{"paper_id":"3028b344-6ec2-4158-bf5c-e2774624a21f","body_text":"Mixed-Integer Constrained Programming for Binary Classification, Feature Selection and Imbalanced Data | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Mixed-Integer Constrained Programming for Binary Classification, Feature Selection and Imbalanced Data Redouane Hakimi, Badreddine Benyacoub, Mohamed Ouzineb This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9199348/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Imbalanced binary classification is a common issue in serious contexts when rare events have practical effects. Traditional cost-sensitive strategies improve minority identification, but they frequently address feature selection and classification separately, consequently leading to suboptimal results. This paper presents MP-CSFS (Mathematical Programming for Cost-Sensitive Feature Selection), a mixed-integer linear programming framework that integrates cost-sensitive classification and feature selection into a single optimization model. The approach use asymmetric misclassification costs and applies binary activation variables to manage feature selection. This mixed optimization technique maintains that specified features enhance differentiation between classes under the cost limits, enhancing both clarity and prediction stability. The proposed method is evaluated on large-scalennumerous high-dimensional benchmarks which display high class imbalance. Experimental results provide average or above-average outcomes against existing approaches, notably in metrics such as AUC and G-mean, while reducing dimensionality significantly and improving computational tractability. The outcomes show that blending feature selection with cost-sensitive learning inside a mathematical programming framework provides an intuitive as well as scalable solution to imbalanced classification in difficult, real-world scenarios. binary classification imbalanced dataset cost sensitivity features selection mathematical programming Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {\"props\":{\"pageProps\":{\"initialData\":{\"identity\":\"rs-9199348\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":true,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":625370322,\"identity\":\"6e6e80f0-0e65-4bb4-8801-46880073613e\",\"order_by\":0,\"name\":\"Redouane Hakimi\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1klEQVRIiWNgGAWjYFACHgbGBgMGHn5mkrVINpOmBUgZHCBWg3kD78GPMwq2yRgf5z384UMNgzx/A3fiB3xaZA7wJUtuMLjNY3aYL01yxjEGwxkHeDdL4NMiwcBjIPkArIXHjJmHjYFxAwPvBkJajH+CtBg38xh//vOPwR6oZfMPAlrMwA4zYOYxkGZsY0gEatmG3xZmHjPLGUAtEkCHSfb2SSTPOMy7zQKvFvYe45s9f27b8/efMf7w45uNbX977+Yb+LQwoEW6BIbIKBgFo2AUjAIyAAA+BT7xOWq6aQAAAABJRU5ErkJggg==\",\"orcid\":\"\",\"institution\":\"Institut National de Statistique et d'Economie Appliquée\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Redouane\",\"middleName\":\"\",\"lastName\":\"Hakimi\",\"suffix\":\"\"},{\"id\":625370323,\"identity\":\"02c458b4-fa6a-4249-8494-5a038162dd57\",\"order_by\":1,\"name\":\"Badreddine Benyacoub\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Institut National de Statistique et d'Economie Appliquée\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Badreddine\",\"middleName\":\"\",\"lastName\":\"Benyacoub\",\"suffix\":\"\"},{\"id\":625370324,\"identity\":\"1d047775-ea14-402e-90db-6fc62001fef6\",\"order_by\":2,\"name\":\"Mohamed Ouzineb\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Institut National de Statistique et d'Economie Appliquée\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Mohamed\",\"middleName\":\"\",\"lastName\":\"Ouzineb\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2026-03-23 10:40:58\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-9199348/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-9199348/v1\",\"draftVersion\":[],\"editorialEvents\":[],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":108651147,\"identity\":\"9a4c3406-670f-4084-9832-84b642b3ed4e\",\"added_by\":\"auto\",\"created_at\":\"2026-05-07 01:56:28\",\"extension\":\"pdf\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":490279,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"Manuscript.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-9199348/v1_covered_3bf8bb91-1f36-4191-94a8-ab1abd5fd01a.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"Mixed-Integer Constrained Programming for Binary Classification, Feature Selection and Imbalanced Data\",\"fulltext\":[],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":false,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":true,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":false,\"isAuthorSuppliedPdf\":true,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":true,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"researchsquare\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":true,\"externalIdentity\":\"\",\"sideBox\":\"\",\"snPcode\":\"\",\"submissionUrl\":\"/submission\",\"title\":\"Research Square\",\"twitterHandle\":\"researchsquare\",\"acdcEnabled\":true,\"dfaEnabled\":false,\"editorialSystem\":\"\",\"reportingPortfolio\":\"\",\"inReviewEnabled\":false,\"inReviewRevisionsEnabled\":true},\"keywords\":\"binary classification, imbalanced dataset, cost sensitivity, features selection, mathematical programming\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-9199348/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-9199348/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"Imbalanced binary classification is a common issue in serious contexts when rare events have practical effects. 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