Improved Topological Approximations by Digitization

Aruni Choudhary, Michael Kerber, Sharath Raghvendra

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

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

Fingerprint

Digitization
Approximation
Approximation Scheme
Euclidean space
Sample point
Computing
Simplicial Complex
Point Sets
Filtration

Fields of Expertise

  • Information, Communication & Computing

Cite this

Choudhary, A., Kerber, M., & Raghvendra, S. (2019). Improved Topological Approximations by Digitization. In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, California, USA, January 6-9, 2019 (pp. 2675-2688). Philadelphia: SIAM - Society of Industrial and Applied Mathematics.

Improved Topological Approximations by Digitization. / Choudhary, Aruni; Kerber, Michael; Raghvendra, Sharath.

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, California, USA, January 6-9, 2019. Philadelphia : SIAM - Society of Industrial and Applied Mathematics, 2019. p. 2675-2688.

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Choudhary, A, Kerber, M & Raghvendra, S 2019, Improved Topological Approximations by Digitization. in Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, California, USA, January 6-9, 2019. SIAM - Society of Industrial and Applied Mathematics, Philadelphia, pp. 2675-2688, 30th Annual ACM-SIAM Symposium on Discrete Algorithms , San Diego, United States, 6/01/19.
Choudhary A, Kerber M, Raghvendra S. Improved Topological Approximations by Digitization. In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, California, USA, January 6-9, 2019. Philadelphia: SIAM - Society of Industrial and Applied Mathematics. 2019. p. 2675-2688
Choudhary, Aruni ; Kerber, Michael ; Raghvendra, Sharath. / Improved Topological Approximations by Digitization. Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, California, USA, January 6-9, 2019. Philadelphia : SIAM - Society of Industrial and Applied Mathematics, 2019. pp. 2675-2688
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