A belief classification rule for imprecise data

The classification of imprecise data is a difficult task in general because the different classes can partially overlap. Moreover, the available attributes used for the classification are often insufficient to make a precise discrimination of the objects in the overlapping zones. A credal partition (classification) based on belief functions has already been proposed in the literature for data clustering. It allows the objects to belong (with different masses of belief) not only to the specific classes, but also to the sets of classes called meta-classes which correspond to the disjunction of several specific classes. In this paper, we propose a new belief classification rule (BCR) for the credal classification of uncertain and imprecise data. This new BCR approach reduces the misclassification errors of the objects difficult to classify by the conventional methods thanks to the introduction of the meta-classes. The objects too far from the others are considered as outliers. The basic belief assignment (bba) of an object is computed from the Mahalanobis distance between the object and the center of each specific class. The credal classification of the object is finally obtained by the combination of these bba's associated with the different classes. This approach offers a relatively low computational burden. Several experiments using both artificial and real data sets are presented at the end of this paper to evaluate and compare the performances of this BCR method with respect to other classification methods.