Nonlinear Discriminant Analysis using Kernel Functions

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Nonlinear Discriminant Analysis using Kernel Functions (1999)

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by Volker Roth , Volker Steinhage

Venue:	Advances in Neural Information Processing Systems
Citations:	99 - 9 self

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@INPROCEEDINGS{Roth99nonlineardiscriminant,
    author = {Volker Roth and Volker Steinhage},
    title = {Nonlinear Discriminant Analysis using Kernel Functions},
    booktitle = {Advances in Neural Information Processing Systems},
    year = {1999},
    pages = {568--574},
    publisher = {MIT Press}
}

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Abstract

Fishers linear discriminant analysis (LDA) is a classical multivariate technique both for dimension reduction and classication. The data vectors are transformed into a low dimensional subspace such that the class centroids are spread out as much as possible. In this subspace LDA works as a simple prototype classier. The resulting decision boundaries are linear. However, in many applications the linear boundaries do not adequately separate the classes and the possibility of modeling more complex boundaries would be desirable. In this paper we present a nonlinear generalization of discriminant analysis that implements the method of representing dot products of pattern vectors by kernel functions. This technique allows to eciently compute discriminant functions in arbitrary feature spaces for which such kernel representations exist. 1 Introduction Classical linear discriminant analysis (LDA) is a statistical method that attempts to project data vectors that belong to c dierent classes...

Keyphrases

kernel function nonlinear discriminant analysis discriminant analysis data vector classical multivariate technique arbitrary feature space nonlinear generalization dot product many application complex boundary linear boundary decision boundary dierent class low dimensional subspace subspace lda discriminant function simple prototype classier statistical method kernel representation pattern vector class centroid dimension reduction introduction classical linear discriminant analysis

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