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Kernel Fisher discriminant functions – a concise and rigorous introduction

  • In the article the application of kernel functions – the so-called »kernel trick« – in the context of Fisher’s approach to linear discriminant analysis is described for data sets subdivided into two groups and having real attributes. The relevant facts about functional Hilbert spaces and kernel functions including their proofs are presented. The approximative algorithm published in [Mik3] to compute a discriminant function given the data and a kernel function is briefly reviewed. As an illustration of the technique an artificial data set is analysed using the algorithm just mentioned.

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Author:H. Knaf
URN (permanent link):urn:nbn:de:hbz:386-kluedo-15393
Serie (Series number):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (117)
Document Type:Report
Language of publication:English
Year of Completion:2007
Year of Publication:2007
Publishing Institute:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Date of the Publication (Server):2008/05/28
Tag:discriminant analysis; functional Hilbert space; kernel function; reproducing kernel
Faculties / Organisational entities:Fraunhofer (ITWM)
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011