Ultrametricity of Dissimilarity Spaces and Its Significance for Data Mining

Dan A. Simovici, Rosanne Vetro, Kaixun Hua

Abstract: We introduce a measureHua, Kaixun of ultrametricitySimovici, Dan A. for dissimilarityVetro, Rosanne 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.