{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T07:20:51Z","timestamp":1777706451916,"version":"3.51.4"},"reference-count":36,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2024,3,23]],"date-time":"2024-03-23T00:00:00Z","timestamp":1711152000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems: Applications in Engineering and Technology"],"published-print":{"date-parts":[[2026,2]]},"abstract":"<jats:p>The Associative Pattern Classifier (APC) was designed as an associative memory, focusing particularly on pattern classification. This implies that the training memory is constructed in a single operation and pattern classification also occurs in a single process. It is important to note that the APC translates the input patterns through a translation vector, which represents the average of all input patterns. Until now, there is no theoretical framework to explain the inner workings of the APC. Its relevance is inferred from the fact that several studies have been conducted using it as a foundation. This paper seeks to provide a theoretical comprehension of the APC\u2019s operation to facilitate future enhancements. We found the APC creates a system in static equilibrium through concurrent vectors at the origin (translation vector), resulting in a balanced separation of patterns. However, the APC cannot achieve complete pattern separation because of the presence of a neutral region. The neutral region is defined by all the points that define the separation hyperplanes. The points over the hyperplanes cannot be classified by the APC. Additionally, we discovered that the APC is unable to accurately classify the translation vector, which could be included as part of the input patterns. Our previous research showed that the APC is unsuccessful in achieving the linear separation of the AND function. In this research, we also broaden the examination of the AND function to illustrate that achieving linear separation is not feasible because the separation line represents a neutral region. The APC demonstrated exceptional performance when tested with artificial datasets where patterns were distributed over balanced regions, thus operating as an efficient multiclass and non-linear classifier. Nevertheless, the performance of the APC is lower when tested with real-world databases, making the APC inaccurate due to its restricted inner workings.<\/jats:p>","DOI":"10.3233\/jifs-219347","type":"journal-article","created":{"date-parts":[[2024,3,26]],"date-time":"2024-03-26T12:03:45Z","timestamp":1711454625000},"page":"307-321","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["The associative pattern classifier: Progress in theoretical understanding"],"prefix":"10.1177","volume":"50","author":[{"given":"Sergio","family":"Valadez-God\u00ednez","sequence":"first","affiliation":[{"name":"Universidad Polit\u00e9cnica de P\u00e9njamo","place":["M\u00e9xico"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Humberto","family":"Sossa","sequence":"additional","affiliation":[{"name":"Instituto Polit\u00e9cnico Nacional","place":["M\u00e9xico"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ra\u00fal","family":"Santiago-Montero","sequence":"additional","affiliation":[{"name":"Instituto Tecnol\u00f3gico de Le\u00f3n","place":["M\u00e9xico"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2024,3,23]]},"reference":[{"key":"e_1_3_2_2_1","unstructured":"ZuradaJ.M. Introduction to Artificial Neural Systems West Publishing Company 1992."},{"key":"e_1_3_2_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2012.08.013"},{"key":"e_1_3_2_4_1","doi-asserted-by":"publisher","DOI":"10.14569\/IJACSA.2010.010619"},{"key":"e_1_3_2_5_1","doi-asserted-by":"publisher","unstructured":"SteinbuchK. Die Lernmatrix Kybernetik 1 (1961) 36\u201345. doi: 10.1007\/BF00293853.","DOI":"10.1007\/BF00293853"},{"key":"e_1_3_2_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00290182"},{"key":"e_1_3_2_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(72)90075-2"},{"key":"e_1_3_2_8_1","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1972.5008975"},{"key":"e_1_3_2_9_1","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.1972.4309133"},{"key":"e_1_3_2_10_1","first-page":"437","article-title":"and C.Ya\u00f1ez-M\u00e1rquez, Lernmatrix: Condiciones necesarias ysuficientes para recuperaci\u00f3n perfecta","author":"S\u00e1nchez-Garfias F.A.","year":"2002","unstructured":"S\u00e1nchez-GarfiasF.A.D\u00edaz-de-Le\u00f3n-SJ.L., and C.Ya\u00f1ez-M\u00e1rquez, Lernmatrix: Condiciones necesarias ysuficientes para recuperaci\u00f3n perfecta, Memoria del CIARP (2002), 437\u2013448.","journal-title":"Memoria del CIARP"},{"issue":"3","key":"e_1_3_2_11_1","first-page":"175","article-title":"Lernmatrix de Steinbuch: Avances Teoricos","volume":"7","author":"S\u00e1nchez-Garfias F.A.","year":"2004","unstructured":"S\u00e1nchez-GarfiasF.A.D\u00edaz-de-Le\u00f3n-S.J.L.Ya\u00f1ez-M\u00e1rquezC., Lernmatrix de Steinbuch: Avances Teoricos, Computacion y Sistemas7(3) (2004), 175\u2013189.","journal-title":"Computacion y Sistemas"},{"key":"e_1_3_2_12_1","doi-asserted-by":"publisher","unstructured":"S\u00e1nchez-GarfiasF.A.J.L.D.-d.-L.S. Y\u00e1\u00f1ez-M\u00e1rquez C. A new theoretical framework for the Steinbuch\u2019s Lernmatrix in: SPIE Proceedings J.T. Astola I. Tabus and J. Barrera eds SPIE 2005. doi:10.1117\/12.621551.","DOI":"10.1117\/12.621551"},{"key":"e_1_3_2_13_1","unstructured":"HassounM.H. Fundamentals of Artificial Neural Networks 1st edn MIT Press Cambridge MA USA 1995."},{"key":"e_1_3_2_14_1","unstructured":"RosenfeldE.AndersonJ.A. Neurocomputing : foundations of research \/ edited by James A. Anderson and Edward Rosenfeld Cambridge Mass: MIT Press 1988."},{"key":"e_1_3_2_15_1","unstructured":"HassounM.H. Associative Neural Memories: Theory and Implementation New York: Oxford University Press 1993."},{"key":"e_1_3_2_16_1","doi-asserted-by":"publisher","DOI":"10.1109\/72.661123"},{"key":"e_1_3_2_17_1","first-page":"257","article-title":"Clasificador Asociativo de Patrones: Avances Teoricos,n.","volume":"3","author":"Santiago-Montero R.","year":"2003","unstructured":"Santiago-MonteroR.Ya\u00f1ez-M\u00e1rquezC.D\u0131az-de-Le\u00f3nJ.L., Clasificador Asociativo de Patrones: Avances Teoricos,n. , Avances en: Ciencias de la Computaci\u00f3n Special Edition, Research on Computing Science Series. Centro de Investigaci\u00f3n en Computaci\u00f3n, IPN, M\u00e9xico3 (2003), 257\u2013267.","journal-title":"Avances en: Ciencias de la Computaci\u00f3n Special Edition, Research on Computing Science Series. Centro de Investigaci\u00f3n en Computaci\u00f3n, IPN, M\u00e9xico"},{"key":"e_1_3_2_18_1","doi-asserted-by":"publisher","unstructured":"Soria-AlcarazJ.A.Santiago-MonteroR.CarpioM. One criterion for the selection of the cardinality of learning set used by the Associative Pattern Classifier in: 2010 IEEE Electronics Robotics and Automotive Mechanics Conference 2010 pp. 80\u201384. doi: 10.1109\/CERMA.2010.20.","DOI":"10.1109\/CERMA.2010.20"},{"key":"e_1_3_2_19_1","doi-asserted-by":"publisher","unstructured":"Santiago-MonteroR.SossaH.Guti\u00e9rrez-Hern\u00e1ndezD.A.ZamudioV.Hern\u00e1ndez-BautistaI.Valadez-God\u00ednezS. Novel Mathematical Model of Breast Cancer Diagnostics Using an Associative Pattern Classification Diagnostics 10(3) (2020) 136\u201310.3390\/diagnostics10030136..","DOI":"10.3390\/diagnostics10030136."},{"issue":"5","key":"e_1_3_2_20_1","first-page":"713","article-title":"A study of the associative pattern classifier method for multi-class processes","volume":"17","author":"Santiago-Montero R.","year":"2015","unstructured":"Santiago-MonteroR.SergioG.SossaH.Guti\u00e9rrez-Hern\u00e1ndezD.A.Ornerlas-Rodr\u0131guezM., A study of the associative pattern classifier method for multi-class processes, Journal of Optoelectronics and Advanced Materials17(5-6) (2015), 713\u2013719.","journal-title":"Journal of Optoelectronics and Advanced Materials"},{"key":"e_1_3_2_21_1","doi-asserted-by":"publisher","unstructured":"Uriarte-ArciaA.V.L\u00f3pez-Y\u00e1\u00f1ezI.Y\u00e1\u00f1ez-M\u00e1rquezC. One-Hot Vector Hybrid Associative Classifier for Medical Data Classification PLoS ONE 9(4) (2014) e95715. doi: 10.1371\/journal.pone.0095715.","DOI":"10.1371\/journal.pone.0095715"},{"key":"e_1_3_2_22_1","doi-asserted-by":"publisher","unstructured":"Cleofas-S\u00e1nchezL.Garc\u0131aV.Mart\u0131n-F\u00e9lezR.ValdovinosR.M.S\u00e1nchezJ.S.Camacho-NietoO. Hybrid Associative Memories for Imbalanced Data Classification: An Experimental Study in: Lecture Notes in Computer Science 2013 pp. 325\u2013334. doi: 10.1007\/978-3-642-38989-4.","DOI":"10.1007\/978-3-642-38989-4"},{"key":"e_1_3_2_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2011.05.002"},{"key":"e_1_3_2_24_1","unstructured":"Padierna-Garc\u0131aL.C. Clasificador Asociativo de Patrones DifusoAplicado al Diagnostico de Diabetes Mellitus Master\u2019s thesis Instituto Tecnologico de Le\u00f3n 2011."},{"key":"e_1_3_2_25_1","first-page":"53","article-title":"Pattern Associative Classifier Applied to Diabetes Mellitus Diagnosis","volume":"2010","author":"Padierna-Garc\u0131a L.C.","year":"2010","unstructured":"Padierna-Garc\u0131aL.C.Santiago-MonteroR.Zamarr\u00f3n-RamirezA., Pattern Associative Classifier Applied to Diabetes Mellitus Diagnosis, Memorias del 3er Congreso Internacional en Ciencias Computacionales CiComp2010 (2010), 53\u201357.","journal-title":"Memorias del 3er Congreso Internacional en Ciencias Computacionales CiComp"},{"key":"e_1_3_2_26_1","first-page":"36","article-title":"Neural associative memories","volume":"36","author":"Palm G.","year":"1993","unstructured":"PalmG.SchwenkerF.SommerF.T.StreyA., Neural associative memories, Biological Cybernetics36 (1993), 36\u201319.","journal-title":"Biological Cybernetics"},{"key":"e_1_3_2_27_1","unstructured":"BuecheF.J. Principles of physics 6th edn McGraw-Hill 1995."},{"key":"e_1_3_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/1656274.1656278"},{"key":"e_1_3_2_29_1","doi-asserted-by":"publisher","unstructured":"FriedmanM.KandelA. Introduction to Pattern Recognition: Statistical Structural Neural and Fuzzy Logic Approaches Series in Machine Perception and Artificial Intelligence World Scientific Publishing Company 1999. doi:10.1142\/3641.","DOI":"10.1142\/3641"},{"key":"e_1_3_2_30_1","unstructured":"DudaR.O.HartP.E.StorkD.G. Pattern classification 2nd Edition Wiley Interscience New York 2001."},{"key":"e_1_3_2_31_1","doi-asserted-by":"publisher","unstructured":"Marques de SaJ.P. Pattern Recognition Concepts Methods and Applications Springer-Verlag 2002. doi:10.1007\/978-3-642-56651-6.","DOI":"10.1007\/978-3-642-56651-6"},{"key":"e_1_3_2_32_1","unstructured":"RishI. An empirical study of the naive Bayes classifier in: IJCAI-01 workshop on Empirical Methods in AI 2001."},{"key":"e_1_3_2_33_1","unstructured":"ZhangH. The Optimality of Naive Bayes in: Proceedings of the Seventeenth International Florida Artificial Intelligence Research Society Conference (FLAIRS 2004) V. Barr and Z. Markov eds AAAI Press 2004."},{"key":"e_1_3_2_34_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(70)90081-1"},{"key":"e_1_3_2_35_1","unstructured":"FrankA.AsuncionA. UCI Machine Learning Repository 2010. http:\/\/archive.ics.uci.edu\/ml."},{"key":"e_1_3_2_36_1","doi-asserted-by":"publisher","unstructured":"SossaH.Barr\u00f3nR.CuevasF.AguilarC.Cort\u00e9sH. Binary Associative Memories Applied to Gray Level Pattern Recalling in: Lecture Notes in Computer Science. Advances in Artificial Intelligence IBERAMIA 2004 Springer Berlin Heidelberg pp. 656\u2013666. doi:10.1007\/978-3-540-30498-2_66.","DOI":"10.1007\/978-3-540-30498-2_66"},{"key":"e_1_3_2_37_1","doi-asserted-by":"publisher","unstructured":"SossaH.Barr\u00f3nR.V\u00e1zquezR.A. Transforming Fundamental Set of Patterns to a Canonical Form to Improve Pattern Recall in: Lecture Notes in Computer Science. Advances in Artificial Intelligence IBERAMIA 2004 Springer Berlin Heidelberg pp. 687\u2013696. doi:10.1007\/978-3-540-30498-2_69.","DOI":"10.1007\/978-3-540-30498-2_69"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems: Applications in Engineering and Technology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-219347","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-219347","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-219347","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:46:51Z","timestamp":1777456011000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-219347"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,23]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["10.3233\/JIFS-219347"],"URL":"https:\/\/doi.org\/10.3233\/jifs-219347","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,3,23]]}}}