--- _id: '6648' abstract: - lang: eng text: "Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability distribution as a point in the standard simplex of the appropriate dimension, we can understand collections of such objects in geometric and topological terms. Importantly, instead of using the standard Euclidean distance, we look into dissimilarity measures with information-theoretic justification, and we develop the theory\r\nneeded for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable the usage of existing computational topology software in this context." alternative_title: - LIPIcs author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Ziga full_name: Virk, Ziga last_name: Virk - first_name: Hubert full_name: Wagner, Hubert id: 379CA8B8-F248-11E8-B48F-1D18A9856A87 last_name: Wagner citation: ama: 'Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information space. In: 35th International Symposium on Computational Geometry. Vol 129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:31:1-31:14. doi:10.4230/LIPICS.SOCG.2019.31' apa: 'Edelsbrunner, H., Virk, Z., & Wagner, H. (2019). Topological data analysis in information space. In 35th International Symposium on Computational Geometry (Vol. 129, p. 31:1-31:14). Portland, OR, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.SOCG.2019.31' chicago: Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data Analysis in Information Space.” In 35th International Symposium on Computational Geometry, 129:31:1-31:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPICS.SOCG.2019.31. ieee: H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information space,” in 35th International Symposium on Computational Geometry, Portland, OR, United States, 2019, vol. 129, p. 31:1-31:14. ista: 'Edelsbrunner H, Virk Z, Wagner H. 2019. Topological data analysis in information space. 35th International Symposium on Computational Geometry. SoCG 2019: Symposium on Computational Geometry, LIPIcs, vol. 129, 31:1-31:14.' mla: Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.” 35th International Symposium on Computational Geometry, vol. 129, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 31:1-31:14, doi:10.4230/LIPICS.SOCG.2019.31. short: H. Edelsbrunner, Z. Virk, H. Wagner, in:, 35th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 31:1-31:14. conference: end_date: 2019-06-21 location: Portland, OR, United States name: 'SoCG 2019: Symposium on Computational Geometry' start_date: 2019-06-18 date_created: 2019-07-17T10:36:09Z date_published: 2019-06-01T00:00:00Z date_updated: 2021-01-12T08:08:23Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.4230/LIPICS.SOCG.2019.31 external_id: arxiv: - '1903.08510' file: - access_level: open_access checksum: 8ec8720730d4c789bf7b06540f1c29f4 content_type: application/pdf creator: dernst date_created: 2019-07-24T06:40:01Z date_updated: 2020-07-14T12:47:35Z file_id: '6666' file_name: 2019_LIPICS_Edelsbrunner.pdf file_size: 1355179 relation: main_file file_date_updated: 2020-07-14T12:47:35Z has_accepted_license: '1' intvolume: ' 129' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 31:1-31:14 project: - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: 35th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959771047' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: 1 status: public title: Topological data analysis in information space tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 129 year: '2019' ...