Granularity selection for cross-validation of SVM

Granularity selection is fundamental to granular computing. Cross-validation (CV) is widely adopted for model selection, where each fold of data set of CV can be considered as an information granule, and the larger the number of the folds is, the smaller the granularity of each fold is. Therefore, for CV, granularity selection is equal to the selection of the number of folds. In this paper, we explore the granularity selection for CV of support vector machine (SVM). We first use the Huber loss to smooth the hinge loss used in SVM, and to approximate CV of SVM. Then, we derive a tight upper bound of the discrepancy between the original and the approximate CV with a high convergence rate. Finally, based on this derived tight bound, we present a granularity selection criterion for trading off the accuracy and time cost. Experimental results demonstrate that the approximate CV with the granularity selection criterion gives the similar accuracies as the traditional CV, and meanwhile significantly improves the efficiency.