Ultrametricity of dissimilarity spaces and its significance for data mining

Abstract

We introduce a measure of ultrametricity for dissimilarity spaces and examine transformations of dissimilarities that impact this measure. Then, we study the influence of ultrametricity on the behavior of two classes of data mining algorithms (kNN classification and PAM clustering) applied on dissimilarity spaces.We show that there is an inverse variation between ultrametricity and performance of classifiers. For clustering, increased ultrametricity generate clusterings with better separation. Lowering ultrametricity produces more compact clusters.