Two criteria for model selection in multiclass support vector machines

Practical applications call for efficient model selection criteria for multiclass support vector machine (SVM) classification. To solve this problem, this paper develops two model selection criteria by combining or redefining the radius-margin bound used in binary SVMs. The combination is justified by linking the test error rate of a multiclass SVM with that of a set of binary SVMs. The redefinition, which is relatively heuristic, is inspired by the conceptual relationship between the radius-margin bound and the class separability measure. Hence, the two criteria are developed from the perspective of model selection rather than a generalization of the radius-margin bound for multiclass SVMs. As demonstrated by extensive experimental study, the minimization of these two criteria achieves good model selection on most data sets. Compared with the κ-fold cross validation which is often regarded as a benchmark, these two criteria give rise to comparable performance with much less computational overhead, particularly when a large number of model parameters are to be optimized.