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• W2964207424 abstract "Recently, multi-scale notions of local homology (a variant of persistent homology) have been used to study the local structure of spaces around a given point from a point cloud sample. Current reconstruction guarantees rely on constructing embedded complexes which become difficult to construct in higher dimensions. We show that the persistence diagrams used for estimating local homology can be approximated using families of Vietoris-Rips complexes, whose simpler construction are robust in any dimension. To the best of our knowledge, our results, for the first time make applications based on local homology, such as stratification learning, feasible in high dimensions." @default.
• W2964207424 created "2019-07-30" @default.
• W2964207424 creator A5020383361 @default.
• W2964207424 creator A5049296186 @default.
• W2964207424 date "2014-01-05" @default.
• W2964207424 modified "2023-09-28" @default.
• W2964207424 title "Approximating local homology from samples" @default.
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• W2964207424 doi "https://doi.org/10.5555/2634074.2634087" @default.
• W2964207424 hasPublicationYear "2014" @default.
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