Effective Parameter Tuning of SVMs Using Radius/Margin Bound Through Data Envelopment Analysis

摘要

This paper presents parameter tuning of multi-class support vector machines (SVMs) using radius–margin bound through data envelopment analysis (DEA). Relative efficiencies of the binary SVMs in one-vs-one multi-class SVM are obtained using radius as the input and margin as the output by employing Charnes, Cooper and Rhodes model (CCR model). The objective is to maximize the sum of the relative efficiencies of individual binary SVMs in one-vs-one multi-class SVM. The proposed formulation is empirically found to be outperforming Keerthi’s radius–margin based parameter tuning. In the best case, the radius obtained through the proposed method is 1,110 times lower than Keerthi’s method. Margin is 4.4 times higher, the number of support vectors are 5.8 times lower and test error rates are competitive. Proposed method is also compared with (i) Widely employed grid search method and (ii) Parameter tuning method proposed in (IEEE Trans Mach Intell 32:1888–1898, 2010. The merit of the proposed method over these tuning methods is shown through experimentation along the four identified dimensions.