Combination of Classifiers with Different Frames of Discernment Based on Belief Functions

Classifier fusion remains an effective method to improve classification performance. In applications, the classifiers learnt using different attributes may work with various frames of discernment (FoD) of classification. There generally exist more or less complementary knowledge among these classifiers. However, how to efficiently combine such classifiers under different FoD is a challenging problem. In this article, we propose a new method for classifier fusion with different FoD based on the belief functions, which allow to well represent and deal with uncertain information. The credal transformation rules are developed to map the various FoD into a common one. It allows to transfer the probability (or mass of belief) of one class in the given FoD not only to several singleton classes but also to the metaclasses (i.e., disjunction of several classes) and the ignorance in other chosen FoD according to a transformation matrix, which is estimated based on the training (pairwise) data by minimizing a certain error criteria. Thus, we can well characterize the uncertainty and imprecision during the transformation of FoD. After that, the outputs of different classifiers represented by basic belief assignments (BBAs) can be transformed to a common FoD. Then, the well-known Dempster's rule is employed to combine these transformed BBA to obtain final classification result under the chosen FoD. Several real data sets are used in the experiment to evaluate the performance of the proposed method. Our experimental results show that this new method can efficiently improve the classification accuracy with respect to other related methods.