A Framework for Admissible Kernel Function in Support Vector Machines using Lévy Distribution

Abstract

With the massive amount of data being generated in everyday life it is increasingly important to develop a powerful framework for analysis interpretation and extraction of interesting knowledge that could help in decision making The confluence of intertwined disciplines like statistics machine learning pattern recognition artificial and computational intelligence have enriched data mining applications in various domains including healthcare security and remote surveillance Due to the rapid incidence of nonlinear ill posedness in real world problems empirical modeling is receiving greater impetus in building up a data model To address and convert an illposed problem into well posed one reliable and flexible models with some form of capacity control is needed to balance the data fitting Regularization statistical learning theory structural risk minimization SRM and kernel based algorithms are elegantly combined to form a defined framework called as support vector machines SVMs The basic idea of SVM is to build an optimal and feasible classifier model with three successful strategies namely learning ability robustness and computational efficiency Two major issues of SVM are kernel selection and maximum margin classifiers In training a SVM it is important to select a kernel and its parameters But there is no premise to determine the choice of an appropriate kernel function for a particular domain This research work focuses on the first issue ie the choice of the kernel function based on which a novel framework for admissible kernel function is proposed Additionally the curse of dimensionality is a major hindrance in machine learning and data mining In order to avoid this problem and strengthen the proposed framework a new technique based on fuzzy rough sets with differential evolution is created and experimented Further the proposed model is proved theoretically and empirically to solve classification problems newline