Similarity classifier using similarities based on modified probabilistic equivalence relations

Abstract

This paper examines a classifier based on similarity measures originating from probabilistic equivalence relations with a generalized mean. Equivalences are weighted and weight optimization is carried out with differential evolution algorithms. In the classifier, a similarity measure based on the Łukasiewicz structure has previously been used, but this paper concentrates on measures which can be considered to be weighted similarity measures defined in a probabilistic framework, applied variable by variable and aggregated along the features using a generalized mean. The weights for these measures are determined using a differential evolution process. The classification accuracy with these measures are tested on different data sets. Classification results are obtained with medical data sets, and the results are compared to other classifiers, which gives quite good results. The result presented in this paper are promising, and in several cases better results were achieved.