Murtagh, Fionn (2007) Hilbert Space Becomes Ultrametric in the High Dimensional Limit: Application to Very High Frequency Data Analysis.
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An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a natural hierarchical embedding. Such hierarchical structure can be global in the data set, or local. By quantifying extent or degree of ultrametricity in a data set, we show that ultrametricity becomes pervasive as dimensionality and/or spatial sparsity increases. This leads us to assert that very highdimensional data are of simple structure. We exemplify this finding through arange of simulated data cases. We discuss also application to very high frequency time series segmentation and modeling.
This is a Submitted version This version's date is: 7/2/2007 This item is not peer reviewed
https://repository.royalholloway.ac.uk/items/db70c337-0242-24f9-6c4b-3a2d03ccad4a/1/
Deposited by Research Information System (atira) on 24-May-2012 in Royal Holloway Research Online.Last modified on 24-May-2012
22 pp., 9 figs., 4 tables