{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T17:54:47Z","timestamp":1777658087133,"version":"3.51.4"},"reference-count":26,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T00:00:00Z","timestamp":1760572800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The Centro Universitario de Ciencias Exactas e Ingenier\u00edas (CUCEI) of Universidad de Guadalajara"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper introduces a modified soft margin optimal hyperplane (MSMOH) algorithm, which enhances the linear separating properties of support vector machines (SVMs) by placing higher penalties on large misclassification errors. This approach improves margin symmetry in both balanced and asymmetric data distributions. The research is divided into two main stages. The first stage evaluates MSMOH for synthetic data classification and its application in heart disease diagnosis. In a cross-validation setting with unknown data, MSMOH demonstrated superior average performance compared to the standard soft margin optimal hyperplane (SMOH). Performance metrics confirmed that MSMOH maximizes the margin and reduces the number of support vectors (SVs), thus improving classification performance, generalization, and computational efficiency. The second stage applies MSMOH as a novel synthesis algorithm to design a neural associative memory (NAM) based on a recurrent neural network (RNN). This NAM is used for fault diagnosis in fossil electric power plants. By promoting more symmetric decision boundaries, MSMOH increases the accurate convergence of 1024 possible input elements. The results show that MSMOH effectively designs the NAM, leading to better performance than other synthesis algorithms like perceptron, optimal hyperplane (OH), and SMOH. Specifically, MSMOH achieved the highest number of converged input elements (1019) and the smallest number of elements converging to spurious memories (5).<\/jats:p>","DOI":"10.3390\/sym17101749","type":"journal-article","created":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T16:33:22Z","timestamp":1760632402000},"page":"1749","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Modified Soft Margin Optimal Hyperplane Algorithm for Support Vector Machines Applied to Fault Patterns and Disease Diagnosis"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0872-062X","authenticated-orcid":false,"given":"Mario Antonio","family":"Ruz Canul","sequence":"first","affiliation":[{"name":"Departamento de Innovacion Basada en la Informacion y el Conocimiento, Centro Universitario de Ciencias Exactas e Ingenierias, Universidad de Guadalajara, Blvd. Marcelino Garcia Barragan 1421, Guadalajara 44430, Jalisco, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8332-4980","authenticated-orcid":false,"given":"Jose A.","family":"Ruz-Hernandez","sequence":"additional","affiliation":[{"name":"Facultad de Ingenieria, Universidad Autonoma del Carmen, C.56 No.4 Esq. Avenida Concordia Col. Benito Juarez, Ciudad del Carmen 24180, Campeche, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9600-779X","authenticated-orcid":false,"given":"Alma Y.","family":"Alanis","sequence":"additional","affiliation":[{"name":"Departamento de Innovacion Basada en la Informacion y el Conocimiento, Centro Universitario de Ciencias Exactas e Ingenierias, Universidad de Guadalajara, Blvd. Marcelino Garcia Barragan 1421, Guadalajara 44430, Jalisco, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5515-1530","authenticated-orcid":false,"given":"Juan Carlos","family":"Gonzalez Gomez","sequence":"additional","affiliation":[{"name":"Facultad de Ingenieria, Universidad Autonoma del Carmen, C.56 No.4 Esq. Avenida Concordia Col. Benito Juarez, Ciudad del Carmen 24180, Campeche, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6595-8605","authenticated-orcid":false,"given":"Jorge","family":"G\u00e1lvez","sequence":"additional","affiliation":[{"name":"Departamento de Innovacion Basada en la Informacion y el Conocimiento, Centro Universitario de Ciencias Exactas e Ingenierias, Universidad de Guadalajara, Blvd. Marcelino Garcia Barragan 1421, Guadalajara 44430, Jalisco, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,16]]},"reference":[{"key":"ref_1","unstructured":"Abe, S. (2005). Support Vector Machines for Pattern Classification, Springer."},{"key":"ref_2","first-page":"1","article-title":"Survey on SVM and their application in image classification","volume":"13","author":"Chandra","year":"2021","journal-title":"Int. J. Inf. 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