Simplicial clustering using the $\alpha$--transformation

Simplicial clustering using the $\alpha$--transformation | 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 Simplicial clustering using the $\alpha$--transformation Michail Tsagris, Christos Adam, Nikolaos Kontemeniotis This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7749449/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 We introduce two simplicial clustering approaches for compositional data, that are adaptations of the $K$--means and of the Gaussian mixture models algorithms, by employing the $\alpha$--transformation. By utilizing clustering validation indices we can decide on the number of clusters and choose the value of $\alpha$ for the $K$--means, while for the model-based clustering approach information criteria complete this task. Extensive simulation studies compare the performance of these two approaches and a real dataset illustrates their performance in real world settings. Applied Statistics compositional data α–transformation K–means model-based clustering Full Text Additional Declarations The authors declare no competing interests. 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-7749449","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":522745074,"identity":"b83f94c2-7ed8-4a25-90bd-a6fcfae9240f","order_by":0,"name":"Michail Tsagris","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAs0lEQVRIiWNgGAWjYPACCQZ+4hWzQbVINpCohYHB4ACxOnTntz/8+HWPhb3xjeSDHxh+3SOsxewYj7G0zDOJxG030pIlGPuKidLCIC1xQCLB7EaOGQNjTwIxWtgf/wZqsTeeQbwWBjPJDwckGDdIALUw/CBKS46ZNcMBicQZZ54lSyQ2EKPl8PHHN38cqLPnbweG2Ic/RGgBAWYeGCuxjTgdDIw/4Mw/RGoZBaNgFIyCEQUAV7g4lTAsFqsAAAAASUVORK5CYII=","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Michail","middleName":"","lastName":"Tsagris","suffix":""},{"id":522745075,"identity":"01a29188-22af-4437-b152-7c353f0c3151","order_by":1,"name":"Christos Adam","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Christos","middleName":"","lastName":"Adam","suffix":""},{"id":522745076,"identity":"037d0417-cb75-4d7b-86bc-0f5b2f1e9a8b","order_by":2,"name":"Nikolaos Kontemeniotis","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Nikolaos","middleName":"","lastName":"Kontemeniotis","suffix":""}],"badges":[],"createdAt":"2025-09-30 08:59:14","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-7749449/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7749449/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":92565547,"identity":"570eaf53-25e3-42dd-ab5e-8632002c96c1","added_by":"auto","created_at":"2025-10-01 06:21:33","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1559694,"visible":true,"origin":"","legend":"","description":"","filename":"sc.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7749449/v1_covered_03102e40-be14-4c39-b908-9d506afab903.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eSimplicial clustering using the $\\alpha$--transformation\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"[email protected]","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":"compositional data, α–transformation, K–means, model-based clustering","lastPublishedDoi":"10.21203/rs.3.rs-7749449/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7749449/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe introduce two simplicial clustering approaches for compositional data, that are adaptations of the $K$--means and of the Gaussian mixture models algorithms, by employing the $\\alpha$--transformation. 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