{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T05:32:04Z","timestamp":1736227924023,"version":"3.32.0"},"reference-count":36,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2016,10,19]],"date-time":"2016-10-19T00:00:00Z","timestamp":1476835200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001824","name":"Czech Science Foundation","doi-asserted-by":"publisher","award":["GA14-07983S"],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Postdok JU","award":["CZ.1.07\/2.3.00\/30.0006"]},{"name":"GAJU","award":["34\/2013\/Z"]},{"DOI":"10.13039\/100014809","name":"TA \u010cR","doi-asserted-by":"publisher","award":["TA01010214"],"id":[{"id":"10.13039\/100014809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"CENAKVA","award":["CZ.1.05\/2.1.00\/01.0024"]},{"name":"CENAKVA II","award":["LO1205"]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"We generalize the point information gain (PIG) and derived quantities, i.e., point information gain entropy (PIE) and point information gain entropy density (PIED), for the case of the R\u00e9nyi entropy and simulate the behavior of PIG for typical distributions. We also use these methods for the analysis of multidimensional datasets. We demonstrate the main properties of PIE\/PIED spectra for the real data with the examples of several images and discuss further possible utilizations in other fields of data processing.<\/jats:p>","DOI":"10.3390\/e18100372","type":"journal-article","created":{"date-parts":[[2016,10,19]],"date-time":"2016-10-19T14:32:57Z","timestamp":1476887577000},"page":"372","source":"Crossref","is-referenced-by-count":7,"title":["Point Information Gain and Multidimensional Data Analysis"],"prefix":"10.3390","volume":"18","author":[{"given":"Renata","family":"Rycht\u00e1rikov\u00e1","sequence":"first","affiliation":[{"name":"Institute of Complex Systems, South Bohemian Research Center of Aquaculture and Biodiversity of Hydrocenoses, Faculty of Fisheries and Protection of Waters (FFWP), University of South Bohemia in \u010cesk\u00e9 Bud\u011bjovice, Z\u00e1mek 136, Nov\u00e9 Hrady 373 33, Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5371-5320","authenticated-orcid":false,"given":"Jan","family":"Korbel","sequence":"additional","affiliation":[{"name":"Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, B\u0159ehov\u00e1 7, Prague 155 19, Czech Republic"}]},{"given":"Petr","family":"Mach\u00e1\u010dek","sequence":"additional","affiliation":[{"name":"Institute of Complex Systems, South Bohemian Research Center of Aquaculture and Biodiversity of Hydrocenoses, Faculty of Fisheries and Protection of Waters (FFWP), University of South Bohemia in \u010cesk\u00e9 Bud\u011bjovice, Z\u00e1mek 136, Nov\u00e9 Hrady 373 33, Czech Republic"}]},{"given":"Petr","family":"C\u00edsa\u0159","sequence":"additional","affiliation":[{"name":"Institute of Complex Systems, South Bohemian Research Center of Aquaculture and Biodiversity of Hydrocenoses, Faculty of Fisheries and Protection of Waters (FFWP), University of South Bohemia in \u010cesk\u00e9 Bud\u011bjovice, Z\u00e1mek 136, Nov\u00e9 Hrady 373 33, Czech Republic"}]},{"given":"Jan","family":"Urban","sequence":"additional","affiliation":[{"name":"Institute of Complex Systems, South Bohemian Research Center of Aquaculture and Biodiversity of Hydrocenoses, Faculty of Fisheries and Protection of Waters (FFWP), University of South Bohemia in \u010cesk\u00e9 Bud\u011bjovice, Z\u00e1mek 136, Nov\u00e9 Hrady 373 33, Czech Republic"}]},{"given":"Dalibor","family":"\u0160tys","sequence":"additional","affiliation":[{"name":"Institute of Complex Systems, South Bohemian Research Center of Aquaculture and Biodiversity of Hydrocenoses, Faculty of Fisheries and Protection of Waters (FFWP), University of South Bohemia in \u010cesk\u00e9 Bud\u011bjovice, Z\u00e1mek 136, Nov\u00e9 Hrady 373 33, Czech Republic"}]}],"member":"1968","published-online":{"date-parts":[[2016,10,19]]},"reference":[{"key":"ref_1","first-page":"3360","article-title":"Analysis of biological time-lapse microscopic experiment from the point of view of the information theory","volume":"42","author":"Urban","year":"2011","journal-title":"Micron"},{"key":"ref_2","unstructured":"Urban, J., Van\u011bk, J., and \u0160tys, D. (2009, January 19\u201321). Preprocessing of microscopy images via Shannon\u2019s entropy. Proceedings of the Pattern Recognition and Information Processing, Minsk, Belarus."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/s10479-005-5724-z","article-title":"A tutorial on the cross-entropy method","volume":"134","author":"Boer","year":"2005","journal-title":"Ann. Oper. Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1945","DOI":"10.3390\/e13111945","article-title":"A characterization of entropy in terms of information loss","volume":"13","author":"Baez","year":"2011","journal-title":"Entropy"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.geomphys.2015.07.018","article-title":"Entropy algebras and Birkhoff factorization","volume":"97","author":"Marcolli","year":"2015","journal-title":"J. Geom. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/BF01016429","article-title":"Possible generalization of Boltzmann\u2013Gibbs statistics","volume":"52","author":"Tsallis","year":"1988","journal-title":"J. Stat. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.aop.2004.01.002","article-title":"The world according to R\u00e9nyi: Thermodynamics of multifractal systems","volume":"312","author":"Jizba","year":"2004","journal-title":"Ann. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1016\/j.physa.2014.07.008","article-title":"Multifractal diffusion entropy analysis: Optimal bin width of probability histograms","volume":"413","author":"Jizba","year":"2014","journal-title":"Physica A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/0167-2789(83)90235-X","article-title":"The infinite number of generalized dimensions of fractals and strange attractors","volume":"8","author":"Hentschel","year":"1983","journal-title":"Physcia D"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/S0019-9958(65)90332-3","article-title":"A coding theorem and R\u00e9nyi\u2019s entropy","volume":"8","author":"Campbel","year":"1965","journal-title":"Inf. Control"},{"key":"ref_11","unstructured":"\u0160tys, D., Jizba, P., Pap\u00e1\u010dek, S., N\u00e1hlik, T., and C\u00edsa\u0159, P. (2012, January 15\u201316). On measurement of internal variables of complex self-organized systems and their relation to multifractal spectra. Proceedings of the 6th IFIP TC 6 International Workshop (WSOS 2012), Delft, The Netherlands."},{"key":"ref_12","unstructured":"R\u00e9nyi, A. (July, January 20). On measures of entropy and information. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA, USA."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1214\/aoms\/1177729694","article-title":"On information and sufficiency","volume":"22","author":"Kullback","year":"1951","journal-title":"Ann. Math. Stat."},{"key":"ref_14","first-page":"146","article-title":"I-divergence geometry of probability distributions and minimization problems","volume":"3","year":"1975","journal-title":"Ann. Prob."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.physa.2006.01.012","article-title":"Interpretations of R\u00e9nyi entropies and divergences","volume":"365","author":"Harremoes","year":"2006","journal-title":"Physica A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3797","DOI":"10.1109\/TIT.2014.2320500","article-title":"R\u00e9nyi divergence and Kullback\u2013Leibler divergence","volume":"60","author":"Harremoes","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Van Erven, T., and Harremo\u00ebs, P. (2010, January 13\u201318). R\u00e9nyi divergence and majorization. Proceedings of the 2010 IEEE International Symposium on Information Theory Proceedings (ISIT), Austin, TX, USA.","DOI":"10.1109\/ISIT.2010.5513784"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2971","DOI":"10.1016\/j.physa.2011.12.064","article-title":"R\u00e9nyi\u2019s information transfer between financial time series","volume":"391","author":"Jizba","year":"2012","journal-title":"Physica A"},{"key":"ref_19","first-page":"30","article-title":"Quantification method of classification processes. Concept of structural \u03b1-entropy","volume":"3","author":"Havrda","year":"1967","journal-title":"Kybernetika"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/0167-2789(83)90298-1","article-title":"Measuring the strangeness of strange attractors","volume":"9","author":"Grassberger","year":"1983","journal-title":"Physica D"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1103\/PhysRevLett.50.346","article-title":"Characterization of strange attractors","volume":"50","author":"Grassberger","year":"1983","journal-title":"Phys. Rev. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1109\/TIT.1985.1057105","article-title":"A new entropy power inequality","volume":"31","author":"Costa","year":"1985","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.aop.2015.01.031","article-title":"Role of information theoretic uncertainty relations in quantum theory","volume":"355","author":"Jizba","year":"2015","journal-title":"Ann. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"026128","DOI":"10.1103\/PhysRevE.69.026128","article-title":"On observability of R\u00e9nyi\u2019s entropy","volume":"69","author":"Jizba","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_26","unstructured":"The USC-SIPI Image Database. Available online: http:\/\/sipi.usc.edu\/database\/database.php?volume=textures &image=61#top."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1023\/A:1010388907793","article-title":"Computational mechanics: Pattern and prediction, structure and simplicity","volume":"104","author":"Shalizi","year":"2001","journal-title":"J. Stat. Phys."},{"key":"ref_28","unstructured":"Shalizi, C.R., and Shalizi, K.L. (2003). Noise in Complex Systems and Stochastic Dynamics, Society of Photo Optical."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"118701","DOI":"10.1103\/PhysRevLett.93.118701","article-title":"Quantifying self-organization with optimal predictors","volume":"93","author":"Shalizi","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1038\/nphys2190","article-title":"Between order and chaos","volume":"8","author":"Crutchfield","year":"2012","journal-title":"Nat. Phys."},{"key":"ref_31","unstructured":"Explore Fractals Beautiful, Colorful Fractals, and More!. Available online: https:\/\/www.pinterest.com\/pin\/254031235202385248\/."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Sanayei, A., Zelinka, N., and R\u00f6ssler, O.E. (2014). ISCS 2013: Interdisciplinary Symposium on Complex Systems, Springer.","DOI":"10.1007\/978-3-642-45438-7"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Ortu\u00f1o, F., and Rojas, I. (2016). Bioinformatics and Biomedical Engineering, Springer.","DOI":"10.1007\/978-3-319-31744-1"},{"key":"ref_34","first-page":"2824","article-title":"The cell monolayer trajectory from the system state point of view","volume":"42","author":"Urban","year":"2011","journal-title":"Mol. BioSyst."},{"key":"ref_35","unstructured":"Available online: http:\/\/cims.nyu.edu\/ kiryl\/Photos\/Fractals1\/ascp011et.html."},{"key":"ref_36","unstructured":"Point Information Gain Supplementary Data. Available online: ftp:\/\/160.217.215.251\/pig."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/10\/372\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,6]],"date-time":"2025-01-06T23:42:13Z","timestamp":1736206933000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/10\/372"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,19]]},"references-count":36,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2016,10]]}},"alternative-id":["e18100372"],"URL":"https:\/\/doi.org\/10.3390\/e18100372","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints201610.0067.v1","asserted-by":"object"}]},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2016,10,19]]}}}