Using generalized choquet integral in projection pursuit based classification

Abstract

A generalized Choquet integral with respect to a nonadditive sign measure is proposed, and serves as an aggregation tool to project the points of feature space onto a real axis to reduce an n-dimensional classification problem into a one-dimensional classification problem. The learning procedure of this new classification algorithm, GCIPP (Generalized Choquet Integral based Projection Pursuit), is just pursuing an appropriate projection direction optimally according to a criterion of minimizing the global misclassification rate. Such a nonlinear projection is characterized by the nonadditive sign measure and two weight vectors. The nonadditive sign measure is a proper representation of the contribution rate of each combination of the feature attributes, including each singleton, toward the classification, and its nonadditivity reflects the interactions among the feature attributes. Optimizing the sign measures and the weights is realized by an adaptive genetic algorithm. This new classifier is successfully tested on some simulated training data generated from the preset sign measures and weights, and it also performs well on several real-world data sets.