A New Complex-Valued Polynomial Model

Abstract

This paper presents a novel complex-valued polynomial model (CPM) for real-valued prediction and classification problems. In a CPM, function, independent variables and dependent variables are complex-valued. Before CPM optimization, real-valued data need to be converted into complex values. As the linear version of additive tree model, additive expression tree is proposed to optimize the complex-valued structure of CPM. Real parts and imaginary parts of the complex-valued coefficients are encoded into a chromosome and brain storm optimization is utilized to evolve the complex-valued coefficients of CPM. CPM is utilized to predict three financial datasets and classify n-class problems. The prediction results show that CPM presents higher forecasting accuracy than real-valued polynomial model, other real-valued neural networks and ordinary differential equation. The classification performance of CPM is compared with existing methods on IRIS, Liver and Ionosphere datasets. And the results reveal that CPM performs better than well-established and newly proposed real-valued classifiers.