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      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
      2011
      Source Title
      INFORMS Journal on Computing
      Print ISSN
      1091-9856
      Electronic ISSN
      1526-5528
      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
      Item Usage Stats
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      Abstract
      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.
      Keywords
      Approximation algorithms
      Core sets
      Frank-Wolfe algorithm
      Linear convergence
      Support vector classification
      Support vector machines
      Permalink
      http://hdl.handle.net/11693/21900
      Published Version (Please cite this version)
      http://dx.doi.org/10.1287/ijoc.1100.0412
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