Development of multidimensional scaling algorithms with application to natural language representation problems

Φωτάκη, Ελένη; Fotaki, Lena

dc.contributor.author	Φωτάκη, Ελένη	el
dc.contributor.author	Fotaki, Lena	en
dc.date.accessioned	2024-05-27T11:10:43Z
dc.date.available	2024-05-27T11:10:43Z
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/59498
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.27194
dc.rights	Default License
dc.subject	Dimensionality Reduction	en
dc.subject	Manifold Learning	en
dc.subject	Multidimensional Scaling	en
dc.subject	Set-MDS	en
dc.subject	Non-linear Algorithms	en
dc.subject	Knot theory Diploma Thesis 3	en
dc.title	Development of multidimensional scaling algorithms with application to natural language representation problems	en
heal.type	bachelorThesis
heal.secondaryTitle	Manifold Learning technique	en
heal.classification	Machine Learning	en
heal.language	el
heal.language	en
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2023-12-07
heal.abstract	In this thesis, we explore and develop Manifold Learning and Dimensionality Reduction algorithms. We focus on algorithms capable of simplifying data with complex and non-linear structures to make them more comprehensible for humans and to reveal possible correlations among the data. The contribution of this thesis consists of two parts. In the first part, we optimize an extension of the classical Multidimensional Scaling (MDS) method using derivative-free optimization techniques. We evaluate our algorithm on synthetic and real-world data, and our conclusion is that the algorithm accurately estimates the geometry of data embedded in high-dimensional spaces. In the second part, we define the Set-MDS problem, where the peculiarity is that our data consists of sets of points rather than individual points. Subsequently, we propose an approximate solution through the COSMOS algorithm. After analyzing the algorithm, we present the results of our experiments.	en
heal.advisorName	Ποταμιάνος, Αλέξανδρος	el
heal.committeeMemberName	Φωτάκης, Δημήτρης	el
heal.committeeMemberName	Τζαφέστας, Κωνσταντίνος	el
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Ηλεκτρολόγων Μηχανικών και Μηχανικών Υπολογιστών. Τομέας Σημάτων, Ελέγχου και Ρομποτικής	el
heal.academicPublisherID	ntua
heal.numberOfPages	93 σ.	el
heal.fullTextAvailability	false