A new concept of higher-order similarity and the role of distance/similarity measures in local classification methods

•This work presents a new family of distances, (i.e. meta-distances), which take into account higher-order dissimilarities.•Higher-order dissimilarities greatly influence the classical distance measures.•The new meta-distances can allow to reach a significantly improve the performance of classifiers based on local similarity.

In this paper, a new concept of similarity is introduced with the aim of detecting higher-order similarities among objects, and meta-distances and meta-similarities are derived from it. A total of 100 meta-distances were obtained from a set of ten classical distances and were compared, in terms of classification performances, against classical distance measures. Classification methods based on local similarity analysis and several benchmark datasets were used. In several cases, the non-error rate (NER) of classifiers based on the new meta-distances significantly increased with respect to that of the classical Euclidean distance.