Binary classification via spherical separator by DC programming and DCA

Binary classification via spherical separator by DC programming and DCA

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Article ID: iaor20134066
Volume: 56
Issue: 4
Start Page Number: 1393
End Page Number: 1407
Publication Date: Aug 2013
Journal: Journal of Global Optimization
Authors: , , ,
Keywords: classification, iterative methods
Abstract:

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 𝒜 equ1 from the set equ2 (i.e. a sphere enclosing all points of 𝒜 equ3 and no points of equ4 ). 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. (010). 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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