Elzbieta Pekalska; Bernard Haasdonk; Elzbieta Pȩkalska

doi:10.1109/ICPR.2008.4761718

Indefinite Kernel Fisher discriminant

Elzbieta Pekalska, Bernard Haasdonk, Elzbieta Pȩkalska

Research output: Chapter in Book/Conference proceeding › Conference contribution

Abstract

Indefinite kernels arise in practice, e.g. from problem-specific kernel construction. Therefore, it is necessary to understand the behavior and suitability of classifiers in the corresponding indefinite inner product spaces. In this paper we address the Indefinite Kernel Fisher Discriminant (IKFD). First, we give the geometric interpretation of the Fisher Discriminant in indefinite inner product spaces. We show that IKFD is closely related to the well-known formulation of the traditional Kernel Fisher Discriminant derived for positive definite kernels. Practical implications are that IKFD can be directly applied to indefinite kernels without manipulation of the kernel matrix. Experiments demonstrate the geometrically intuitive classification and enable comparisons to other indefinite kernel classifiers. © 2008 IEEE.

Original language	English
Title of host publication	Proceedings - International Conference on Pattern Recognition\|Proc. Int. Conf. Pattern Recognit.
Place of Publication	Tampa, Florida, USA
Publisher	IEEE
ISBN (Print)	9781424421756
DOIs	https://doi.org/10.1109/ICPR.2008.4761718
Publication status	Published - 2008
Event	2008 19th International Conference on Pattern Recognition, ICPR 2008 - Tampa, FL Duration: 1 Jul 2008 → … http://dblp.uni-trier.de/db/conf/icpr/icpr2008.html#HaasdonkP08http://dblp.uni-trier.de/rec/bibtex/conf/icpr/HaasdonkP08.xmlhttp://dblp.uni-trier.de/rec/bibtex/conf/icpr/HaasdonkP08

Conference

Conference	2008 19th International Conference on Pattern Recognition, ICPR 2008
City	Tampa, FL
Period	1/07/08 → …
Internet address	http://dblp.uni-trier.de/db/conf/icpr/icpr2008.html#HaasdonkP08http://dblp.uni-trier.de/rec/bibtex/conf/icpr/HaasdonkP08.xmlhttp://dblp.uni-trier.de/rec/bibtex/conf/icpr/HaasdonkP08

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10.1109/ICPR.2008.4761718

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title = "Indefinite Kernel Fisher discriminant",

abstract = "Indefinite kernels arise in practice, e.g. from problem-specific kernel construction. Therefore, it is necessary to understand the behavior and suitability of classifiers in the corresponding indefinite inner product spaces. In this paper we address the Indefinite Kernel Fisher Discriminant (IKFD). First, we give the geometric interpretation of the Fisher Discriminant in indefinite inner product spaces. We show that IKFD is closely related to the well-known formulation of the traditional Kernel Fisher Discriminant derived for positive definite kernels. Practical implications are that IKFD can be directly applied to indefinite kernels without manipulation of the kernel matrix. Experiments demonstrate the geometrically intuitive classification and enable comparisons to other indefinite kernel classifiers. {\textcopyright} 2008 IEEE.",

author = "Elzbieta Pekalska and Bernard Haasdonk and Elzbieta Pȩkalska",

year = "2008",

doi = "10.1109/ICPR.2008.4761718",

language = "English",

isbn = "9781424421756",

booktitle = "Proceedings - International Conference on Pattern Recognition|Proc. Int. Conf. Pattern Recognit.",

publisher = "IEEE",

address = "United States",

note = "2008 19th International Conference on Pattern Recognition, ICPR 2008 ; Conference date: 01-07-2008",

url = "http://dblp.uni-trier.de/db/conf/icpr/icpr2008.html#HaasdonkP08http://dblp.uni-trier.de/rec/bibtex/conf/icpr/HaasdonkP08.xmlhttp://dblp.uni-trier.de/rec/bibtex/conf/icpr/HaasdonkP08",

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TY - GEN

T1 - Indefinite Kernel Fisher discriminant

AU - Pekalska, Elzbieta

AU - Haasdonk, Bernard

AU - Pȩkalska, Elzbieta

PY - 2008

Y1 - 2008

N2 - Indefinite kernels arise in practice, e.g. from problem-specific kernel construction. Therefore, it is necessary to understand the behavior and suitability of classifiers in the corresponding indefinite inner product spaces. In this paper we address the Indefinite Kernel Fisher Discriminant (IKFD). First, we give the geometric interpretation of the Fisher Discriminant in indefinite inner product spaces. We show that IKFD is closely related to the well-known formulation of the traditional Kernel Fisher Discriminant derived for positive definite kernels. Practical implications are that IKFD can be directly applied to indefinite kernels without manipulation of the kernel matrix. Experiments demonstrate the geometrically intuitive classification and enable comparisons to other indefinite kernel classifiers. © 2008 IEEE.

AB - Indefinite kernels arise in practice, e.g. from problem-specific kernel construction. Therefore, it is necessary to understand the behavior and suitability of classifiers in the corresponding indefinite inner product spaces. In this paper we address the Indefinite Kernel Fisher Discriminant (IKFD). First, we give the geometric interpretation of the Fisher Discriminant in indefinite inner product spaces. We show that IKFD is closely related to the well-known formulation of the traditional Kernel Fisher Discriminant derived for positive definite kernels. Practical implications are that IKFD can be directly applied to indefinite kernels without manipulation of the kernel matrix. Experiments demonstrate the geometrically intuitive classification and enable comparisons to other indefinite kernel classifiers. © 2008 IEEE.

U2 - 10.1109/ICPR.2008.4761718

DO - 10.1109/ICPR.2008.4761718

M3 - Conference contribution

SN - 9781424421756

BT - Proceedings - International Conference on Pattern Recognition|Proc. Int. Conf. Pattern Recognit.

PB - IEEE

CY - Tampa, Florida, USA

T2 - 2008 19th International Conference on Pattern Recognition, ICPR 2008

Y2 - 1 July 2008

ER -

Indefinite Kernel Fisher discriminant

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