A linearly convergent linear - time first - order algorithm for support vector classification with a core set result

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Author
Kumar, P.
Yıldırım, E. A.
Date
2011Journal Title
INFORMS Journal on Computing
ISSN
1091-9856 (print) 1526-5528 (online)
Publisher
Institute for Operations Research and the Management Sciences (I N F O R M S)
Volume
23
Issue
3
Pages
377 - 391
Language
English
Type
Article
Metadata
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http://hdl.handle.net/11693/21900Abstract
We present a simple first-order approximation algorithm for the support vector classification problem. Given a pair of linearly separable data sets and. ε (0,1), the proposed algorithm computes a separating hyperplane whose margin is within a factor of (1-ε) of that of the maximum-margin separating hyperplane. We discuss how our algorithm can be extended to nonlinearly separable and inseparable data sets. The running time of our algorithm is linear in the number of data points and in 1/ε. In particular, the number of support vectors computed by the algorithm is bounded above by O(ζ/ε. for all sufficiently small ε >, where ζ is the square of the ratio of the distances between the farthest and closest pairs of points in the two data sets. Furthermore, we establish that our algorithm exhibits linear convergence. Our computational experiments, presented in the online supplement, reveal that the proposed algorithm performs quite well on standard data sets in comparison with other first-order algorithms. We adopt the real number model of computation in our analysis.