Tenzorske dekompozicije za prepoznavanje radnje

master's thesis

• Author: Maja Tonček
• Mentor: Zlatko Drmač (mentor)
• Committee member: Zlatko Drmač (predsjednik povjerenstva)
• Committee member: Goran Muić (član povjerenstva)
• Committee member: Slaven Kožić (član povjerenstva)
• Committee member: Tina Bosner (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-02-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu dan je pregled osnovnih obilježja multilinearne algebre čiji su središnji objekti tenzori. Potom su detaljno opisane najpopularnije tenzorske dekompozicije CP i Tucker, dotičući se pojma ranga, svojstva (ne)jedinstvenosti, algoritama za računanje dekompozicija te općenite primjene i primjene u prepoznavanju radnje. Također su opisane i dekompozicije vlačna, prstenasta i blokovska, koje se tek posljednjih godina koriste u području prepoznavanja radnje. Na kraju je implementiran algoritam Tuckerove ridge regularizacije, koji kombinacijom Tuckerove dekompozicije i ridge regularizacije uspjeva relativno dobro raspoznavati kretnje sa statičnih slika s raznolikim pozadinama.

Abstract (english)

In this thesis we first give an overview of the basic concepts in multilinear algebra whose core objects are tensors. Then we introduce the most known and used tensor decompositions CP and Tucker, where we also discuss ranks of these decompositions, their uniqueness property or the lack of it, algorithms for computing the decompositions and the various applications, with a special emphasis on action recognition. We also talk about the tensor train, tensor ring and block term decompositions which have recently been more used in the field of action recognition. The end of the thesis we dedicate to the implementation of Tucker ridge regression, an algorithm for recognizing actions from static images.

• Keywords: multilinearna algebra; tenzori; Tuckerova ridge regularizacija
• Keywords (english): multilinear algebra; tensors; Tucker ridge regression
• Language: croatian
• URN:NBN: urn:nbn:hr:217:017585
• Study programme: Title: Computer Science and Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-10-27 11:05:23