A new nonlinear classification model based on cross-oriented Choquet integrals

The nonadditive set function defined on the power set of all considered feature attributes can describe the interaction among the contributions from various feature attributes towards classification. The Choquet integral with respect to nonadditive set functions then is a proper aggregation tool in classifications with a nonlinear classifying boundary. Regarding the Choquet integral as a nonlinear projection from a high-dimensional feature space onto an axis, the current study provides a new nonlinear classification model consisting of two Choquet integrals with a common projection axis. The values of unknown parameters in the new model can be optimally determined via a genetic algorithm when a proper training data set is available. The new model is more powerful than the nonlinear classification model based on only a single Choquet integral and is a generalization of the latter. It is more suitable to be applied in bioinformatics.