A new approach to multivariate adaptive regression splines by using Tikhonov regularization and continuous optimization

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dc.contributor.authorTaylan, Pakize
dc.contributor.authorWeber, Gerhard-Wilhelm
dc.contributor.authorOzkurt, Fatma Yerlikaya
dc.date.accessioned2024-04-24T16:02:33Z
dc.date.available2024-04-24T16:02:33Z
dc.date.issued2010
dc.departmentDicle Üniversitesien_US
dc.description.abstractThis paper introduces a model-based approach to the important data mining tool Multivariate adaptive regression splines (MARS), which has originally been organized in a more model-free way. Indeed, MARS denotes a modern methodology from statistical learning which is important in both classification and regression, with an increasing number of applications in many areas of science, economy and technology. It is very useful for high-dimensional problems and shows a great promise for fitting nonlinear multivariate functions. The MARS algorithm for estimating the model function consists of two algorithms, these are the forward and the backward stepwise algorithm. In our paper, we propose not to use the backward stepwise algorithm. Instead, we construct a penalized residual sum of squares for MARS as a Tikhonov regularization problem which is also known as ridge regression. We treat this problem using continuous optimization techniques which we consider to become an important complementary technology and model-based alternative to the concept of the backward stepwise algorithm. In particular, we apply the elegant framework of conic quadratic programming. This is an area of convex optimization which is very well-structured, herewith, resembling linear programming and, hence, permitting the use of powerful interior point methods. Based on these theoretical and algorithmical studies, this paper also contains an application to diabetes data. We evaluate and compare the performance of the established MARS and our new CMARS in classifying diabetic persons, where CMARS turns out to be very competitive and promising.en_US
dc.description.sponsorshipTUBITAKen_US
dc.description.sponsorshipThe authors wish to thank the two anonymous referees for their rigorous and contructive criticism, and the members of the TUBITAK project on Use and Development of Data Mining Methods for Quality Control in Manufacturing for support during of this study. They thank Prof. Dr. Leonidas Sakalauskas for his valuable guidance and encouragement.en_US
dc.identifier.doi10.1007/s11750-010-0155-7
dc.identifier.endpage395en_US
dc.identifier.issn1134-5764
dc.identifier.issn1863-8279
dc.identifier.issue2en_US
dc.identifier.scopus2-s2.0-85027914630
dc.identifier.scopusqualityQ1
dc.identifier.startpage377en_US
dc.identifier.urihttps://doi.org/10.1007/s11750-010-0155-7
dc.identifier.urihttps://hdl.handle.net/11468/14834
dc.identifier.volume18en_US
dc.identifier.wosWOS:000285424000005
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.relation.ispartofTop
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectRegressionen_US
dc.subjectStatistical Learningen_US
dc.subjectMarsen_US
dc.subjectClusteringen_US
dc.subjectCurvatureen_US
dc.subjectPenalty Methodsen_US
dc.subjectClassificationen_US
dc.subjectContinuous Optimizationen_US
dc.subjectConic Quadratic Programmingen_US
dc.subjectWell-Structured Convex Problemsen_US
dc.subjectInterior Point Methodsen_US
dc.titleA new approach to multivariate adaptive regression splines by using Tikhonov regularization and continuous optimizationen_US
dc.titleA new approach to multivariate adaptive regression splines by using Tikhonov regularization and continuous optimization
dc.typeArticleen_US

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