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.     

Polarized Emission of Molecular Film With Lanthanide (Ⅲ) Complex

1 Results In the coordination system by using complexation with organic ligand, the ff emission of lanthanide(Ⅲ) (Ln(Ⅲ)) is induced the excitation energy transfer form the organic chromophore under the light-irradiation. However, there are not so much number of reports to discuss the energy relaxation mechanism in such complexes with Ln(Ⅲ). Recently, we succeeded firstly to estimate the rate constant of the energy transfer between the ligand and Ln(Ⅲ) in Pr(Ⅲ)-phenanthroline analogs[1]. Here, we will di...