A mathematical programming approach to the kernel fisher algorithm

Sebastian Mika, Gunnar Ratsch, Klaus Muller

Research output: Chapter in Book/Report/Conference proceedingConference contribution

113 Citations (Scopus)

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 languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems
PublisherNeural information processing systems foundation
ISBN (Print)0262122413, 9780262122412
Publication statusPublished - 2001 Jan 1
Externally publishedYes
Event14th Annual Neural Information Processing Systems Conference, NIPS 2000 - Denver, CO, United States
Duration: 2000 Nov 272000 Dec 2

Other

Other14th Annual Neural Information Processing Systems Conference, NIPS 2000
CountryUnited States
CityDenver, CO
Period00/11/2700/12/2

Fingerprint

Mathematical programming
Support vector machines
Classifiers

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

Cite this

Mika, S., Ratsch, G., & Muller, K. (2001). A mathematical programming approach to the kernel fisher algorithm. In Advances in Neural Information Processing Systems Neural information processing systems foundation.

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

Advances in Neural Information Processing Systems. Neural information processing systems foundation, 2001.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Mika, S, Ratsch, G & Muller, K 2001, A mathematical programming approach to the kernel fisher algorithm. in 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.
Mika S, Ratsch G, Muller K. A mathematical programming approach to the kernel fisher algorithm. In Advances in Neural Information Processing Systems. Neural information processing systems foundation. 2001
Mika, Sebastian ; Ratsch, Gunnar ; Muller, Klaus. / A mathematical programming approach to the kernel fisher algorithm. Advances in Neural Information Processing Systems. Neural information processing systems foundation, 2001.
@inproceedings{96e83045ce8f4e0cb992b65cedb24001,
title = "A mathematical programming approach to the kernel fisher algorithm",
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.",
author = "Sebastian Mika and Gunnar Ratsch and Klaus Muller",
year = "2001",
month = "1",
day = "1",
language = "English",
isbn = "0262122413",
booktitle = "Advances in Neural Information Processing Systems",
publisher = "Neural information processing systems foundation",

}

TY - GEN

T1 - A mathematical programming approach to the kernel fisher algorithm

AU - Mika, Sebastian

AU - Ratsch, Gunnar

AU - Muller, Klaus

PY - 2001/1/1

Y1 - 2001/1/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84898965347&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898965347&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84898965347

SN - 0262122413

SN - 9780262122412

BT - Advances in Neural Information Processing Systems

PB - Neural information processing systems foundation

ER -