Conic Relaxations for Semi-supervised Support Vector Machines

Yanqin Bai () and Xin Yan ()
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Yanqin Bai: Shanghai University
Xin Yan: Shanghai University

Journal of Optimization Theory and Applications, 2016, vol. 169, issue 1, No 15, 299-313

Abstract: Abstract Semi-supervised support vector machines arise in machine learning as a model of mixed integer programming problem for classification. In this paper, we propose two convex conic relaxations for the original mixed integer programming problem. The first one is a new semi-definite relaxation, and its possibly maximal ratio of the optimal value is estimated approximately. The second one is a doubly nonnegative relaxation, which is relaxed from a well-known conic programming problem called completely positive programming problem that is equivalent to the original problem. Furthermore, we prove that the doubly nonnegative relaxation is tighter than the semi-definite relaxation. Finally, the numerical results show that two proposed relaxations not only generate proper classifiers but also outperform some existing methods in classification accuracy.

Keywords: Semi-supervised support vector machines; Convex conic relaxation; Semi-definite relaxation; Completely positive programming; Doubly nonnegative relaxation; 62H30; 90C11; 90C22 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-015-0843-4

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