{"ddc":["510"],"volume":26,"year":"2024","oa_version":"Published Version","date_published":"2024-08-01T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"file":[{"file_size":8025139,"relation":"main_file","file_id":"17948","date_created":"2024-09-09T09:01:12Z","file_name":"2024_Entropy_Edelsbrunner.pdf","checksum":"624a9e2c5b49d6c38b88b0f675467ba3","content_type":"application/pdf","success":1,"creator":"dernst","access_level":"open_access","date_updated":"2024-09-09T09:01:12Z"}],"abstract":[{"lang":"eng","text":"Abstract\r\nMethods used in topological data analysis naturally capture higher-order interactions in point cloud data embedded in a metric space. This methodology was recently extended to data living in an information space, by which we mean a space measured with an information theoretical distance. One such setting is a finite collection of discrete probability distributions embedded in the probability simplex measured with the relative entropy (Kullback–Leibler divergence). More generally, one can work with a Bregman divergence parameterized by a different notion of entropy. While theoretical algorithms exist for this setup, there is a paucity of implementations for exploring and comparing geometric-topological properties of various information spaces. The interest of this work is therefore twofold. First, we propose the first robust algorithms and software for geometric and topological data analysis in information space. Perhaps surprisingly, despite working with Bregman divergences, our design reuses robust libraries for the Euclidean case. Second, using the new software, we take the first steps towards understanding the geometric-topological structure of these spaces. In particular, we compare them with the more familiar spaces equipped with the Euclidean and Fisher metrics."}],"citation":{"ama":"Edelsbrunner H, Ölsböck K, Wagner H. Understanding higher-order interactions in information space. <i>Entropy</i>. 2024;26(8). doi:<a href=\"https://doi.org/10.3390/e26080637\">10.3390/e26080637</a>","ieee":"H. Edelsbrunner, K. Ölsböck, and H. Wagner, “Understanding higher-order interactions in information space,” <i>Entropy</i>, vol. 26, no. 8. MDPI, 2024.","ista":"Edelsbrunner H, Ölsböck K, Wagner H. 2024. Understanding higher-order interactions in information space. Entropy. 26(8), 637.","short":"H. Edelsbrunner, K. Ölsböck, H. Wagner, Entropy 26 (2024).","mla":"Edelsbrunner, Herbert, et al. “Understanding Higher-Order Interactions in Information Space.” <i>Entropy</i>, vol. 26, no. 8, 637, MDPI, 2024, doi:<a href=\"https://doi.org/10.3390/e26080637\">10.3390/e26080637</a>.","apa":"Edelsbrunner, H., Ölsböck, K., &#38; Wagner, H. (2024). Understanding higher-order interactions in information space. <i>Entropy</i>. MDPI. <a href=\"https://doi.org/10.3390/e26080637\">https://doi.org/10.3390/e26080637</a>","chicago":"Edelsbrunner, Herbert, Katharina Ölsböck, and Hubert Wagner. “Understanding Higher-Order Interactions in Information Space.” <i>Entropy</i>. MDPI, 2024. <a href=\"https://doi.org/10.3390/e26080637\">https://doi.org/10.3390/e26080637</a>."},"language":[{"iso":"eng"}],"type":"journal_article","has_accepted_license":"1","scopus_import":"1","publisher":"MDPI","article_type":"original","date_updated":"2024-09-09T09:05:05Z","related_material":{"link":[{"url":"https://git.ista.ac.at/katharina.oelsboeck/wrap_2_3-public/","relation":"software"}]},"publication":"Entropy","day":"01","status":"public","quality_controlled":"1","acknowledgement":"We thank Anton Nikitenko for first observing that the Wrap complex can be characterized as stated in Claim (ii) of the Wrap Complex Lemma, and Ondrej Draganov for correcting a critical mistake in one of our formulas in Section 2.","intvolume":"        26","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4672-8297","first_name":"Katharina","last_name":"Ölsböck","full_name":"Ölsböck, Katharina"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","last_name":"Wagner","full_name":"Wagner, Hubert"}],"file_date_updated":"2024-09-09T09:01:12Z","publication_identifier":{"eissn":["1099-4300"]},"_id":"17891","external_id":{"pmid":["39202107"]},"article_number":"637","pmid":1,"date_created":"2024-09-08T22:01:11Z","issue":"8","oa":1,"title":"Understanding higher-order interactions in information space","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"08","publication_status":"published","department":[{"_id":"HeEd"}],"doi":"10.3390/e26080637","article_processing_charge":"Yes"}