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

@article{Murtagh2009TheRS,
  title={The Remarkable Simplicity of Very High Dimensional Data: Application of Model-Based Clustering},
  author={Fionn Murtagh},
  journal={Journal of Classification},
  year={2009},
  volume={26},
  pages={249-277}
}
  • Fionn Murtagh
  • Published 2009
  • Mathematics, Computer Science
  • Journal of Classification
  • 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… CONTINUE READING

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