diplomsko delo
Matej Klančar (Author), Aljaž Zalar (Mentor)

Abstract

Problem matričnih napolnitev sprejme matriko, ki nima določenih vrednosti vseh elementov, cilj pa je določiti vrednosti teh elementov tako, da bo rang napolnjene matrike najmanjši možen. V diplomskem delu predstavimo teoretično ozadje petih različnih algoritmov, ki rešujejo ta problem (NNM, SVT, TNNM, ASD, LMaFit), in jih testiramo. Pri testiranju se osredotočimo na problem rekonstrukcije slik, kjer vrednosti nekaterih pikslov ne poznamo. Analiziramo različne vidike rekonstrukcij, rezultate pa interpretiramo prek matematičnega ozadja algoritmov. Rezultate primerjamo tudi z uveljavljeno metodo rekonstrukcije slik, ki temelji na reševanju Laplaceove diferencialne enačbe.

Keywords

matrične napolnitve;minimizacija ranga;rekonstrukcija slik;priporočilni sistemi;diplomske naloge;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UL FRI - Faculty of Computer and Information Science
Publisher: [M. Klančar]
UDC: 004(043.2)
COBISS: 163657987 Link will open in a new window
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Other data

Secondary language: English
Secondary title: Algorithms for solving matrix completion problem
Secondary abstract: The matrix completion problem considers a matrix in which some elements are unknown. The goal is to determine the elements, such that the rank of the filled matrix is minimal. In this thesis, we present the theoretical background of five different algorithms used to solve this problem (NNM, SVT, TNNM, ASD, LMaFit) and test them. In testing, we focus on the reconstruction of images where the values of some pixels are unknown. We analyze different aspects of reconstructions and interpret the results referring to the mathematical background of the algorithms. We also compare the results with a more standard method of image reconstruction, based on solving the Laplace differential equations.
Secondary keywords: matrix completion;rank minimization;image reconstruction;recommendation systems;computer and information science;diploma;Računalništvo;Univerzitetna in visokošolska dela;
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: 53 str.
ID: 21439471