Tenzorske dekompozicije u prepoznavanju akcije

master's thesis

• Title (english): Tensor decompositions in action recognition
• Author: Matija Šantek
• Mentor: Zlatko Drmač (mentor)
• Committee member: Zlatko Drmač (predsjednik povjerenstva)
• Committee member: Nela Bosner (član povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Matko Ljulj (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-07-17, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Ovaj rad započeli smo detaljnim istraživanjem nekih ključnih područja u vezi s tenzorima i njihovim dekompozicijama u kontekstu računalnog vida. Prvo smo se posvetili definiranju nekih matričnih množenja koja su neophodna pri radu s tenzorima i njihovim dekompozicijama. Nakon toga, usredotočili smo se na definiciju tenzora i njihovih osnovnih komponenti, kao što su niti i odsječci tenzora. Konačno, u kraćem opisu, predstavili smo SVD (Singular Value Decomposition) koji je tehnika za dekompoziciju matrica. Sva ova teorijska podloga predstavlja osnovu za daljnje istraživanje i primjenu tenzorskih dekompozicija u računalnom vidu. Zatim smo opisali Tuckerovu dekompoziciju koja predstavlja snažan alat za analizu tenzora. Tuckerova dekompozicija rastavlja tenzor na njegove osnovne komponente - jezgru i faktorske matrice za svaku dimenziju. Ova dekompozicija omogućuje nam razumijevanje strukture tenzora i izdvajanje bitnih karakteristika. Posebno smo istaknuli HOSVD, specijalnu verziju Tuckerove dekompozicije koja se može smatrati generaliziranom verzijom SVD-a za višedimenzionalne tenzore. Naposljetku, predstavili smo Tenzorski vlak dekompoziciju, najmlađu dekompoziciju koja se razvila kako bi riješila određene probleme ostalih dekompozicija.

Abstract (english)

We initiated this work with in-depth research on key areas related to tensors and their decompositions in the context of computer vision. First, we focused on defining certain matrix multiplications that are necessary when working with tensors and their decompositions. After that, we delved into the definition of tensors and their basic components, such as fibers and tensor slices. Additionally, we defined fundamental tensor operations required for their processing. Finally, in a brief description, we presented Singular Value Decomposition (SVD) as a technique for matrix decomposition. All this theoretical foundation serves as a basis for further research and application of tensor decompositions in computer vision. Next, we described Tucker decomposition, which is a powerful tool for tensor analysis. Tucker decomposition breaks down a tensor into its core and factor matrices for each dimension. This decomposition enables us to understand the structure of tensors and extract significant characteristics. We particularly highlighted HOSVD, a special version of Tucker decomposition that can be considered a generalized version of SVD for multidimensional tensors. Lastly, we presented the Tensor Train decomposition, the most recent decomposition developed to address specific issues of other decompositions. This decomposition provides flexibility and efficiency in handling large-dimensional tensors.

• Keywords: računalni vid; matrična množenja; SVD (Singular Value Decomposition); tehnika za dekompoziciju matrica; Tuckerova dekompozicija; HOSVD
• Language: croatian
• URN:NBN: urn:nbn:hr:217:179821
• Study programme: Title: Computer Science and Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar računarstva i matematike (sveučilišni magistar računarstva i matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-02-13 10:19:40