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Stable Components and Layers

Part of:Applied homological algebra and category theoryDiscrete mathematics in relation to computer scienceMultivariate analysis

Published online by Cambridge University Press:  23 October 2019

J. F. Jardine
J. F. Jardine*
Affiliation:
Department of Mathematics, University of Western Ontario, London, Ontario Email: jardine@uwo.ca
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Abstract

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Component graphs $\unicode[STIX]{x1D6E4}_{0}(F)$ are defined for arrays of sets $F$, and, in particular, for arrays of path components for Vietoris–Rips complexes and Lesnick complexes. The path components of $\unicode[STIX]{x1D6E4}_{0}(F)$ are the stable components of the array $F$. The stable components for the system of Lesnick complexes $\{L_{s,k}(X)\}$ for a finite data set $X$ decompose into layers, which are themselves path components of a graph. Combinatorial scoring functions are defined for layers and stable components.

Keywords

clustergraphstable componentlayer

MSC classification

Primary:55U10: Simplicial sets and complexes
Secondary:68R10: Graph theory (including graph drawing)62H30: Classification and discrimination; cluster analysis

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 3 , September 2020, pp. 562 - 576
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Copyright
© Canadian Mathematical Society 2019

Footnotes

This research was partially supported by the Natural Sciences and Engineering Research Council of Canada.

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