A new belief-based K-nearest neighbor classification method

The K-nearest neighbor (K-NN) classification method originally developed in the probabilistic framework has serious difficulties to classify correctly the close data points (objects) originating from different classes. To cope with such difficult problem and make the classification result more robust to misclassification errors, we propose a new belief-based K-nearest neighbor (BK-NN) method that allows each object to belong both to the specific classes and to the sets of classes with different masses of belief. BK-NN is able to provide a hyper-credal classification on the specific classes, the rejection classes and the meta-classes as well. Thus, the objects hard to classify correctly are automatically committed to a meta-class or to a rejection class, which can reduce the misclassification errors. The basic belief assignment (bba) of each object is defined from the distance between the object and its neighbors and from the acceptance and rejection thresholds. The bba's are combined using a new combination method specially developed for the BK-NN. Several experiments based on simulated and real data sets have been carried out to evaluate the performances of the BK-NN method with respect to several classical K-NN approaches.