Classification of uncertain and imprecise data based on evidence theory

In this paper, we present a new belief c×. K neighbor (BCKN) classifier based on evidence theory for data classification when the available attribute information appears insufficient to correctly classify objects in specific classes. In BCKN, the query object is classified according to its K nearest neighbors in each class, and c×. K neighbors are involved in the BCKN approach (c being the number of classes). BCKN works with the credal classification introduced in the belief function framework. It allows to commit, with different masses of belief, an object not only to a specific class, but also to a set of classes (called meta-class), or eventually to the ignorant class characterizing the outlier. The objects that lie in the overlapping zone of different classes cannot be reasonably committed to a particular class, and that is why such objects will be assigned to the associated meta-class defined by the union of these different classes. Such an approach allows to reduce the misclassification errors at the price of the detriment of the overall classification precision, which is usually preferable in some applications. The objects too far from the others will be naturally considered as outliers. The credal classification is interesting to explore the imprecision of class, and it can also provide a deeper insight into the data structure. The results of several experiments are given and analyzed to illustrate the potential of this new BCKN approach.