Polynomial nonlinear integrals

Abstract

Nonlinear Integrals is a useful integration tool. It can get a set of virtual values by projecting original data to a virtual space using Nonlinear Integrals. The classical Nonlinear Integrals implement projection along with a line with respect to the attributes. But in many cases the linear projection is not applicable to achieve better performance for classification or regression. In this paper, we propose a generalized Nonlinear Integrals-Polynomial Nonlinear Integrals(PNI). A polynomial function with respect to the attributes is used as the integrand of Nonlinear Integrals. It makes the projection being along different kinds of curves to the virtual space, so that the virtual values gotten by Nonlinear Integrals can be more regularized well and better to deal with. For testing the capability of the Polynomial Nonlinear Integrals, we apply the Polynomial Nonlinear Integrals to classification on some real datasets. Due to limitation of computational complexity, we take feature selection method studied in another our paper to do preprocessing. We select the value of the highest power of polynomial from 1 to 5 to observe the change of performance of PNI and the effect of the highest power. Experiments show that there is evident advancement of performance for PNI compared to classical NI and the performance is not definitely rising as the highest power is increased. © 2008 Springer-Verlag Berlin Heidelberg.