Abstract
The weakly indexed paired-hierarchies (shortly, p-hierarchies) provide a clustering model that allows overlapping clusters and extends the hierarchical model. There exists a bijection between weakly indexed p-hierarchies and the so-called paired-ultrametrics (shortly, p-ultrametrics), this correspondence being a restriction of the bijection between weakly indexed pyramids and Robinsonian dissimilarities. This paper proposes a generalization of the well-known HAC clustering method to compute a weakly indexed p-hierarchy from a given dissimilarity d. Moreover, the p-ultrametric associated to such a weakly indexed p-hierarchy is proved to be lower-maximal for d and larger than the sub-dominant ultrametric of d.
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Bertrand, P., Brucker, F. (2007). On Lower-Maximal Paired-Ultrametrics. In: Brito, P., Cucumel, G., Bertrand, P., de Carvalho, F. (eds) Selected Contributions in Data Analysis and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73560-1_42
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DOI: https://doi.org/10.1007/978-3-540-73560-1_42
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