Pattern classification with missing data using belief functions

The missing data in incomplete pattern can have different estimations, and the classification result of pattern with different estimations may be quite distinct. Such uncertainty (ambiguity) of classification is mainly caused by the loss of information in missing data. A new prototype-based credal classification (PCC) method is proposed to classify incomplete patterns using belief functions. The class prototypes obtained by the training data are respectively used to estimate the missing values. Typically, in a c-class problem, one has to deal with c prototypes which yields c estimations. The different edited patterns based on each possible estimation are then classified by a standard classifier and one can get c classification results for an incomplete pattern. Because all these classification results are potentially admissible, they are fused altogether to obtain the credal classification of the incomplete pattern. A new credal combination method is introduced for solving the classification problem, and it is able to characterize the inherent uncertainty due to the possible conflicting results delivered by the different estimations of missing data. The incomplete patterns that are hard to correctly classify will be reasonably committed to some proper meta-classes by PCC method in order to reduce the misclassification rate. The use and potential of PCC method is illustrated through several experiments with artificial and real data sets.