Improved Topological Approximations by Digitization

Aruni Choudhary, Michael Kerber, Sharath Raghvendra

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem KonferenzbandForschungBegutachtung

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.
Originalspracheenglisch
TitelProceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, California, USA, January 6-9, 2019
ErscheinungsortPhiladelphia
Herausgeber (Verlag)SIAM - Society of Industrial and Applied Mathematics
Seiten2675-2688
PublikationsstatusVeröffentlicht - 2019
Veranstaltung30th Annual ACM-SIAM Symposium on Discrete Algorithms - San Diego, USA / Vereinigte Staaten
Dauer: 6 Jan 20199 Jan 2019

Konferenz

Konferenz30th Annual ACM-SIAM Symposium on Discrete Algorithms
KurztitelSODA '19
LandUSA / Vereinigte Staaten
OrtSan Diego
Zeitraum6/01/199/01/19

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

Fields of Expertise

  • Information, Communication & Computing

Dies zitieren

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 (S. 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. S. 2675-2688.

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem KonferenzbandForschungBegutachtung

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, S. 2675-2688, San Diego, USA / Vereinigte Staaten, 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. S. 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. S. 2675-2688
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