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

Piyush Kumar*, E. Alper Yildirim

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)377-391
Number of pages15
JournalINFORMS Journal on Computing
Volume23
Issue number3
DOIs
Publication statusPublished - 1 Jun 2011

Keywords

  • Approximation algorithms
  • Core sets
  • Frank-Wolfe algorithm
  • Linear convergence
  • Support vector classification
  • Support vector machines

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