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Wagner, Journal of Computational Geometry 11 (2020) 162–182.","chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data Analysis in Information Space.” Journal of Computational Geometry. Carleton University, 2020. https://doi.org/10.20382/jocg.v11i2a7.","ista":"Edelsbrunner H, Virk Z, Wagner H. 2020. Topological data analysis in information space. Journal of Computational Geometry. 11(2), 162–182."},"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"id":"2E36B656-F248-11E8-B48F-1D18A9856A87","first_name":"Ziga","full_name":"Virk, Ziga","last_name":"Virk"},{"first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","full_name":"Wagner, Hubert"}],"article_processing_charge":"Yes","title":"Topological data analysis in information space","acknowledgement":"This research is partially supported by the Office of Naval Research, through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","publisher":"Carleton University","quality_controlled":"1","oa":1,"has_accepted_license":"1","year":"2020","day":"14","publication":"Journal of Computational Geometry","page":"162-182","doi":"10.20382/jocg.v11i2a7","date_published":"2020-12-14T00:00:00Z","date_created":"2021-07-04T22:01:26Z","_id":"9630","article_type":"original","type":"journal_article","tmp":{"short":"CC BY (3.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)"},"status":"public","date_updated":"2021-08-11T12:26:34Z","ddc":["510","000"],"file_date_updated":"2021-08-11T11:55:11Z","department":[{"_id":"HeEd"}],"abstract":[{"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 needed 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.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"12","intvolume":" 11","publication_identifier":{"eissn":["1920180X"]},"publication_status":"published","file":[{"date_created":"2021-08-11T11:55:11Z","file_name":"2020_JournalOfComputationalGeometry_Edelsbrunner.pdf","date_updated":"2021-08-11T11:55:11Z","file_size":1449234,"creator":"asandaue","checksum":"f02d0b2b3838e7891a6c417fc34ffdcd","file_id":"9882","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"issue":"2","volume":11,"license":"https://creativecommons.org/licenses/by/3.0/"},{"department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:47:35Z","ddc":["510"],"date_updated":"2021-01-12T08:08:23Z","status":"public","conference":{"name":"SoCG 2019: Symposium on Computational Geometry","end_date":"2019-06-21","location":"Portland, OR, United States","start_date":"2019-06-18"},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"conference","_id":"6648","license":"https://creativecommons.org/licenses/by/4.0/","volume":129,"language":[{"iso":"eng"}],"file":[{"creator":"dernst","date_updated":"2020-07-14T12:47:35Z","file_size":1355179,"date_created":"2019-07-24T06:40:01Z","file_name":"2019_LIPICS_Edelsbrunner.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"6666","checksum":"8ec8720730d4c789bf7b06540f1c29f4"}],"publication_status":"published","publication_identifier":{"isbn":["9783959771047"]},"intvolume":" 129","month":"06","scopus_import":1,"alternative_title":["LIPIcs"],"oa_version":"Published Version","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."}],"title":"Topological data analysis in information space","external_id":{"arxiv":["1903.08510"]},"author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Virk","full_name":"Virk, Ziga","first_name":"Ziga"},{"first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Hubert","last_name":"Wagner"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","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","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","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.","ieee":"H. Edelsbrunner, Z. Virk, and H. 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We compare CMB maps observed by the Planck satellite with a thousand simulated maps generated according to the ΛCDM paradigm with Gaussian distributed fluctuations. The comparison is multi-scale, being performed on a sequence of degraded maps with mean pixel separation ranging from 0.05 to 7.33°. The survey of the CMB over 𝕊2 is incomplete due to obfuscation effects by bright point sources and other extended foreground objects like our own galaxy. To deal with such situations, where analysis in the presence of “masks” is of importance, we introduce the concept of relative homology. The parametric χ2-test shows differences between observations and simulations, yielding p-values at percent to less than permil levels roughly between 2 and 7°, with the difference in the number of components and holes peaking at more than 3σ sporadically at these scales. The highest observed deviation between the observations and simulations for b0 and b1 is approximately between 3σ and 4σ at scales of 3–7°. There are reports of mildly unusual behaviour of the Euler characteristic at 3.66° in the literature, computed from independent measurements of the CMB temperature fluctuations by Planck’s predecessor, the Wilkinson Microwave Anisotropy Probe (WMAP) satellite. The mildly anomalous behaviour of the Euler characteristic is phenomenologically related to the strongly anomalous behaviour of components and holes, or the zeroth and first Betti numbers, respectively. Further, since these topological descriptors show consistent anomalous behaviour over independent measurements of Planck and WMAP, instrumental and systematic errors may be an unlikely source. These are also the scales at which the observed maps exhibit low variance compared to the simulations, and approximately the range of scales at which the power spectrum exhibits a dip with respect to the theoretical model. Non-parametric tests show even stronger differences at almost all scales. Crucially, Gaussian simulations based on power-spectrum matching the characteristics of the observed dipped power spectrum are not able to resolve the anomaly. Understanding the origin of the anomalies in the CMB, whether cosmological in nature or arising due to late-time effects, is an extremely challenging task. Regardless, beyond the trivial possibility that this may still be a manifestation of an extreme Gaussian case, these observations, along with the super-horizon scales involved, may motivate the study of primordial non-Gaussianity. Alternative scenarios worth exploring may be models with non-trivial topology, including topological defect models."}],"oa_version":"Published Version","author":[{"last_name":"Pranav","full_name":"Pranav, Pratyush","first_name":"Pratyush"},{"last_name":"Adler","full_name":"Adler, Robert J.","first_name":"Robert J."},{"first_name":"Thomas","full_name":"Buchert, Thomas","last_name":"Buchert"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Bernard J.T.","last_name":"Jones","full_name":"Jones, Bernard J.T."},{"full_name":"Schwartzman, Armin","last_name":"Schwartzman","first_name":"Armin"},{"first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","full_name":"Wagner, Hubert"},{"first_name":"Rien","last_name":"Van De Weygaert","full_name":"Van De Weygaert, Rien"}],"external_id":{"isi":["000475839300003"],"arxiv":["1812.07678"]},"article_processing_charge":"No","title":"Unexpected topology of the temperature fluctuations in the cosmic microwave background","citation":{"ista":"Pranav P, Adler RJ, Buchert T, Edelsbrunner H, Jones BJT, Schwartzman A, Wagner H, Van De Weygaert R. 2019. Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. 627, A163.","chicago":"Pranav, Pratyush, Robert J. Adler, Thomas Buchert, Herbert Edelsbrunner, Bernard J.T. Jones, Armin Schwartzman, Hubert Wagner, and Rien Van De Weygaert. “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.” Astronomy and Astrophysics. EDP Sciences, 2019. https://doi.org/10.1051/0004-6361/201834916.","short":"P. Pranav, R.J. Adler, T. Buchert, H. Edelsbrunner, B.J.T. Jones, A. Schwartzman, H. Wagner, R. Van De Weygaert, Astronomy and Astrophysics 627 (2019).","ieee":"P. Pranav et al., “Unexpected topology of the temperature fluctuations in the cosmic microwave background,” Astronomy and Astrophysics, vol. 627. EDP Sciences, 2019.","ama":"Pranav P, Adler RJ, Buchert T, et al. Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. 2019;627. doi:10.1051/0004-6361/201834916","apa":"Pranav, P., Adler, R. J., Buchert, T., Edelsbrunner, H., Jones, B. J. T., Schwartzman, A., … Van De Weygaert, R. (2019). Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. EDP Sciences. https://doi.org/10.1051/0004-6361/201834916","mla":"Pranav, Pratyush, et al. “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.” Astronomy and Astrophysics, vol. 627, A163, EDP Sciences, 2019, doi:10.1051/0004-6361/201834916."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"grant_number":"M62909-18-1-2038","name":"Toward Computational Information Topology","_id":"265683E4-B435-11E9-9278-68D0E5697425"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"article_number":"A163","doi":"10.1051/0004-6361/201834916","date_published":"2019-07-17T00:00:00Z","date_created":"2019-08-04T21:59:18Z","has_accepted_license":"1","isi":1,"year":"2019","day":"17","publication":"Astronomy and Astrophysics","publisher":"EDP Sciences","quality_controlled":"1","oa":1},{"oa":1,"quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","acknowledgement":"This research is partially supported by the Office of Naval Research, through grant no. 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I02979-N35 of the Austrian Science Fund","date_created":"2018-12-11T11:45:05Z","doi":"10.4230/LIPIcs.SoCG.2018.35","date_published":"2018-06-11T00:00:00Z","page":"35:1 - 35:13","day":"11","year":"2018","has_accepted_license":"1","project":[{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"title":"Smallest enclosing spheres and Chernoff points in Bregman geometry","publist_id":"7733","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"first_name":"Ziga","last_name":"Virk","full_name":"Virk, Ziga"},{"last_name":"Wagner","full_name":"Wagner, Hubert","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Edelsbrunner, Herbert, et al. Smallest Enclosing Spheres and Chernoff Points in Bregman Geometry. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13, doi:10.4230/LIPIcs.SoCG.2018.35.","short":"H. Edelsbrunner, Z. Virk, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13.","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Smallest enclosing spheres and Chernoff points in Bregman geometry,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99, p. 35:1-35:13.","apa":"Edelsbrunner, H., Virk, Z., & Wagner, H. (2018). Smallest enclosing spheres and Chernoff points in Bregman geometry (Vol. 99, p. 35:1-35:13). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.35","ama":"Edelsbrunner H, Virk Z, Wagner H. Smallest enclosing spheres and Chernoff points in Bregman geometry. In: Vol 99. 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Focusing on Bregman divergences to measure dissimilarity, we prove bounds on the location of the center of a smallest enclosing sphere. These bounds depend on the range of radii for which Bregman balls are convex.","lang":"eng"}],"volume":99,"language":[{"iso":"eng"}],"file":[{"date_created":"2018-12-17T16:31:31Z","file_name":"2018_LIPIcs_Edelsbrunner.pdf","date_updated":"2020-07-14T12:45:20Z","file_size":489080,"creator":"dernst","checksum":"7509403803b3ac1aee94bbc2ad293d21","file_id":"5724","content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"publication_status":"published","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2018-06-14","location":"Budapest, Hungary","start_date":"2018-06-11"},"type":"conference","_id":"188","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:45:20Z","ddc":["000"],"date_updated":"2021-01-12T06:53:48Z"},{"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","oa":1,"page":"391-3916","doi":"10.4230/LIPIcs.SoCG.2017.39","date_published":"2017-06-01T00:00:00Z","date_created":"2018-12-11T11:47:56Z","has_accepted_license":"1","year":"2017","day":"01","publist_id":"7021","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","last_name":"Wagner","full_name":"Wagner, Hubert"}],"title":"Topological data analysis with Bregman divergences","citation":{"short":"H. Edelsbrunner, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916.","ieee":"H. Edelsbrunner and H. Wagner, “Topological data analysis with Bregman divergences,” presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia, 2017, vol. 77, pp. 391–3916.","ama":"Edelsbrunner H, Wagner H. Topological data analysis with Bregman divergences. In: Vol 77. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017:391-3916. doi:10.4230/LIPIcs.SoCG.2017.39","apa":"Edelsbrunner, H., & Wagner, H. (2017). Topological data analysis with Bregman divergences (Vol. 77, pp. 391–3916). Presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2017.39","mla":"Edelsbrunner, Herbert, and Hubert Wagner. Topological Data Analysis with Bregman Divergences. Vol. 77, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916, doi:10.4230/LIPIcs.SoCG.2017.39.","ista":"Edelsbrunner H, Wagner H. 2017. Topological data analysis with Bregman divergences. Symposium on Computational Geometry, SoCG, LIPIcs, vol. 77, 391–3916.","chicago":"Edelsbrunner, Herbert, and Hubert Wagner. “Topological Data Analysis with Bregman Divergences,” 77:391–3916. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. https://doi.org/10.4230/LIPIcs.SoCG.2017.39."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","alternative_title":["LIPIcs"],"scopus_import":1,"month":"06","intvolume":" 77","abstract":[{"text":"We show that the framework of topological data analysis can be extended from metrics to general Bregman divergences, widening the scope of possible applications. Examples are the Kullback - Leibler divergence, which is commonly used for comparing text and images, and the Itakura - Saito divergence, popular for speech and sound. In particular, we prove that appropriately generalized čech and Delaunay (alpha) complexes capture the correct homotopy type, namely that of the corresponding union of Bregman balls. Consequently, their filtrations give the correct persistence diagram, namely the one generated by the uniformly growing Bregman balls. Moreover, we show that unlike the metric setting, the filtration of Vietoris-Rips complexes may fail to approximate the persistence diagram. We propose algorithms to compute the thus generalized čech, Vietoris-Rips and Delaunay complexes and experimentally test their efficiency. Lastly, we explain their surprisingly good performance by making a connection with discrete Morse theory. ","lang":"eng"}],"oa_version":"Published Version","volume":77,"publication_identifier":{"issn":["18688969"]},"publication_status":"published","file":[{"checksum":"067ab0cb3f962bae6c3af6bf0094e0f3","file_id":"4856","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"IST-2017-895-v1+1_LIPIcs-SoCG-2017-39.pdf","date_created":"2018-12-12T10:11:03Z","creator":"system","file_size":990546,"date_updated":"2020-07-14T12:47:42Z"}],"language":[{"iso":"eng"}],"type":"conference","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"conference":{"location":"Brisbane, Australia","end_date":"2017-07-07","start_date":"2017-07-04","name":"Symposium on Computational Geometry, SoCG"},"status":"public","pubrep_id":"895","_id":"688","file_date_updated":"2020-07-14T12:47:42Z","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"date_updated":"2021-01-12T08:09:26Z","ddc":["514","516"]},{"date_created":"2018-12-11T11:51:59Z","date_published":"2017-01-01T00:00:00Z","doi":"10.1016/j.jsc.2016.03.008","page":"76 - 90","publication":"Journal of Symbolic Computation","day":"01","year":"2017","isi":1,"oa":1,"publisher":"Academic Press","quality_controlled":"1","title":"Phat - Persistent homology algorithms toolbox","article_processing_charge":"No","external_id":{"isi":["000384396000005"]},"author":[{"first_name":"Ulrich","full_name":"Bauer, Ulrich","last_name":"Bauer"},{"first_name":"Michael","last_name":"Kerber","full_name":"Kerber, Michael"},{"first_name":"Jan","last_name":"Reininghaus","full_name":"Reininghaus, Jan"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","full_name":"Wagner, Hubert","last_name":"Wagner"}],"publist_id":"5765","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Bauer, Ulrich, et al. “Phat - Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation, vol. 78, Academic Press, 2017, pp. 76–90, doi:10.1016/j.jsc.2016.03.008.","ieee":"U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “Phat - Persistent homology algorithms toolbox,” Journal of Symbolic Computation, vol. 78. Academic Press, pp. 76–90, 2017.","short":"U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, Journal of Symbolic Computation 78 (2017) 76–90.","apa":"Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2017). Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. Academic Press. https://doi.org/10.1016/j.jsc.2016.03.008","ama":"Bauer U, Kerber M, Reininghaus J, Wagner H. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 2017;78:76-90. doi:10.1016/j.jsc.2016.03.008","chicago":"Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “Phat - Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation. Academic Press, 2017. https://doi.org/10.1016/j.jsc.2016.03.008.","ista":"Bauer U, Kerber M, Reininghaus J, Wagner H. 2017. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 78, 76–90."},"project":[{"name":"Topological Complex Systems","grant_number":"318493","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"ec_funded":1,"related_material":{"record":[{"id":"10894","status":"public","relation":"earlier_version"}]},"volume":78,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":[" 07477171"]},"intvolume":" 78","month":"01","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.jsc.2016.03.008"}],"scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"Phat is an open-source C. ++ library for the computation of persistent homology by matrix reduction, targeted towards developers of software for topological data analysis. We aim for a simple generic design that decouples algorithms from data structures without sacrificing efficiency or user-friendliness. We provide numerous different reduction strategies as well as data types to store and manipulate the boundary matrix. We compare the different combinations through extensive experimental evaluation and identify optimization techniques that work well in practical situations. We also compare our software with various other publicly available libraries for persistent homology.","lang":"eng"}],"department":[{"_id":"HeEd"}],"date_updated":"2023-09-20T09:42:40Z","status":"public","type":"journal_article","article_type":"original","_id":"1433"},{"department":[{"_id":"HeEd"}],"date_updated":"2023-09-26T16:10:03Z","status":"public","type":"conference","conference":{"location":"Ystad, Sweden","end_date":"2017-08-24","start_date":"2017-08-22","name":"CAIP: Computer Analysis of Images and Patterns"},"_id":"833","volume":10424,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["03029743"]},"publication_status":"published","month":"07","intvolume":" 10424","scopus_import":"1","alternative_title":["LNCS"],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.02045"}],"oa_version":"Submitted Version","abstract":[{"text":"We present an efficient algorithm to compute Euler characteristic curves of gray scale images of arbitrary dimension. In various applications the Euler characteristic curve is used as a descriptor of an image. Our algorithm is the first streaming algorithm for Euler characteristic curves. The usage of streaming removes the necessity to store the entire image in RAM. Experiments show that our implementation handles terabyte scale images on commodity hardware. Due to lock-free parallelism, it scales well with the number of processor cores. Additionally, we put the concept of the Euler characteristic curve in the wider context of computational topology. In particular, we explain the connection with persistence diagrams.","lang":"eng"}],"editor":[{"full_name":"Felsberg, Michael","last_name":"Felsberg","first_name":"Michael"},{"last_name":"Heyden","full_name":"Heyden, Anders","first_name":"Anders"},{"last_name":"Krüger","full_name":"Krüger, Norbert","first_name":"Norbert"}],"title":"Streaming algorithm for Euler characteristic curves of multidimensional images","author":[{"last_name":"Heiss","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","first_name":"Teresa"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","full_name":"Wagner, Hubert","last_name":"Wagner"}],"publist_id":"6815","article_processing_charge":"No","external_id":{"isi":["000432085900032"]},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Heiss, Teresa, and Hubert Wagner. “Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images.” edited by Michael Felsberg, Anders Heyden, and Norbert Krüger, 10424:397–409. Springer, 2017. https://doi.org/10.1007/978-3-319-64689-3_32.","ista":"Heiss T, Wagner H. 2017. Streaming algorithm for Euler characteristic curves of multidimensional images. CAIP: Computer Analysis of Images and Patterns, LNCS, vol. 10424, 397–409.","mla":"Heiss, Teresa, and Hubert Wagner. Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images. Edited by Michael Felsberg et al., vol. 10424, Springer, 2017, pp. 397–409, doi:10.1007/978-3-319-64689-3_32.","ama":"Heiss T, Wagner H. Streaming algorithm for Euler characteristic curves of multidimensional images. In: Felsberg M, Heyden A, Krüger N, eds. Vol 10424. Springer; 2017:397-409. doi:10.1007/978-3-319-64689-3_32","apa":"Heiss, T., & Wagner, H. (2017). Streaming algorithm for Euler characteristic curves of multidimensional images. In M. Felsberg, A. Heyden, & N. Krüger (Eds.) (Vol. 10424, pp. 397–409). Presented at the CAIP: Computer Analysis of Images and Patterns, Ystad, Sweden: Springer. https://doi.org/10.1007/978-3-319-64689-3_32","short":"T. Heiss, H. Wagner, in:, M. Felsberg, A. Heyden, N. Krüger (Eds.), Springer, 2017, pp. 397–409.","ieee":"T. Heiss and H. Wagner, “Streaming algorithm for Euler characteristic curves of multidimensional images,” presented at the CAIP: Computer Analysis of Images and Patterns, Ystad, Sweden, 2017, vol. 10424, pp. 397–409."},"date_published":"2017-07-28T00:00:00Z","doi":"10.1007/978-3-319-64689-3_32","date_created":"2018-12-11T11:48:45Z","page":"397 - 409","day":"28","isi":1,"year":"2017","publisher":"Springer","quality_controlled":"1","oa":1}]