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DAM
2006

Sub-dominant theory in numerical taxonomy

13 years 11 months ago
Sub-dominant theory in numerical taxonomy
Sub-dominant theory provides efficient tools for clustering. However it classically works only for ultrametrics and ad hoc extensions like Jardine and Sibson's 2ultrametrics. In this paper we study the extension of the notion of sub-dominant to other distance models in classification accounting for overlapping clusters. We prove that a given dissimilarity admits one and only one lower-maximal quasiultrametric and one and only one lower-maximal weak k-ultrametric. In addition, we also prove the existence of (several) lower-maximal strongly Robinsonian dissimilarities. The construction of the lower-maximal weak k-ultrametric (for k = 2) and quasi-ultrametric can be performed in polynomial time. Key words: dissimilarity, sub-dominant, quasi-ultrametric, strongly Robinsonian dissimilarities
François Brucker
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where DAM
Authors François Brucker
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