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- W4283209600 abstract "The natural occurrence of singular spaces in application has led to recent investigations on performing topological data analysis (TDA) in a stratified framework. In many applications, there is no a priori information on what points in a point cloud should be regarded as singular or regular. For this purpose we describe a fully implementable process that provably approximates the stratification for a large class of two-strata Whitney stratified spaces from sufficiently close non-stratified samples. Additionally, we establish a notion of persistent stratified homotopy type obtained from a sample with two strata. In analogy to the use of persistent homology in TDA, which relies on a series of convenient properties of (persistent) homotopy types of sufficiently regular spaces, we show that our persistent stratified homotopy type behaves much like its non-stratified counterpart and exhibits many properties (such as stability, and inference results) necessary for an application in TDA." @default.
- W4283209600 created "2022-06-22" @default.
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- W4283209600 date "2022-06-17" @default.
- W4283209600 modified "2023-09-29" @default.
- W4283209600 title "From Samples to Persistent Stratified Homotopy Types" @default.
- W4283209600 doi "https://doi.org/10.48550/arxiv.2206.08926" @default.
- W4283209600 hasPublicationYear "2022" @default.
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