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Canadian Mathematical Bulletin Canadian Mathematical Bulletin

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Stable Components and Layers

Part of: Multivariate analysis Applied homological algebra and category theory Discrete mathematics in relation to computer science

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
Corresponding
E-mail address:
jardine@uwo.ca
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Abstract

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

cluster graph stable component layer

MSC classification

Primary: 55U10: Simplicial sets and complexes
Secondary: 68R10: Graph theory (including graph drawing) 62H30: Classification and discrimination; cluster analysis
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 3 , September 2020 , pp. 562 - 576
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Copyright
© Canadian Mathematical Society 2019

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Footnotes

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

References

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