Improving kernel incapability by equivalent probability in flexible naïve Bayesian

In flexible naïve Bayesian (FNB), the excellent qualities of Gaussian kernel have been demonstrated by the theoretical analyses and experimental comparisons with normal naïve Bayesian (NNB). There are also several types of kernel functions commonly used for probability density estimation, i.e., uniform, triangular, epanechnikov, biweight, triweight and cosine. We call them discontinuous kernels. In this paper, we verify the feasibility and efficiency of applying these alternative kernels in FNB. Our works mainly focus on three aspects: firstly, we give the application conditions of these kernels for the given domain data by analyzing the structural difference between the discontinuous kernel and Gaussian kernel; secondly, the equivalent probability is proposed to improve the capabilities of discontinuous kernels when such problem of kernel incapability occurs; finally, we carry out the experimental demonstration of our proposed method based on 15 UCI datasets. The results show that the discontinuous kernels can obtain better classification accuracies with the help of equivalent probabilities.