{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T05:11:51Z","timestamp":1778562711145,"version":"3.51.4"},"reference-count":39,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,10,26]],"date-time":"2020-10-26T00:00:00Z","timestamp":1603670400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010198","name":"Ministerio de Econom\u00eda, Industria y Competitividad, Gobierno de Espa\u00f1a","doi-asserted-by":"publisher","award":["FPA2015-70420-C2-2-R"],"award-info":[{"award-number":["FPA2015-70420-C2-2-R"]}],"id":[{"id":"10.13039\/501100010198","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010198","name":"Ministerio de Econom\u00eda, Industria y Competitividad, Gobierno de Espa\u00f1a","doi-asserted-by":"publisher","award":["FPA2017-85197-P"],"award-info":[{"award-number":["FPA2017-85197-P"]}],"id":[{"id":"10.13039\/501100010198","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010198","name":"Ministerio de Econom\u00eda, Industria y Competitividad, Gobierno de Espa\u00f1a","doi-asserted-by":"publisher","award":["RTI2018-101674-B-I0"],"award-info":[{"award-number":["RTI2018-101674-B-I0"]}],"id":[{"id":"10.13039\/501100010198","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The main goal of this work is to adapt a Physics problem to the Machine Learning (ML) domain and to compare several techniques to solve it. The problem consists of how to perform muon count from the signal registered by particle detectors which record a mix of electromagnetic and muonic signals. Finding a good solution could be a building block on future experiments. After proposing an approach to solve the problem, the experiments show a performance comparison of some popular ML models using two different hadronic models for the test data. The results show that the problem is suitable to be solved using ML as well as how critical the feature selection stage is regarding precision and model complexity.<\/jats:p>","DOI":"10.3390\/e22111216","type":"journal-article","created":{"date-parts":[[2020,10,27]],"date-time":"2020-10-27T09:22:45Z","timestamp":1603790565000},"page":"1216","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Comparative Analysis of Machine Learning Techniques for Muon Count in UHECR Extensive Air-Showers"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9918-3238","authenticated-orcid":false,"given":"Alberto","family":"Guill\u00e9n","sequence":"first","affiliation":[{"name":"Computer Technology and Architecture, University of Granada, 18071 Granada, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9","family":"Mart\u00ednez","sequence":"additional","affiliation":[{"name":"Cosmos and Theoretical Physics Department, Univerisity of Granada, 18071 Granada, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan Miguel","family":"Carceller","sequence":"additional","affiliation":[{"name":"Cosmos and Theoretical Physics Department, Univerisity of Granada, 18071 Granada, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3220-9389","authenticated-orcid":false,"given":"Luis Javier","family":"Herrera","sequence":"additional","affiliation":[{"name":"Computer Technology and Architecture, University of Granada, 18071 Granada, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"The Pierre Auger Cosmic Ray Observatory (2015). Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. Nucl. Instrum. Methods Phys. Res. A, 798, 172\u2013213.","DOI":"10.1016\/j.nima.2015.06.058"},{"key":"ref_2","unstructured":"Heck, D., Knapp, J., Capdevielle, J.N., Schatz, G., and Thouw, T. (1998). CORSIKA: A Monte Carlo Code to Simulate Extensive Air Showers, Forschungszentrum Karlsruhe GmbH."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.nuclphysbps.2005.07.026","article-title":"QGSJET-II: Towards reliable description of very high energy hadronic interactions","volume":"151","author":"Ostapchenko","year":"2006","journal-title":"Nucl. Phys. Proc. Suppl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"034906","DOI":"10.1103\/PhysRevC.92.034906","article-title":"EPOS LHC: Test of collective hadronization with data measured at the CERN Large Hadron Collider","volume":"92","author":"Pierog","year":"2015","journal-title":"Phys. Rev. C"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"S226","DOI":"10.1016\/j.nima.2010.10.119","article-title":"The offline software package for analysis of radio emission from air showers at the Pierre Auger Observatory","volume":"662","author":"Fraenkel","year":"2012","journal-title":"Nucl. Instrum. Methods Phys. Res. Sect. A"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/S0168-9002(97)00048-X","article-title":"ROOT\u2014An object oriented data analysis framework","volume":"389","author":"Brun","year":"1997","journal-title":"Nucl. Instrum. Methods Phys. Res. Sect. A"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1016\/S0893-6080(00)00026-5","article-title":"Independent component analysis: Algorithms and applications","volume":"13","author":"Oja","year":"2000","journal-title":"Neural Netw."},{"key":"ref_8","first-page":"2825","article-title":"Scikit-learn: Machine Learning in Python","volume":"12","author":"Pedregosa","year":"2011","journal-title":"J. Mach. Learn. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"122003","DOI":"10.1103\/PhysRevD.96.122003","article-title":"Inferences on mass composition and tests of hadronic interactions from 0.3 to 100 EeV using the water-Cherenkov detectors of the Pierre Auger Observatory","volume":"96","author":"Aab","year":"2017","journal-title":"Phys. Rev. D"},{"key":"ref_10","unstructured":"S\u00e1nchez Lucas, P. (2016). The \u2329\u0394\u232a Method: An Estimator for the Mass Composition Of Ultra-High-Energy Cosmic Rays, University of Granada."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.astropartphys.2019.03.001","article-title":"Deep learning techniques applied to the physics of extensive air showers","volume":"111","author":"Bueno","year":"2019","journal-title":"Astropart. Phys."},{"key":"ref_12","unstructured":"Breiman, L., Friedman, J., Olshen, R., and Stone, C. (1984). Classification and Regression Trees, Wadsworth and Brooks."},{"key":"ref_13","unstructured":"Quinlan, J.R. (1993). C4.5: Programs for Machine Learning, Morgan Kaufmann Publishers Inc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"119","DOI":"10.2307\/2986296","article-title":"An Exploratory Technique for Investigating Large Quantities of Categorical Data","volume":"29","author":"Kass","year":"1980","journal-title":"Appl. Stat."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1214\/009053607000000677","article-title":"Kernel methods in machine learning","volume":"36","author":"Hofmann","year":"2008","journal-title":"Ann. Stat."},{"key":"ref_16","unstructured":"Vapnik, V.N. (1998). Statistical Learning Theory, Wiley."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Chang, C.C., and Lin, C.J. (2011). LIBSVM: A Library for Support Vector Machines. ACM Trans. Intell. Syst. Technol., 2.","DOI":"10.1145\/1961189.1961199"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Sch\u00f6lkopf, B., and Smola, A. (2001). Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond, MIT Press. Adaptive Computation and Machine Learning.","DOI":"10.7551\/mitpress\/4175.001.0001"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1023\/B:STCO.0000035301.49549.88","article-title":"A Tutorial on Support Vector Regression","volume":"14","author":"Smola","year":"2004","journal-title":"Stat. Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.1214\/aos\/1013203451","article-title":"Greedy function approximation: A gradient boosting machine","volume":"29","author":"Friedman","year":"2001","journal-title":"Ann. Stat."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Chen, T., and Guestrin, C. (2016). XGBoost: A Scalable Tree Boosting System. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, ACM.","DOI":"10.1145\/2939672.2939785"},{"key":"ref_22","unstructured":"XGBoost Developers (2020, October 01). XGBoost Python Package. Available online: https:\/\/xgboost.readthedocs.io\/en\/latest\/python\/index.html."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/BF02478259","article-title":"A logical calculus of the ideas immanent in nervous activity","volume":"5","author":"McCulloch","year":"1943","journal-title":"Bull. Math. Biophys."},{"key":"ref_24","first-page":"321","article-title":"Multivariable Functional Interpolation and Adaptive Networks","volume":"2","author":"Broomhead","year":"1988","journal-title":"Complex Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1038\/323533a0","article-title":"Learning representations by back-propagating errors","volume":"323","author":"Rumelhart","year":"1986","journal-title":"Nature"},{"key":"ref_26","unstructured":"Goodfellow, I., Bengio, Y., and Courville, A. (2016). Deep Learning, MIT Press."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1016\/j.neucom.2016.09.021","article-title":"Adding reliability to ELM forecasts by confidence intervals","volume":"219","author":"Akusok","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1002\/int.21749","article-title":"Decision Support System to Determine Intention to Use Mobile Payment Systems on Social Networks: A Methodological Analysis","volume":"31","author":"Herrera","year":"2016","journal-title":"Int. J. Intell. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4050","DOI":"10.1016\/j.eswa.2009.11.056","article-title":"Applying multiobjective RBFNNs optimization and feature selection to a mineral reduction problem","volume":"37","author":"Rubio","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Eirola, E., Lendasse, A., and Karhunen, J. (2014, January 6\u201311). Variable selection for regression problems using Gaussian mixture models to estimate mutual information. Proceedings of the 2014 International Joint Conference on Neural Networks (IJCNN 2014), Beijing, China.","DOI":"10.1109\/IJCNN.2014.6889561"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1080\/18756891.2016.1204120","article-title":"A Mutual Information estimator for continuous and discrete variables applied to Feature Selection and Classification problems","volume":"9","author":"Coelho","year":"2016","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_32","unstructured":"Bonnlander, B.V., and Weigend, A.S. (1994, January 26\u201329). Selecting input variables using mutual information and nonparametric density estimation. Proceedings of the 1994 International Symposium on Artificial Neural Networks (ISANN\u201994), Sorrento, Italy."},{"key":"ref_33","first-page":"066138","article-title":"Estimating mutual information","volume":"69","author":"Kraskov","year":"2004","journal-title":"Phys. Rev."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1226","DOI":"10.1109\/TPAMI.2005.159","article-title":"Feature selection based on mutual information criteria of max-dependency, max-relevance, and min-redundancy","volume":"27","author":"Peng","year":"2005","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_35","unstructured":"(2020, October 01). Joblib: Running Python Functions as Pipeline Jobs. Available online: https:\/\/joblib.readthedocs.io\/en\/latest\/."},{"key":"ref_36","unstructured":"Rosner, B. (2011). Fundamentals of Biostatistics, Brooks\/Cole, Cengage Learning. Chapter 12."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1093\/biomet\/52.3-4.591","article-title":"An analysis of variance test for normality (complete samples)","volume":"52","author":"Shapiro","year":"1965","journal-title":"Biometrika"},{"key":"ref_38","unstructured":"The Pierre Auger Collaboration (2020, October 01). The Pierre Auger Observatory Upgrade-Preliminary Design Report, Available online: http:\/\/xxx.lanl.gov\/abs\/1604.03637."},{"key":"ref_39","first-page":"1","article-title":"QGSjet II and EPOS hadronic interaction models: Comparison with the Yakutsk EAS array data","volume":"Volume 196","author":"Knurenko","year":"2009","journal-title":"Nuclear Physics B-Proceedings Supplements, Proceedings of the XV International Symposium on Very High Energy Cosmic Ray Interactions (ISVHECRI 2008), Paris, France, 1\u20136 September 2009"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/11\/1216\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:28:40Z","timestamp":1760178520000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/11\/1216"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,26]]},"references-count":39,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["e22111216"],"URL":"https:\/\/doi.org\/10.3390\/e22111216","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,26]]}}}