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Identifying the ultrametricity of time series

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  • F. Murtagh

Abstract

High dimensional, sparsely populated data spaces have been characterized in terms of ultrametric topology. There are natural, not necessarily unique, tree or hierarchy structures defined by the ultrametric topology. Once such a structure is known, and can be defined, there are various implications including the feasibility of improved computational complexity for operations such as nearest neighbor searching. In this work, we consider the case where the data under investigation is temporal data, in the form of a time series. We develop an approach to characterizing how well time series data can be embedded in an ultrametric topology. Possible applications of this work include: (i) unique fingerprinting of a time series; (ii) discriminating between time series from various domains; and (iii) if data are inherently hierarchical, then using such hierarchies to model and predict. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Suggested Citation

  • F. Murtagh, 2005. "Identifying the ultrametricity of time series," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 43(4), pages 573-579, February.
  • Handle: RePEc:spr:eurphb:v:43:y:2005:i:4:p:573-579
    DOI: 10.1140/epjb/e2005-00092-8
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    Cited by:

    1. A. P. Zubarev, 2017. "On the Ultrametric Generated by Random Distribution of Points in Euclidean Spaces of Large Dimensions with Correlated Coordinates," Journal of Classification, Springer;The Classification Society, vol. 34(3), pages 366-383, October.
    2. Fionn Murtagh, 2009. "The Remarkable Simplicity of Very High Dimensional Data: Application of Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 26(3), pages 249-277, December.

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