A Graph Theoretic Analysis of Pattern Classification via Tamura´s Fuzzy Relation

Graph theoretical arguments are used to show that the hierarchical clustering scheme induced by Tamura´s N-step fuzzy relation f is contained in the maximal single linkage hierarchy. A method of computing f is proposed, based upon Prim´s algorithm for generating maximal spanning trees and a result reported by Hu on maximal capacity routes in maximal spanning trees. It is shown that this procedure is superior to Tamura´s generalized matrix multiplication algorithm with regard to both computing time and storage requirements.