Binary classification via spherical separator by DC programming and DCA

In this paper, we consider a binary supervised classification problem, called spherical separation, that consists of finding, in the input space or in the feature space, a minimal volume sphere separating the set from the set (i.e. a sphere enclosing all points of and no points of ). The problem can...

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Bibliographic Details
Published in:Journal of global optimization Vol. 56; no. 4; pp. 1393 - 1407
Main Authors: Le Thi, Hoai An, Le, Hoai Minh, Pham Dinh, Tao, Van Huynh, Ngai
Format: Journal Article
Language:English
Published: Boston Springer US 01.08.2013
Springer
Springer Nature B.V
Springer Verlag
Subjects:
Algorithms
Classification
Computational efficiency
Computer programming
Computer Science
Convex analysis
Customizing
Data mining
Direct current
Investigations
Laboratories
Mathematical models
Mathematics
Mathematics and Statistics
Numerical analysis
Operations Research/Decision Theory
Optimization
Programming
Real Functions
Simulation
Studies
Support vector machines
DC programming
90C90
DCA
90C30
Spherical separation
Classification
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:In this paper, we consider a binary supervised classification problem, called spherical separation, that consists of finding, in the input space or in the feature space, a minimal volume sphere separating the set from the set (i.e. a sphere enclosing all points of and no points of ). The problem can be cast into the DC (Difference of Convex functions) programming framework and solved by DCA (DC Algorithm) as shown in the works of Astorino et al. (J Glob Optim 48(4):657–669, 2010 ). The aim of this paper is to investigate more attractive DCA based algorithms for this problem. We consider a new optimization model and propose two interesting DCA schemes. In the first scheme we have to solve a quadratic program at each iteration, while in the second one all calculations are explicit. Numerical simulations show the efficiency of our customized DCA with respect to the methods developed in Astorino et al.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-012-9859-6