An evidence-theoretic k-NN rule with parameter optimization

This paper presents a learning procedure for optimizing the parameters in the evidence-theoretic k-nearest neighbor rule, a pattern classification method based on the Dempster-Shafer theory of belief functions. In this approach, each neighbor of a pattern to be classified is considered as an item of evidence supporting certain hypotheses concerning the class membership of that pattern. Based on this evidence, basic belief masses are assigned to each subset of the set of classes. Such masses are obtained for each of the k-nearest neighbors of the pattern under consideration and aggregated using the Dempster's rule of combination. In many situations, this method was found experimentally to yield lower error rates than other methods using the same information. However, the problem of tuning the parameters of the classification rule was so far unresolved. In this paper, we determine optimal or near-optimal parameter values from the data by minimizing an error function. This refinement of the original method is shown experimentally to result in substantial improvement of classification accuracy.