{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T10:10:14Z","timestamp":1782123014600,"version":"3.54.5"},"reference-count":23,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,6,6]],"date-time":"2018-06-06T00:00:00Z","timestamp":1528243200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Kernel based classifiers, such as SVM, are considered state-of-the-art algorithms and are widely used on many classification tasks. However, this kind of methods are hardly interpretable and for this reason they are often considered as black-box models. In this paper, we propose a new family of Boolean kernels for categorical data where features correspond to propositional formulas applied to the input variables. The idea is to create human-readable features to ease the extraction of interpretation rules directly from the embedding space. Experiments on artificial and benchmark datasets show the effectiveness of the proposed family of kernels with respect to established ones, such as RBF, in terms of classification accuracy.<\/jats:p>","DOI":"10.3390\/e20060444","type":"journal-article","created":{"date-parts":[[2018,6,6]],"date-time":"2018-06-06T10:53:28Z","timestamp":1528282408000},"page":"444","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Novel Boolean Kernels Family for Categorical Data"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4890-5020","authenticated-orcid":false,"given":"Mirko","family":"Polato","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Padova, via Trieste 63, 35121 Padova, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ivano","family":"Lauriola","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Padova, via Trieste 63, 35121 Padova, Italy"},{"name":"Fondazione Bruno Kessler, via Sommarive 18, 38123 Trento, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5823-7540","authenticated-orcid":false,"given":"Fabio","family":"Aiolli","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Padova, via Trieste 63, 35121 Padova, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,6,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.neucom.2010.02.016","article-title":"Rule extraction from support vector machines: A review","volume":"74","author":"Barakat","year":"2010","journal-title":"Neurocomputing"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Polato, M., Lauriola, I., and Aiolli, F. (2017, January 11\u201314). Classification of Categorical Data in the Feature Space of Monotone DNFs. Proceedings of the 2017 International Conference on Artificial Neural Networks and Machine Learning, Alghero (Sardinia), Italy.","DOI":"10.1007\/978-3-319-68612-7_32"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Abe, N., Khardon, R., and Zeugmann, T. (2001, January 25\u201328). Learning of Boolean Functions Using Support Vector Machines. Proceedings of the 12th International Conference on Algorithmic Learning Theory, Washington, DC, USA.","DOI":"10.1007\/3-540-45583-3"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/0022-247X(71)90184-3","article-title":"Some Results on Tchebycheffian Spline Functions","volume":"33","author":"Kimeldorf","year":"1971","journal-title":"J. Math. Anal. Appl."},{"key":"ref_5","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_6","unstructured":"Watkins, C. (1999). Kernels from Matching Operations, Department of Computer Science, Royal Holloway, University of London. Technical Report."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Khardon, R., Roth, D., and Servedio, R. (2001, January 3\u20138). Efficiency Versus Convergence of Boolean Kernels for On-line Learning Algorithms. Proceedings of the 14th International Conference on Neural Information Processing Systems: Natural and Synthetic, Vancouver, BC, Canada.","DOI":"10.7551\/mitpress\/1120.003.0059"},{"key":"ref_8","unstructured":"Sadohara, K. (2002, January 9\u201312). On a Capacity Control Using Boolean Kernels for the Learning of Boolean Functions. Proceedings of the 2002 IEEE International Conference on Data Mining, Maebashi City, Japan."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Nguyen, S.H., and Nguyen, H.S. (2014, January 9\u201313). Applications of Boolean Kernels in Rough Sets. Proceedings of the Second International Conference on Rough Sets and Intelligent Systems Paradigms, Granada and Madrid, Spain.","DOI":"10.1007\/978-3-319-08729-0_6"},{"key":"ref_10","unstructured":"Zhang, Y., Li, Z., Kang, M., and Yan, J. (2003, January 15\u201318). Improving the classification performance of boolean kernels by applying Occam\u2019s razor. Proceedings of the 2nd International Conference on Computational Intelligence, Robotics and Autonomous Systems (CIRAS \u201903), Singapore."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Shawe-Taylor, J., and Cristianini, N. (2004). Kernel Methods for Pattern Analysis, Cambridge University Press.","DOI":"10.1017\/CBO9780511809682"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Kusunoki, Y., and Tanino, T. (2014, January 22\u201324). Boolean kernels and clustering with pairwise constraints. Proceedings of the 2014 IEEE International Conference on Granular Computing (GrC), Noboribetsu, Japan.","DOI":"10.1109\/GRC.2014.6982823"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Kowalczyk, A., Smola, A.J., and Williamson, R.C. (2001). Kernel Machines and Boolean Functions. Advances in Neural Information Processing Systems 14, Proceedings of the Neural Information Processing Systems, Natural and Synthetic, Vancouver, BC, Canada, 3\u20138 December 2001, MIT Press.","DOI":"10.7551\/mitpress\/1120.003.0061"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Khardon, R., and Servedio, R.A. (2003). Maximum Margin Algorithms with Boolean Kernels. Learning Theory and Kernel Machines, Proceedings of the 16th Annual Conference on Learning Theory and 7th Kernel Workshop, COLT\/Kernel 2003, Washington, DC, USA, 24\u201327 August 2003, Springer.","DOI":"10.1007\/978-3-540-45167-9_8"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Cui, K., Han, F., and Wang, P. (2008, January 18\u201320). Research on Face Recognition Based on Boolean Kernel SVM. Proceedings of the 2008 Fourth International Conference on Natural Computation, Jinan, China.","DOI":"10.1109\/ICNC.2008.721"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Cui, K., and Du, Y. (2009, January 25\u201326). Application of Boolean Kernel Function SVM in Face Recognition. Proceedings of the 2009 International Conference on Networks Security, Wireless Communications and Trusted Computing, Wuhan, China.","DOI":"10.1109\/NSWCTC.2009.172"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"27","DOI":"10.5539\/mas.v3n10p27","article-title":"Applications of Support Vector Machine Based on Boolean Kernel to Spam Filtering","volume":"3","author":"Liu","year":"2009","journal-title":"Modern Appl. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Cui, K., and Du, Y. (2009, January 25\u201326). Short-Term Load Forecasting Based on the BKF-SVM. Proceedings of the 2009 International Conference on Networks Security, Wireless Communications and Trusted Computing, Wuhan, China.","DOI":"10.1109\/NSWCTC.2009.170"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/j.neucom.2018.01.057","article-title":"Boolean kernels for collaborative filtering in top-N item recommendation","volume":"286","author":"Polato","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_20","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_21","unstructured":"Lichman, M. (2018, February 28). UCI Machine Learning Repository. Available online: https:\/\/archive.ics.uci.edu\/ml\/."},{"key":"ref_22","first-page":"255","article-title":"Keel data-mining software tool: Data set repository, integration of algorithms and experimental analysis framework","volume":"17","author":"Luengo","year":"2011","journal-title":"J. Mult. Valued Logic Soft Comput."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Harris, D.M., and Harris, S.L. (2013). Digital Design and Computer Architecture, Morgan Kaufmann. [2nd ed.].","DOI":"10.1016\/B978-0-12-394424-5.00006-9"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/6\/444\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:07:37Z","timestamp":1760195257000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/6\/444"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,6]]},"references-count":23,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2018,6]]}},"alternative-id":["e20060444"],"URL":"https:\/\/doi.org\/10.3390\/e20060444","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6,6]]}}}