Frequency component Kernel for SVM

Abstract

Finding a proper kernel for Support vector machine and adjusting the involved parameters for a better classification remain immense challenges. This paper addresses both challenges in two parts. In part one, a new kernel, called Frequency Component Kernel, is presented; and in the second part, a couple of techniques to form objective functions are introduced to estimate its shape parameter. In designing the FCK, a new Frequency-Based Regressor Matrix is designed based on data structure discovery through curve fitting. The inner product of this regressor matrix with itself produces an intermediary kernel. FCK is a smoothed version of this intermediary kernel. The FCK’s classification accuracy with a 95% confidence interval is compared to well-known kernels, namely Gaussian, Linear, Polynomial, and Sigmoid kernels, for fifteen sets of data. A grid search method is employed for parameter assignments in all kernels. This comparison shows the superiority of FCK in most cases. In part two, the first technique to form an objective function is based on variances of data groups, distances between the centers of data groups, and upper bound classification errors; and the second technique is based on distances between all data, SVM margin, and distance between the centers of data groups. Both techniques take advantage of the FCK development so that all data are converted to the new space via the FBRM. Then, the data distances in this space are calculated. The comparative results show that both suggested techniques to form objective functions outperform the current state-of-the-art parameter estimation methods. The inclusive results show that the combination of our FCK with our two automatic shape parameter estimation methods, could be used as a superlative choice in many related SVM usages and applications. © 2022, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.