Types of (dis-)similarities and adaptive mixtures thereof for improved classification learning

In this paper, we introduce taxonomies for similarity and dissimilarity measures, respectively, based on their mathematical properties. Further, we propose a definition for rank equivalence of (dis)similarities regarding given data for prototype based methods. Starting with this definition we provide a measure to judge the degree of equivalence, which can be used to compare respective measures as well as to consider the influence of data preprocessing regarding a single (dis)similarity measure. In the last part of the paper an adaptive mixture approach of (dis)similarity measures for improved classification learning is presented.