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.     

The humoral immune response to heat shock proteins.

Humoral immune reactions to heat shock proteins (hsp) from microorganisms are one aspect of microbial infections in humans. The production of antibodies which are specific to epitopes present on procaryotic hsp leads also to the appearance of cross-reactive serum antibodies in the host organism that react with human hsp. This article discusses the consequences of such autoreactive antibodies for the host in context with the development of immune tolerance and autoimmune diseases, especially rheumatoid arthritis (RA), and in experimental animal models for arthritis such as adjuvant arthritis in rats. On the basis of epitope cross-reactivity between hsp and other host proteins, a hypothesis is presented for the development of autoimmune disease following the production of hsp-specific antibodies.