The Remarkable Simplicity of Very High Dimensional Data: Application of Model-Based Clustering

Details The Remarkable Simplicity of Very High Dimensional Data: Application of Model-Based Clustering The Remarkable Simplicity of Very High Dimensional Data: Application of Model-Based Clustering

2008-05-18

arxiv.org/abs/0805.2756v2

Journal of Classification, 26 (3), 249-277, 2009

Statistics

Methodology

36 pages, 18 figures, 36 references

Scientific paper

10.1007/s00357-009-9037-9

An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a 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 high dimensional data are of simple structure. We exemplify this finding through a range of simulated data cases. We discuss also application to very high frequency time series segmentation and modeling.

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