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Classical and Modern Approaches to Classification and Dimensionality Reduction Techniques

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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


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Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα Except where otherwise noted, this item's license is described as Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα