Stable components and layers
Abstract
Component graphs 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 0(F) are the stable components of the array F. The stable components for the system of Lesnick complexes \ Ls,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.
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