期刊名称：International Journal of Network Security & Its Applications
印刷版ISSN：0975-2307
电子版ISSN：0974-9330
出版年度：2019
卷号：11
期号：4
页码：87-103
DOI：10.5121/ijnsa.2019.11406
出版社：Academy & Industry Research Collaboration Center (AIRCC)
摘要：In this paper, we introduce a set of new kernel functions derived from the generalized Legendre polynomials to obtain more robust and higher support vector machine (SVM) classification accuracy. The generalized Legendre kernel functions are suggested to provide a value of how two given vectors are like each other by changing the inner product of these two vectors into a greater dimensional space. The proposed kernel functions satisfy the Mercer’s condition and orthogonality properties for reaching the optimal result with low number support vector (SV). For that, the new set of Legendre kernel functions could be utilized in classification applications as effective substitutes to those generally used like Gaussian, Polynomial and Wavelet kernel functions. The suggested kernel functions are calculated in compared to the current kernels such as Gaussian, Polynomial, Wavelets and Chebyshev kernels by application to various non-separable data sets with some attributes. It is seen that the suggested kernel functions could give competitive classification outcomes in comparison with other kernel functions. Thus, on the basis test outcomes, we show that the suggested kernel functions are more robust about the kernel parameter change and reach the minimal SV number for classification generally.
关键词：Legendre Polynomials; Kernel Functions; Functional Analysis; SVMS; Classification Problem
