Empirical geodesic graphs and CAT(k) metrics for data analysis

Kei Kobayashi, Henry P. Wynn

研究成果: Article査読

4 被引用数 (Scopus)

抄録

A methodology is developed for data analysis based on empirically constructed geodesic metric spaces. For a probability distribution, the length along a path between two points can be defined as the amount of probability mass accumulated along the path. The geodesic, then, is the shortest such path and defines a geodesic metric. Such metrics are transformed in a number of ways to produce parametrised families of geodesic metric spaces, empirical versions of which allow computation of intrinsic means and associated measures of dispersion. These reveal properties of the data, based on geometry, such as those that are difficult to see from the raw Euclidean distances. Examples of application include clustering and classification. For certain parameter ranges, the spaces become CAT(0) spaces and the intrinsic means are unique. In one case, a minimal spanning tree of a graph based on the data becomes CAT(0). In another, a so-called “metric cone” construction allows extension to CAT(k) spaces. It is shown how to empirically tune the parameters of the metrics, making it possible to apply them to a number of real cases.

本文言語English
ページ(範囲)1-18
ページ数18
ジャーナルStatistics and Computing
30
1
DOI
出版ステータスPublished - 2020 2月 1

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • 統計学および確率
  • 統計学、確率および不確実性
  • 計算理論と計算数学

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