A comparative study among different kernel functions in flexible naïve Bayesian classification

When determining the class of the unknown example by using naïve Bayesian classifier, we need to estimate the class conditional probabilities for the continuous attributes. In flexible Bayesian classifier, the Gaussian kernel function is frequently used for classification task under the framework of Parzen window method. In this paper, the other six kernel functions (uniform, triangular, epanechnikov, biweight, triweight and cosine) are introduced in the flexible naïve Bayesian. The performances of these seven kernels are compared in 30 UCI datasets. The experimental comparisons are carried out according to the following three aspects: the classification accuracy, ranking performance and the class probability estimation. The latter two are measured by the area under the ROC curve (AUC) and the conditional log likelihood (CLL). The related kernels are compared via two-tailed t-test with a 95 percent confidence level and the Friedman´s test using the 0.05 critical level. The experimental results show that the most commonly used Gaussian kernel can not achieve the best classification accuracy and AUC. However, on the CLL, the Gaussian kernel is statistically significantly better than the other six kernels. Finally, the corresponding analyses are given based on the experimental results.