Solving Non-Uniqueness in Agglomerative Hierarchical Clustering Using Multidendrograms

In agglomerative hierarchical clustering, pair-group methods suffer from a problem of non-uniqueness when two or more distances between different clusters coincide during the amalgamation process. The traditional approach for solving this drawback has been to take any arbitrary criterion in order to break ties between distances, which results in different hierarchical classifications depending on the criterion followed. In this article we propose a variable-group algorithm that consists in grouping more than two clusters at the same time when ties occur. We give a tree representation for the results of the algorithm, which we call a multidendrogram, as well as a generalization of the Lance andWilliams’ formula which enables the implementation of the algorithm in a recursive way. The authors thank A. Arenas for discussion and helpful comments. This work was partially supported by DGES of the Spanish Government Project No. FIS2006–13321–C02–02 and by a grant of Universitat Rovira i Virgili.     

Die Wirkung des Toluidinblaus und der Thrombokinase auf den Vorgang der Thrombininaktivierung

Summary The disappearance of thrombin—formed in the blood, or added to serum-follows a manomolecular reaction-type. Heparin increases the reaction-velocity of this thrombin-inactivating process.Our investigation established that toluidine blue or kinase, which, according to the literature, bind heparin, strongly reduce the speed of thrombin-inactivation too. Therefore the heparin-binding capacity of these substances is also manifested in the decrease of thrombin-inactivation.