Extended k-Nearest Neighbours based on Evidence Theory

An evidence theoretic classification method is proposed in this paper. In order to classify a pattern we consider its neighbours, which are taken as parts of a single source of evidence to support the class membership of the pattern. A single mass function or basic belief assignment is then derived, and the belief function and the pignistic (“betting rates”) probability function can be calculated. Then the (posterior) conditional pignistic probability function is calculated and used to decide the class label for the pattern. It is shown that such a classifier extends the standard majority voting based k-nearest neighbour classifier, and it is an approximation to the optimal Bayes classifier. In experiments this classifier performed as well as or better than the voting and distance weighted k-nearest neighbours classifiers with best k, and its performance became stable when the number of neighbours considered is greater than 4.