Reproducing kernel hilbert spaces with applications to support vector machines

Κοντογιάννης, Φίλιππος; Kontogiannis, Filippos

dc.contributor.author	Κοντογιάννης, Φίλιππος	el
dc.contributor.author	Kontogiannis, Filippos	en
dc.date.accessioned	2025-01-28T12:07:14Z
dc.date.available	2025-01-28T12:07:14Z
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/60995
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.28691
dc.description	Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Εφαρμοσμένες Μαθηματικές Επιστήμες”	el
dc.rights	Default License
dc.subject	Reproducing kernels	en
dc.subject	Support vector machines	en
dc.subject	Hilbert spaces	en
dc.subject	Representer theorem	en
dc.subject	Ridge regression	en
dc.title	Reproducing kernel hilbert spaces with applications to support vector machines	en
dc.title	Αναπαγωγικοί πυρήνες χώρων χίλμπερτ με εφαρμογές σε μηχανές διανυσμάτων υποστήριξης	el
heal.type	masterThesis
heal.classification	Μαθηματικά	el
heal.classification	Machine learning	en
heal.language	en
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2024-09-26
heal.abstract	Support Vector Machines (SVM) are supervised learning models that deal with both classification and regression problems. For a k-classification problem, the main idea behind support vector machines models is constructing k − 1 hyperplanes, so as to split the data into data categories. In the context of regression models, SVM aims to find a function that fits the data in such a way that ”splits” the dependent variable into ”two cases.” One advantage of SVMs is the flexibility that the prediction formula provides, which arises naturally from kernel theory (kernel trick). Using the kernel trick and various types of kernels, we can avoid using the primal input space and construct feature spaces for each kernel that is more suitable for the studied problem by constructing non-linear models. Kernel-based methods heavily depend on the Theory of Reproducing Kernel Hilbert Space (RKHS), a powerful tool widely utilized across diverse scientific domains, particularly in scenarios where non-linear models are indispensable. The main result of RKHS theory is that a function belonging to an RKHS can be written as the span of an already chosen kernel function. Thus, given the variety of kernels, various function spaces can be generated to best fit the problem we are dealing with. Within the RKHS framework, it can be proven that, under specific assumptions on the kernel function, SVM problems admit a unique solution that belongs to the Reproducing Kernel Hilbert Space.	en
heal.advisorName	Γιαννακόπουλος, Αθανάσιος	el
heal.committeeMemberName	Γιαννακόπουλος, Αθανάσιος	el
heal.committeeMemberName	Γιαννακάκης, Νικόλαος	el
heal.committeeMemberName	Σμυρλής, Γεώργιος	el
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Εφαρμοσμένων Μαθηματικών και Φυσικών Επιστημών	el
heal.academicPublisherID	ntua
heal.numberOfPages	72 σ.	el
heal.fullTextAvailability	false