PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Nearest hyperdisk methods for high-dimensional classification
Hakan Cevikalp, William Triggs and Robi Polikar
In: ICML 2008, 5-7 July 2008, Helsinki.

Abstract

In high-dimensional classification problems it is infeasible to include enough training samples to cover the class regions densely. Irregularities in the resulting sparse sample distributions cause local classifiers such as Nearest Neighbors (NN) and kernel methods to have irregular decision boundaries. One solution is to "fill in the holes'' by building a convex model of the region spanned by the training samples of each class and classifying examples based on their distances to these approximate models. Methods of this kind based on affine and convex hulls and bounding hyperspheres have already been studied. Here we propose a method based on the bounding hyperdisk of each class -- the intersection of the affine hull and the smallest bounding hypersphere of its training samples. We argue that in many cases hyperdisks are preferable to affine and convex hulls and hyperspheres: they bound the classes more tightly than affine hulls or hyperspheres while avoiding much of the sample overfitting and computational complexity that is inherent in high-dimensional convex hulls. We show that the hyperdisk method can be kernelized to provide nonlinear classifiers based on non-Euclidean distance metrics. Experiments on several classification problems show promising results.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Machine Vision
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:4365
Deposited By:William Triggs
Deposited On:13 March 2009