{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:42:40Z","timestamp":1760240560801,"version":"build-2065373602"},"reference-count":73,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,7,16]],"date-time":"2019-07-16T00:00:00Z","timestamp":1563235200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["ECP Alpine project"],"award-info":[{"award-number":["ECP Alpine project"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>With increasing computing capabilities of modern supercomputers, the size of the data generated from the scientific simulations is growing rapidly. As a result, application scientists need effective data summarization techniques that can reduce large-scale multivariate spatiotemporal data sets while preserving the important data properties so that the reduced data can answer domain-specific queries involving multiple variables with sufficient accuracy. While analyzing complex scientific events, domain experts often analyze and visualize two or more variables together to obtain a better understanding of the characteristics of the data features. Therefore, data summarization techniques are required to analyze multi-variable relationships in detail and then perform data reduction such that the important features involving multiple variables are preserved in the reduced data. To achieve this, in this work, we propose a data sub-sampling algorithm for performing statistical data summarization that leverages pointwise information theoretic measures to quantify the statistical association of data points considering multiple variables and generates a sub-sampled data that preserves the statistical association among multi-variables. Using such reduced sampled data, we show that multivariate feature query and analysis can be done effectively. The efficacy of the proposed multivariate association driven sampling algorithm is presented by applying it on several scientific data sets.<\/jats:p>","DOI":"10.3390\/e21070699","type":"journal-article","created":{"date-parts":[[2019,7,17]],"date-time":"2019-07-17T02:44:03Z","timestamp":1563331443000},"page":"699","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Multivariate Pointwise Information-Driven Data Sampling and Visualization"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5030-9979","authenticated-orcid":false,"given":"Soumya","family":"Dutta","sequence":"first","affiliation":[{"name":"Los Alamos National Laboratory, Los Alamos, NM 87545, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ayan","family":"Biswas","sequence":"additional","affiliation":[{"name":"Los Alamos National Laboratory, Los Alamos, NM 87545, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"James","family":"Ahrens","sequence":"additional","affiliation":[{"name":"Los Alamos National Laboratory, Los Alamos, NM 87545, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,16]]},"reference":[{"key":"ref_1","unstructured":"Ahern, S., Shoshani, A., Ma, K.L., Choudhary, A., Critchlow, T., Klasky, S., Pascucci, V., Ahrens, J., Bethel, E., and Childs, H. (2011, January 22\u201323). Scientific Discovery at the Exascale. Proceedings of the The DOE ASCR 2011 Workshop on Exascale Data Management, Houston, TX, USA."},{"key":"ref_2","first-page":"5","article-title":"Data Exploration at the Exascale","volume":"2","author":"Childs","year":"2015","journal-title":"Supercomput. Front. Innov."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Ahrens, J., Jourdain, S., OLeary, P., Patchett, J., Rogers, D.H., and Petersen, M. (2014, January 16\u201321). An Image-Based Approach to Extreme Scale in Situ Visualization and Analysis. Proceedings of the SC14: International Conference for High Performance Computing, Networking, Storage and Analysis, New Orleans, LA, USA.","DOI":"10.1109\/SC.2014.40"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Nouanesengsy, B., Woodring, J., Patchett, J., Myers, K., and Ahrens, J. (2014, January 9\u201310). ADR visualization: A generalized framework for ranking large-scale scientific data using Analysis-Driven Refinement. Proceedings of the 2014 IEEE 4th Symposium on Large Data Analysis and Visualization (LDAV), Paris, France.","DOI":"10.1109\/LDAV.2014.7013203"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Tikhonova, A., Correa, C.D., and Ma, K. (2010, January 2\u20135). Explorable images for visualizing volume data. Proceedings of the 2010 IEEE Pacific Visualization Symposium (PacificVis), Taipei, Taiwan.","DOI":"10.1109\/PACIFICVIS.2010.5429595"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1109\/TVCG.2016.2598604","article-title":"In Situ Distribution Guided Analysis and Visualization of Transonic Jet Engine Simulations","volume":"23","author":"Dutta","year":"2017","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1109\/TVCG.2015.2467411","article-title":"In Situ Eddy Analysis in a High-Resolution Ocean Climate Model","volume":"22","author":"Woodring","year":"2016","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1109\/MCSE.2007.42","article-title":"Visualizing Multivariate Volume Data from Turbulent Combustion Simulations","volume":"9","author":"Akiba","year":"2007","journal-title":"Comput. Sci. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1109\/TVCG.2010.80","article-title":"An Application of Multivariate Statistical Analysis for Query-Driven Visualization","volume":"17","author":"Gosink","year":"2011","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1214","DOI":"10.1109\/TVCG.2018.2864801","article-title":"CoDDA: A Flexible Copula-based Distribution Driven Analysis Framework for Large-Scale Multivariate Data","volume":"25","author":"Hazarika","year":"2019","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"955","DOI":"10.1109\/TVCG.2015.2467431","article-title":"Association Analysis for Visual Exploration of Multivariate Scientific Data Sets","volume":"22","author":"Liu","year":"2016","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2683","DOI":"10.1109\/TVCG.2013.133","article-title":"An Information-Aware Framework for Exploring Multivariate Data Sets","volume":"19","author":"Biswas","year":"2013","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_13","first-page":"1384","article-title":"Multifield visualization using local statistical complexity","volume":"13","author":"Wiebel","year":"2007","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_14","unstructured":"Stockinger, K., Shalf, J., Wu, K., and Bethel, E.W. (2005, January 23\u201328). Query-driven visualization of large data sets. Proceedings of the IEEE Visualization 2005 (VIS 05), Minneapolis, MN, USA."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Wang, K., Shareef, N., and Shen, H. (2018, January 10\u201313). Image and Distribution Based Volume Rendering for Large Data Sets. Proceedings of the 2018 IEEE Pacific Visualization Symposium (PacificVis), Kobe, Japan.","DOI":"10.1109\/PacificVis.2018.00013"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Wang, K., Wei, T., Shareef, N., and Shen, H. (2017, January 18\u201321). Statistical visualization and analysis of large data using a value-based spatial distribution. Proceedings of the 2017 IEEE Pacific Visualization Symposium (PacificVis), Seoul, Korea.","DOI":"10.1109\/PACIFICVIS.2017.8031590"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Dutta, S., Woodring, J., Shen, H.W., Chen, J.P., and Ahrens, J. (2017, January 18\u201321). Homogeneity guided probabilistic data summaries for analysis and visualization of large-scale data sets. Proceedings of the 2017 IEEE Pacific Visualization Symposium (PacificVis), Seoul, Korea.","DOI":"10.1109\/PACIFICVIS.2017.8031585"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1088\/1367-2630\/9\/8\/301","article-title":"Interactive desktop analysis of high resolution simulations: application to turbulent plume dynamics and current sheet formation","volume":"9","author":"Clyne","year":"2007","journal-title":"New J. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Li, S., Sane, S., Orf, L., Mininni, P., Clyne, J., and Childs, H. (2017, January 5\u20138). Spatiotemporal Wavelet Compression for Visualization of Scientific Simulation Data. Proceedings of the 2017 IEEE International Conference on Cluster Computing (CLUSTER), Honolulu, HI, USA.","DOI":"10.1109\/CLUSTER.2017.15"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Li, S., Gruchalla, K., Potter, K., Clyne, J., and Childs, H. (2015, January 25\u201326). Evaluating the efficacy of wavelet configurations on turbulent-flow data. Proceedings of the 2015 IEEE 5th Symposium on Large Data Analysis and Visualization (LDAV), Chicago, IL, USA.","DOI":"10.1109\/LDAV.2015.7348075"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Jeannot, E., Namyst, R., and Roman, J. (2011). Compressing the Incompressible with ISABELA: In-situ Reduction of Spatio-temporal Data. Euro-Par 2011 Parallel Processing, Springer.","DOI":"10.1007\/978-3-642-23400-2"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Biswas, A., Dutta, S., Pulido, J., and Ahrens, J. (2018, January 12). In Situ Data-driven Adaptive Sampling for Large-scale Simulation Data Summarization. Proceedings of the Workshop on In Situ Infrastructures for Enabling Extreme-Scale Analysis and Visualization, Dallas, TX, USA.","DOI":"10.1145\/3281464.3281467"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Wei, T., Dutta, S., and Shen, H. (2018, January 10\u201313). Information Guided Data Sampling and Recovery Using Bitmap Indexing. Proceedings of the 2018 IEEE Pacific Visualization Symposium (PacificVis), Kobe, Japan.","DOI":"10.1109\/PacificVis.2018.00016"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Woodring, J., Ahrens, J., Figg, J., Wendelberger, J., Habib, S., and Heitmann, K. (2011, January 1\u20133). In-situ Sampling of a Large-scale Particle Simulation for Interactive Visualization and Analysis. Proceedings of the 13th Eurographics\/IEEE\u2014VGTC Conference on Visualization, Bergen, Norway.","DOI":"10.1111\/j.1467-8659.2011.01964.x"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Su, Y., Agrawal, G., Woodring, J., Myers, K., Wendelberger, J., and Ahrens, J. (2013, January 17\u201321). Taming Massive Distributed Datasets: Data Sampling Using Bitmap Indices. Proceedings of the 22nd International Symposium on High-performance Parallel and Distributed Computing, New York, NY, USA.","DOI":"10.1145\/2493123.2462906"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Church, K.W., and Hanks, P. (1989, January 26\u201329). Word association norms, mutual information, and lexicography. Proceedings of the 27th Annual Meeting on Association for Computational Linguistics, Vancouver, BC, Canada.","DOI":"10.3115\/981623.981633"},{"key":"ref_27","unstructured":"Van de Cruys, T. (2011, January 24). Two multivariate generalizations of pointwise mutual information. Proceedings of the Workshop on Distributional Semantics and Compositionality, Portland, OR, USA."},{"key":"ref_28","unstructured":"Cover, T.M., and Thomas, J.A. (2006). Elements of Information Theory, Wiley-Interscience. [2nd ed.]."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1145\/584091.584093","article-title":"A Mathematical Theory of Communication","volume":"5","author":"Shannon","year":"2001","journal-title":"SIGMOBILE Mob. Comput. Commun. Rev."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2057","DOI":"10.1109\/18.720531","article-title":"Fifty years of Shannon theory","volume":"44","year":"1998","journal-title":"Inf. Theory IEEE Trans."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1109\/TVCG.2006.152","article-title":"Importance-Driven Focus of Attention","volume":"12","author":"Viola","year":"2006","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_32","first-page":"263","article-title":"Automated multi-modality image registration based on information theory","volume":"3","author":"Collignon","year":"1995","journal-title":"Inf. Process. Med. Imaging"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"R1","DOI":"10.1088\/0031-9155\/46\/3\/201","article-title":"Medical image registration","volume":"46","author":"Hill","year":"2001","journal-title":"Phys. Med. Biol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/S1361-8415(01)80004-9","article-title":"Multi-modal volume registration by maximization of mutual information","volume":"1","author":"Wells","year":"1996","journal-title":"Med. Image Anal."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1109\/42.563664","article-title":"Multimodality image registration by maximization of mutual information","volume":"16","author":"Maes","year":"1997","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"986","DOI":"10.1109\/TMI.2003.815867","article-title":"Mutual-information-based registration of medical images: A survey","volume":"22","author":"Pluim","year":"2003","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Feixas, M., Acebo, E.D., Bekaert, P., and Sbert, M. (1999). An Information Theory Framework for the Analysis of Scene Complexity. Computer Graphics Forum, Blackwell Publishers, Ltd.","DOI":"10.1111\/1467-8659.00331"},{"key":"ref_38","unstructured":"Rigau, J., Feixas, M., and Sbert, M. (2005, January 13\u201317). Shape complexity based on mutual information. Proceedings of the 2005 International Conference on Shape Modeling and Applications, Cambridge, MA, USA."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Feixas, M., Sbert, M., and Gonz\u00e1lez, F. (2009). A unified information-theoretic framework for viewpoint selection and mesh saliency. ACM Trans. Appl. Percept.","DOI":"10.1145\/1462055.1462056"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1111\/j.1467-8659.2009.01689.x","article-title":"Isosurface Similarity Maps","volume":"29","author":"Bruckner","year":"2010","journal-title":"Comput. Graph. Forum"},{"key":"ref_41","unstructured":"Wei, T.H., Lee, T.Y., and Shen, H.W. (2013, January 17\u201321). Evaluating Isosurfaces with Level-set-based Information Maps. Proceedings of the 15th Eurographics Conference on Visualization, Leipzig, Germany."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1111\/cgf.12128","article-title":"An Information-Theoretic Observation Channel for Volume Visualization","volume":"32","author":"Bramon","year":"2013","journal-title":"Comput. Graph. Forum"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Ma, J., Wang, C., and Shene, C.K. (2013). Coherent view-dependent streamline selection for importance-driven flow visualization. Proc. SPIE, 8654.","DOI":"10.1117\/12.2001887"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1109\/TVCG.2012.143","article-title":"A Unified Approach to Streamline Selection and Viewpoint Selection for 3D Flow Visualization","volume":"19","author":"Tao","year":"2013","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1574","DOI":"10.1109\/TVCG.2011.280","article-title":"Multimodal Data Fusion Based on Mutual Information","volume":"18","author":"Bramon","year":"2012","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"870","DOI":"10.1109\/JBHI.2013.2263227","article-title":"Information Theory-Based Automatic Multimodal Transfer Function Design","volume":"17","author":"Bramon","year":"2013","journal-title":"IEEE J. Biomed. Health Inform."},{"key":"ref_47","unstructured":"Botha, C.P., Kindlmann, G., Niessen, W., and Preim, B. (2008, January 6\u20137). Information-based Transfer Functions for Multimodal Visualization. Proceedings of the First Eurographics conference on Visual Computing for Biomedicine, Delft, The Netherlands."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Dutta, S., Liu, X., Biswas, A., Shen, H.W., and Chen, J.P. (2017, January 27\u201330). Pointwise Information Guided Visual Analysis of Time-varying Multi-fields. Proceedings of the SIGGRAPH Asia 2017 Symposium on Visualization, Bangkok, Thailand.","DOI":"10.1145\/3139295.3139298"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Chen, M., Feixas, M., Viola, I., Bardera, A., Shen, H.W., and Sbert, M. (2016). Information Theory Tools for Visualization, CRC Press.","DOI":"10.1201\/9781315369228"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1206","DOI":"10.1109\/TVCG.2010.132","article-title":"An Information-theoretic Framework for Visualization","volume":"16","author":"Chen","year":"2010","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1109\/MCG.2008.34","article-title":"Informational Aesthetics Measures","volume":"28","author":"Rigau","year":"2008","journal-title":"IEEE Comput. Graph. Appl."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Sbert, M., Feixas, M., Rigau, J., Chover, M., and Viola, I. (2009). Information Theory Tools for Computer Graphics, Morgan and Claypool Publishers. Synthesis Lectures on Computer Graphics and Animation.","DOI":"10.1007\/978-3-031-79546-6"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"254","DOI":"10.3390\/e13010254","article-title":"Information Theory in Scientific Visualization","volume":"13","author":"Wang","year":"2011","journal-title":"Entropy"},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Park, Y., Cafarella, M.J., and Mozafari, B. (2015). Visualization-Aware Sampling for Very Large Databases. arXiv.","DOI":"10.1109\/ICDE.2016.7498287"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Nguyen, T.T., and Song, I. (2016, January 24\u201329). Centrality clustering-based sampling for big data visualization. Proceedings of the 2016 International Joint Conference on Neural Networks (IJCNN), Vancouver, BC, Canada.","DOI":"10.1109\/IJCNN.2016.7727433"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1093\/biomet\/81.3.457","article-title":"Weighted Finite Population Sampling to Maximize Entropy","volume":"81","author":"Chen","year":"1994","journal-title":"Biometrika"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1287\/opre.43.4.684","article-title":"An Exact Algorithm for Maximum Entropy Sampling","volume":"43","author":"Ko","year":"1995","journal-title":"Oper. Res."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1080\/02664768700000020","article-title":"Maximum entropy sampling","volume":"14","author":"Shewry","year":"1987","journal-title":"J. Appl. Stat."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1109\/TVCG.2006.165","article-title":"Multifield-Graphs: An Approach to Visualizing Correlations in Multifield Scalar Data","volume":"12","author":"Sauber","year":"2006","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"1400","DOI":"10.1109\/TVCG.2007.70519","article-title":"Variable Interactions in Query-Driven Visualization","volume":"13","author":"Gosink","year":"2007","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_61","unstructured":"Wong, P.C., and Bergeron, R.D. (1997). 30 Years of Multidimensional Multivariate Visualization. Scientific Visualization, Overviews, Methodologies, and Techniques, IEEE Computer Society."},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Fuchs, R., and Hauser, H. (2009). Visualization of Multi-Variate Scientific Data. InComputer Graphics Forum, Blackwell Publishing Ltd.","DOI":"10.1111\/j.1467-8659.2009.01429.x"},{"key":"ref_63","unstructured":"Lohr, S. (2009). Sampling: Design and Analysis, Advanced, Cengage Learning."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Albert, J. (2009). Bayesian Computation with R, Springer. Use R.","DOI":"10.1007\/978-0-387-92298-0"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1147\/rd.41.0066","article-title":"Information theoretical analysis of multivariate correlation","volume":"4","author":"Watanabe","year":"1960","journal-title":"IBM J. Res. Dev."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1023\/A:1008935410038","article-title":"On Sequential Monte Carlo Sampling Methods for Bayesian Filtering","volume":"10","author":"Doucet","year":"2000","journal-title":"Stat. Comput."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1080\/00401706.2013.822424","article-title":"Model Bank State Estimation for Power Grids Using Importance Sampling","volume":"55","author":"Lawrence","year":"2013","journal-title":"Technometrics"},{"key":"ref_68","unstructured":"Patchett, J., and Gisler, G. (2019, July 16). Deep Water Impact Ensemble Data Set. Los Alamos National Laboratory, LA-UR-17-21595, Available online: https:\/\/oceans11.lanl.gov\/deepwaterimpact\/."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.jsse.2018.06.001","article-title":"Three-dimensional simulations of oblique asteroid impacts into water","volume":"5","author":"Gisler","year":"2018","journal-title":"J. Space Saf. Eng."},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Levandowsky, M., and Winter, D. (1971). Distance between Sets. Nature, 234.","DOI":"10.1038\/234034a0"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/TIP.2003.819861","article-title":"Image quality assessment: From error visibility to structural similarity","volume":"13","author":"Bovik","year":"2004","journal-title":"IEEE Trans. Image Process."},{"key":"ref_72","first-page":"2769","article-title":"Measuring and Testing Dependence by Correlation of Distances","volume":"35","author":"Rizzo","year":"2007","journal-title":"Ann. Stat."},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Lu, K., and Shen, H. (2015, January 25\u201326). A compact multivariate histogram representation for query-driven visualization. Proceedings of the 2015 IEEE 5th Symposium on Large Data Analysis and Visualization (LDAV), Chicago, IL, USA.","DOI":"10.1109\/LDAV.2015.7348071"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/7\/699\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:06:07Z","timestamp":1760187967000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/7\/699"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,16]]},"references-count":73,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2019,7]]}},"alternative-id":["e21070699"],"URL":"https:\/\/doi.org\/10.3390\/e21070699","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2019,7,16]]}}}