Tuning kernel parameters for SVM based on expected square distance ratio

The performance of a support vector machine (SVM) depends highly on the selection of the kernel function type and relevant parameters. To choose the kernel parameters properly, methods analyzing the class separability have been widely adopted for their efficiency compared with other methods, such as the popular grid search algorithm. This paper proposes a novel index called the Expected Square Distance Ratio (ESDR), which can serve as a better class separability criterion than the existing ones. Experiments on real-world datasets show that, compared with common kernel parameter selection methods that utilize the between-class separation, the variations in ESDR with respect to the kernel parameter are much more in line with those of the classification accuracy, leading to better kernel parameters. Moreover, ESDR takes the exact data distribution into account and can thus be used to study the model selection problem of an SVM for certain forms of data distribution. As an example, we employ the ESDR to analyze the selection of RBF (Radial Basis Function) kernel parameters for Gaussian data classification.