Murtagh, Fionn (2004) Quantifying ultrametricity In: Compstat 2004: Proceedings in Computational Statistics. Springer-Verlag, Berlin.
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The ultrametric properties of hierarchic clustering are well-known. In recent years, there has been interest in ultrametric properties found in statistical mechanics, optimization theory, and physics. It has been shown that sparse, high-dimensional spaces tend to be ultrametric. Given the pervasiveness of ultrametricity, it is important to be able to quantify how close given metric data are to being ultrametric. In this article we assess previously used coefficients of ultrametricity. We present a new coefficient of ultrametricity, and exemplify its properties experimentally. Our immediate objective in this work is to show that sparse, high-dimensional spaces, that are typical of many new data analysis problems in such areas as genomics and proteomics, and speech, tend to be inherently ultrametric.
This is a Published version This version's date is: 2004 This item is not peer reviewed
https://repository.royalholloway.ac.uk/items/88e7c7bd-31b3-446d-64c4-e88c42246d55/1/
Deposited by () on 23-Dec-2009 in Royal Holloway Research Online.Last modified on 23-Dec-2009