Polynomial kernel function and its application in locally polynomial neurofuzzy models

Polynomials are one of the most powerful functions that have been used in many fields of mathematics such as curve fitting and regression. Low order polynomials are desired for their smoothness, good local approximation and interpolation. Being smooth, they can be used to locally approximate almost any derivable function. This means that when linear functions fail in approximation (e.g. where the first order Taylor expansion equals zero) polynomial functions can be used in local approximation, such that one can achieve better estimations at extremums. In this paper, application of polynomial kernel functions in locally linear neurofuzzy models is shown. Using polynomial kernels in local models, better local approximations in prediction of chaotic time series such as Mackey-Glass is achieved, and the capability of the neurofuzzy network is enhanced.