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arXiv · 0805.2756

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

Fionn Murtagh
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Abstract

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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Fionn Murtagh. 2008-11-16. The Remarkable Simplicity of Very High Dimensional Data: Application of Model-Based Clustering. https://doi.org/10.1007/s00357-009-9037-9

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