Problem matričnih napolnitev preko optimizacije na Riemannovih mnogoterostih

diplomsko delo

Ana Poklukar (Author), Aljaž Zalar (Mentor)

Abstract

V diplomski nalogi obravnavamo problem matričnih napolnitev, pri katerem je cilj obnoviti manjkajoče vrednosti v matriki na podlagi razpoložljivih podatkov in minimizirati rang matrike. Osredotočimo se na algoritem, ki temelji na tehnikah Riemannovih mnogoterosti. V delu implementiramo algoritem, predstavljen v članku "Low-rank matrix completion by Riemannian optimization", in ga preizkusimo v kakovosti rekonstrukcije na sintetičnih podatkih in različnih slikovnih podatkih z dodanimi motnjami, šumom ali manjkajočimi piksli. Rezultate analiziramo in interpretiramo s pomočjo matematičnega ozadja algoritma.

Keywords

matrične napolnitve;Riemannove mnogoterosti;optimizacija;minimizacija ranga;rekonstrukcija slik;univerzitetni študij;diplomske naloge;

Data

Language:	Slovenian
Year of publishing:	2024
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FRI - Faculty of Computer and Information Science
Publisher:	[A. Poklular]
UDC:	004(043.2)
COBISS:	211501827
Views:	114
Downloads:	42
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Matrix Completion Problem Through Optimization on Riemannian Manifolds
Secondary abstract:	In this thesis, we address the problem of matrix completion, where the goal is to recover missing values in a matrix based on the available data and minimizing the rank of the matrix. We focus on an algorithm that relies on Riemannian manifold techniques. In the work, we implement the algorithm presented in the paper "Low-rank matrix completion by Riemannian optimization" and test its reconstruction quality on synthetic data and on various image data with added disturbances, noise, or missing pixels. The results are then analyzed and interpreted with the help of the mathematical background of the algorithm.
Secondary keywords:	matrix completion;Riemannian manifolds;optimization;rank minimization;image reconstruction;computer and information science;diploma;
Type (COBISS):	Bachelor thesis/paper
Study programme:	1000468
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za računalništvo in informatiko
Pages:	1 spletni vir (1 datoteka PDF (55 str.))
ID:	24985110