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 von synthetischen Antihistaminkörpern auf die Senfölchemosis am Kaninchenauge

Summary Intravenous or subcutaneous administration of pyribenzamine and other antihistaminics is able to decrease, and to delay the appearance of chemosis produced by mustard oils in the eye of the rabbit. Simultaneously occurring vascular reactions, on the other hand, are but slightly affected by antihistaminics. Intravenous or subcutaneous administration of rutin has no clear-cut effect on chemosis; it is however able to inhibit the vascular reaction.