Pattern Classification via Single Spheres

Wang, Jigang; Neskovic, Predrag; Cooper, Leon N.

doi:10.1007/11563983_21

Cited by 26 publications

(33 citation statements)

References 6 publications

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“…There are already a number of methods based on affine hulls or bounding hyperspheres -for example hyperspheres have been used for outlier detection (Tax & Duin, 2004, Shawe-Taylor & Cristianini, 2004 and binary classification (Wang et al, 2005) -but we are not aware of any previous machine learning method based on hyperdisks. The bounding hypersphere of class c is characterized by its center s c and radius r c .…”

Section: Global Nearest Hyperdisk Methodsmentioning

confidence: 99%

Nearest hyperdisk methods for high-dimensional classification

Çevikalp

Triggs

Polikar

2008

Proceedings of the 25th International Conference on Machine Learning - ICML '08

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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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Section: Global Nearest Hyperdisk Methodsmentioning

confidence: 99%

Nearest hyperdisk methods for high-dimensional classification

Çevikalp

Triggs

Polikar

2008

Proceedings of the 25th International Conference on Machine Learning - ICML '08

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“…For instance, [8,12,26,31] present fully-supervised variants of the classical support vector data description (SVDD) [24]. However, the objective functions are no longer convex and the proposed optimizations in dual space may suffer from duality gaps.…”

Section: Related Workmentioning

confidence: 99%

“…[8, 12,26,23] propose extensions of the SVDD to incorporate labeled data into the learning process. The corresponding optimization problems are however not convex and the dual solution might suffer from a duality gap.…”

Section: Support Vector Data Descriptionmentioning

confidence: 99%

Active and Semi-supervised Data Domain Description

Görnitz

Kloft

Brefeld

2009

Machine Learning and Knowledge Discovery in Databases

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Abstract. Data domain description techniques aim at deriving concise descriptions of objects belonging to a category of interest. For instance, the support vector domain description (SVDD) learns a hypersphere enclosing the bulk of provided unlabeled data such that points lying outside of the ball are considered anomalous. However, relevant information such as expert and background knowledge remain unused in the unsupervised setting. In this paper, we rephrase data domain description as a semi-supervised learning task, that is, we propose a semi-supervised generalization of data domain description (SSSVDD) to process unlabeled and labeled examples. The corresponding optimization problem is nonconvex. We translate it into an unconstraint, continuous problem that can be optimized accurately by gradient-based techniques. Furthermore, we devise an effective active learning strategy to query low-confidence observations. Our empirical evaluation on network intrusion detection and object recognition tasks shows that our SSSVDDs consistently outperform baseline methods in relevant learning settings.

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“…The same class of data being bound by an optimal class-specific hypersphere, the whole data space is then divided by a number of such hyperspheres. Experimental results have showed that the spherical-structured SVMs perform comparable to the standard hyperplanebased SVMs [14,27,29,30].…”

Section: Introductionmentioning

confidence: 97%

A new maximal-margin spherical-structured multi-class support vector machine

2007

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Support vector machines (SVMs), initially proposed for two-class classification problems, have been very successful in pattern recognition problems. For multiclass classification problems, the standard hyperplane-based SVMs are made by constructing and combining several maximal-margin hyperplanes, and each class of data is confined into a certain area constructed by those hyperplanes. Instead of using hyperplanes, hyperspheres that tightly enclosed the data of each class can be used. Since the classspecific hyperspheres are constructed for each class separately, the spherical-structured SVMs can be used to deal with the multi-class classification problem easily. In addition, the center and radius of the class-specific hypersphere characterize the distribution of examples from that class, and may be useful for dealing with imbalance problems. In this paper, we incorporate the concept of maximal margin into the spherical-structured SVMs. Besides, the proposed approach has the advantage of using a new parameter on controlling the number of support vectors. Experimental results show that the proposed method performs well on both artificial and benchmark datasets.

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Pattern Classification via Single Spheres

Cited by 26 publications

References 6 publications

Nearest hyperdisk methods for high-dimensional classification

Nearest hyperdisk methods for high-dimensional classification

Active and Semi-supervised Data Domain Description

A new maximal-margin spherical-structured multi-class support vector machine

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