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Abstract
We present a new model based on two nonlinear generalized Choquet integral projections for classification. Two signed efficiency measures represent the interaction of the feature attributes. The nonadditivity of the signed efficiency measures reflects the interactions among the feature attributes towards the classification. The generalized Choquet integrals serve as aggregation tools, optimally projecting the feature space onto a real axis by minimizing the misclassification rate. Based on the given training data, the unknown parameters and the values of singed efficiency measures need to be decided. This can be determined by running a genetic algorithm on the given training data. The experiments on real data show encouraging results. This model is applied to learn the scaling requirements of the projection line and the interactions amongst feature attributes. It gives us a better intuitive understanding for the accurate classification.
Here is a summary of this work’s results: (1) Two Choquet integrals are applied with respective signed efficiency measures to enhance the classification power. (2) Based on two Choquet integrals and classification calculation formula, we successfully project the 2-dimensional feature space onto a real axis. Then each point becomes a value of the virtual variable which is optimal with respect to classification. (3) This new model based on two Choquet integrals enhances the classification power by better classifying the data which are hard to be classified by the old models based on one Choquet integral. It is a generalization of the models based on one Choquet integral. (4) A genetic algorithm is applied to search the optimal parameters on a global scale and to keep the well-defined and well-formed ones by fully exploring the geometrical meaning of the parameters in nonlinear integral projections.
