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- W1658297171 abstract "Recently, a multi-scale notions of local homology was proposed (Bendich et al) to study the local structure of a stratified space around a given point from a point cloud sample. To give reconstruction guarantees, the approach relied on constructing embedded complexes which become difficult to construct in high dimensions. We derive sampling conditions under which the emph{persistence diagrams} used for estimating local homology, can be approximated using families of Vietoris-Rips complexes, whose simple construction is robust in any dimension. To the best of our knowledge, our results, for the first time, make stratification learning using local homology feasible in high-dimensions." @default.
- W1658297171 created "2016-06-24" @default.
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- W1658297171 date "2012-06-05" @default.
- W1658297171 modified "2023-09-27" @default.
- W1658297171 title "Sampling for Local Homology with Vietoris-Rips Complexes" @default.
- W1658297171 hasPublicationYear "2012" @default.
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