Classical and Modern Approaches to Classification and Dimensionality Reduction Techniques

Μπαρμπάκου, Δωροθέα; Barmpakou, Dorothea

dc.contributor.author	Μπαρμπάκου, Δωροθέα	el
dc.contributor.author	Barmpakou, Dorothea	en
dc.date.accessioned	2019-12-20T10:03:12Z
dc.date.available	2019-12-20T10:03:12Z
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/49604
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.17302
dc.description	Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Εφαρμοσμένες Μαθηματικές Επιστήμες”	el
dc.rights	Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/gr/	*
dc.subject	Classification	en
dc.subject	Κατηγοριοποίηση	el
dc.subject	Κλασικές Εφαρμογές	el
dc.subject	Dimensionality Reduction	en
dc.subject	Classical Applications	en
dc.subject	Modern Approaches	en
dc.subject	Methods	en
dc.subject	Mείωση Διαστάσεων	el
dc.subject	Σύγχρονες Μέθοδοι	el
dc.subject	Μέθοδοι	el
dc.title	Classical and Modern Approaches to Classification and Dimensionality Reduction Techniques	en
dc.title	Κλασικές και Σύγχρονες Μέθοδοι για Κατηγοριοποίηση και Μείωση Διαστάσεων	el
heal.type	masterThesis
heal.classification	Statistics	en
heal.classification	Στατιστική	el
heal.language	en
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2019-06-27
heal.abstract	In this thesis, we focus on techniques for dimensionality reduction and classi cation problems, which facilitate the statistical analysis and interpretation of complex data. In Chapter 1, we present Principal Components Analysis (PCA): a dimensionality reduction technique. We introduce its aim and the theoretical basis, we de ne the properties of Principal Components and their correlation structure. The loadings, component scores and correlation circle are analysed. Methods for extracting the appropriate number of Principal Components are included. Furthermore, we carry out a classical and a modern application of PCA to two di erent datasets. Speci cally, we describe and inspect the Irish dataset, in which the number of variables is lower than the number of the individuals (classical application), and the Chicken dataset which includes far fewer individuals than variables (modern application). In Chapter 2, Classi cation is introduced and some of the most important parametric classi ers are analysed. Firstly, we introduce Logistic Regression Analysis, the interpretation and estimation of its coe cients and the ROC Curve and we apply it to the Irish dataset. Then, Linear Discriminant Analysis is introduced, its method and application to the Irish data. Lastly, the theoretical basis of Quadratic Discriminant Analysis is presented and its application to the Irish dataset as well. In Chapter 3, we introduce K Nearest Neighbors non parametric method for classi cation, its method and application to the Irish dataset and to a more complex one: Khan dataset. We extract important insights. Chapter 4 is devoted to methods based on Trees. More precisely, Classi cation Trees and Regression Trees methods are analysed. Regarding the Classi cation Trees, we introduce the method, present the building procedure of a classi cation tree, the tree pruning and some advantages of Classi cation Trees method, and we apply it to the Irish dataset. Regarding the Regression Trees, we introduce the method and the pruning procedure, and we apply it to the Boston dataset. Finally, Chapter 5 includes important remarks and conclusions, taking into account all of the methods applied to the Irish data.	en
heal.advisorName	Barranco--Chamorro, Inmaculada	en
heal.advisorName	Καρώνη, Χρυσηΐς	el
heal.committeeMemberName	Καρώνη, Χρυσηΐς	el
heal.committeeMemberName	Barranco--Chamorro, Inmaculada	es
heal.committeeMemberName	Fernández Ponce, Fernández Ponce	el
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Εφαρμοσμένων Μαθηματικών και Φυσικών Επιστημών	el
heal.academicPublisherID	ntua
heal.numberOfPages	118 σ.	el
heal.fullTextAvailability	true