diplomsko delo
Biljana Vitanova (Author), Aljaž Zalar (Mentor)

Abstract

Analiza glavnih komponent (PCA) je metoda, ki projecira podatke na ortogonalne podprostore. Težave PCA nastopijo ob prisotnosti osamelcev. Metoda robustne analize glavnih komponent (RPCA) odpravlja te težave z učinkovitim obravnavanjem osamelcev na matrikah. Z uporabo operacij, definiranih s tenzorsko algebro, so te metode razširjene na tenzorske pristope za obravnavo bolj kompleksnih, večdimenzionalnih podatkov. Aproksimacija tenzorjev s tenzorji nizkega ranga naredi te metode še posebej uporabne za odstranjevanje šuma iz signalov. Glavni cilj te diplomske naloge je preučiti dva algoritma, ki temeljita na tenzorskih pristopih, s poudarkom na razlagi matematičnega ozadja, izbiri parametrov in analizi učinkovitosti za odstranjevanje šuma. Zaradi možnosti vizualnega vrednotenja smo te metode testirali na zašumljenih slikah.

Keywords

analiza glavnih komponent;tenzorska algebra;aproksimacija nizkega ranga;rekonstrukcija slik;univerzitetni študij;diplomske naloge;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UL FRI - Faculty of Computer and Information Science
Publisher: [B. Vitanova]
UDC: 004(043.2)
COBISS: 211557635 Link will open in a new window
Views: 222
Downloads: 73
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Other data

Secondary language: English
Secondary title: Principal Component Analysis of Multidimensional data
Secondary abstract: Traditional Principal Component Analysis (PCA) aims to project data onto orthogonal subspaces. However, a limitation of PCA is that it struggles in presence of outliers. Robust Principal Component Analysis (RPCA) improves upon this by effectively handling outliers. Using operations defined with tensor algebra, these methods are further extended to tensor-methods, to handle more complex, multidimensional data. By approximating with low-rank data, these methods are particularly useful for signal denoising. The main goal of this thesis is to examine two such tensor-based algorithms. With emphasis to explain the mathematical background, parameter selection, and performance analysis. To provide visual explanation and validation, we test these algorithms on noisy images.
Secondary keywords: principal component analysis;tensor algebra;low-rank approximation;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 (63 str.))
ID: 24985108