Improved Topological Approximations by Digitization

Aruni Choudhary, Michael Kerber, Sharath Raghvendra

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Čech complexes are useful simplicial complexes for computing and analyzing topological features of data that lies in Euclidean space. Unfortunately, computing these complexes becomes prohibitively expensive for large-sized data sets even for medium-to-low dimensional data. We present an approximation scheme for (1 + ε)-approximating the topological information of the Čech complexes for n points in Rd, for ε ∈ (0, 1]. Our approximation has a total size of [MATH HERE] for constant dimension d, improving all the currently available (1 + ε)-approximation schemes of simplicial filtrations in Euclidean space. Perhaps counter-intuitively, we arrive at our result by adding additional [MATH HERE] sample points to the input. We achieve a bound that is independent of the spread of the point set by pre-identifying the scales at which the Čech complexes changes and sampling accordingly.
Original languageEnglish
Title of host publicationProceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, California, USA, January 6-9, 2019
Place of PublicationPhiladelphia
PublisherSIAM - Society of Industrial and Applied Mathematics
Pages2675-2688
Publication statusPublished - 2019
Event30th Annual ACM-SIAM Symposium on Discrete Algorithms - San Diego, United States
Duration: 6 Jan 20199 Jan 2019

Conference

Conference30th Annual ACM-SIAM Symposium on Discrete Algorithms
Abbreviated titleSODA '19
CountryUnited States
CitySan Diego
Period6/01/199/01/19

Fields of Expertise

  • Information, Communication & Computing

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