A mathematical programming approach to the kernel fisher algorithm

Sebastian Mika; Gunnar Ratsch; Klaus Robert Müller

A mathematical programming approach to the kernel fisher algorithm

Sebastian Mika, Gunnar Ratsch, Klaus Robert Müller

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

Abstract

We investigate a new kernel-based classifier: the Kernel Fisher Discriminant (KFD). A mathematical programming formulation based on the observation that KFD maximizes the average margin permits an interesting modification of the original KFD algorithm yielding the sparse KFD. We find that both, KFD and the proposed sparse KFD, can be understood in an unifying probabilistic context. Furthermore, we show connections to Support Vector Machines and Relevance Vector Machines. From this understanding, we are able to outline an interesting kernel-regression technique based upon the KFD algorithm. Simulations support the usefulness of our approach.

Original language	English
Title of host publication	Advances in Neural Information Processing Systems 13 - Proceedings of the 2000 Conference, NIPS 2000
Publisher	Neural information processing systems foundation
ISBN (Print)	0262122413, 9780262122412
Publication status	Published - 2001
Externally published	Yes
Event	14th Annual Neural Information Processing Systems Conference, NIPS 2000 - Denver, CO, United States Duration: 2000 Nov 27 → 2000 Dec 2

Publication series

Name	Advances in Neural Information Processing Systems
ISSN (Print)	1049-5258

Other

Other	14th Annual Neural Information Processing Systems Conference, NIPS 2000
Country/Territory	United States
City	Denver, CO
Period	00/11/27 → 00/12/2

ASJC Scopus subject areas

Computer Networks and Communications
Information Systems
Signal Processing

Cite this

A mathematical programming approach to the kernel fisher algorithm. / Mika, Sebastian; Ratsch, Gunnar; Müller, Klaus Robert.

Advances in Neural Information Processing Systems 13 - Proceedings of the 2000 Conference, NIPS 2000. Neural information processing systems foundation, 2001. (Advances in Neural Information Processing Systems).

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

Mika, S, Ratsch, G & Müller, KR 2001, A mathematical programming approach to the kernel fisher algorithm. in Advances in Neural Information Processing Systems 13 - Proceedings of the 2000 Conference, NIPS 2000. Advances in Neural Information Processing Systems, Neural information processing systems foundation, 14th Annual Neural Information Processing Systems Conference, NIPS 2000, Denver, CO, United States, 00/11/27.

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AB - We investigate a new kernel-based classifier: the Kernel Fisher Discriminant (KFD). A mathematical programming formulation based on the observation that KFD maximizes the average margin permits an interesting modification of the original KFD algorithm yielding the sparse KFD. We find that both, KFD and the proposed sparse KFD, can be understood in an unifying probabilistic context. Furthermore, we show connections to Support Vector Machines and Relevance Vector Machines. From this understanding, we are able to outline an interesting kernel-regression technique based upon the KFD algorithm. Simulations support the usefulness of our approach.

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T3 - Advances in Neural Information Processing Systems

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T2 - 14th Annual Neural Information Processing Systems Conference, NIPS 2000

Y2 - 27 November 2000 through 2 December 2000

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A mathematical programming approach to the kernel fisher algorithm

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