Support vector machine via nonlinear rescaling method

Roman Polyak, Shen Shyang Ho, Igor Griva

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


In this paper we construct the linear support vector machine (SVM) based on the nonlinear rescaling (NR) methodology (see [Polyak in Math Program 54:177-222, 1992; Polyak in Math Program Ser A 92:197-235, 2002; Polyak and Teboulle in Math Program 76:265-284, 1997] and references therein). The formulation of the linear SVM based on the NR method leads to an algorithm which reduces the number of support vectors without compromising the classification performance compared to the linear soft-margin SVM formulation. The NR algorithm computes both the primal and the dual approximation at each step. The dual variables associated with the given data-set provide important information about each data point and play the key role in selecting the set of support vectors. Experimental results on ten benchmark classification problems show that the NR formulation is feasible. The quality of discrimination, in most instances, is comparable to the linear soft-margin SVM while the number of support vectors in several instances were substantially reduced.

Original languageEnglish (US)
Pages (from-to)367-378
Number of pages12
JournalOptimization Letters
Issue number4
StatePublished - Sep 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Optimization


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