Classification of incomplete patterns based on the fusion of belief functions

The influence of the missing values in the classification of incomplete pattern mainly depends on the context. In this paper, we present a fast classification method for incomplete pattern based on the fusion of belief functions where the missing values are selectively (adaptively) estimated. At first, it is assumed that the missing information is not crucial for the classification, and the object (incomplete pattern) is classified based only on the available attribute values. However, if the object cannot be clearly classified, it implies that the missing values play an important role to obtain an accurate classification. In this case, the missing values will be imputed based on the K-nearest neighbor (K-NN) and self-organizing map (SOM) techniques, and the edited pattern with the imputation is then classified. The (original or edited) pattern is respectively classified according to each training class, and the classification results represented by basic belief assignments (BBA's) are fused with proper combination rules for making the credal classification. The object is allowed to belong with different masses of belief to the specific classes and meta-classes (i.e. disjunctions of several single classes). This credal classification captures well the uncertainty and imprecision of classification, and reduces effectively the rate of misclassifications thanks to the introduction of meta-classes. The effectiveness of the proposed method with respect to other classical methods is demonstrated based on several experiments using artificial and real data sets.