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A block coordinate descent-based projected gradient algorithm for orthogonal non-negative matrix factorization
ID Asadi, Soodabeh (Author), ID Povh, Janez (Author)

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Abstract
This article uses the projected gradient method (PG) for a non-negative matrix factorization problem (NMF), where one or both matrix factors must have orthonormal columns or rows. We penalize the orthonormality constraints and apply the PG method via a block coordinate descent approach. This means that at a certain time one matrix factor is fixed and the other is updated by moving along the steepest descent direction computed from the penalized objective function and projecting onto the space of non-negative matrices. Our method is tested on two sets of synthetic data for various values of penalty parameters. The performance is compared to the well-known multiplicative update (MU) method from Ding (2006), and with a modified global convergent variant of the MU algorithm recently proposed by Mirzal (2014). We provide extensive numerical results coupled with appropriate visualizations, which demonstrate that our method is very competitive and usually outperforms the other two methods.

Language:English
Keywords:non-negative matrix factorization, orthogonality conditions, projected gradient method, multiplicative update algorithm, block coordinate descent
Work type:Article (dk_c)
Typology:1.01 - Original Scientific Article
Organization:FS - Faculty of Mechanical Engineering
Year:2021
Publication status in journal:Published
Article version:Publisher's version of article
Number of pages:22 str.
Numbering:Vol. 9, iss. 5, art. 540
UDC:519.61(045)
ISSN on article:2227-7390
DOI:10.3390/math9050540 This link opens in a new window
COBISS.SI-ID:56467971 This link opens in a new window
Publication date in RUL:19.03.2021
Views:261
Downloads:119
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Record is a part of a journal

Title:Mathematics
Shortened title:Mathematics
Publisher:MDPI
ISSN:2227-7390
COBISS.SI-ID:523267865 This link opens in a new window

Licences

License:CC BY 4.0, Creative Commons Attribution 4.0 International
Link:http://creativecommons.org/licenses/by/4.0/
Description:This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
Licensing start date:04.03.2021

Secondary language

Language:Slovenian
Keywords:nenegativna matrična faktorizacija, pogoji pravokotnosti, metoda projiciranega gradienta, multiplikativni algoritem posodabljanja, koordinatni spust

Document is financed by a project

Funder:Drugi - Drug financer ali več financerjev
Funding programme:Swiss Government Excellence Scholarships
Project number:ESKAS-2019.0147

Funder:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS)
Project number:P2-0162
Name:Tranzientni dvofazni tokovi

Funder:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS)
Project number:J1-2453
Name:Matrično konveksne množice in realna algebraična geometrija

Funder:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS)
Project number:N1-0071
Name:Razširitev algoritmov prvega in drugega reda za izbrane razrede optimizacijskih problemov s ciljem rešiti računsko zahtevne industrijske probleme

Funder:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS)
Project number:J5-2552
Name:Napovedovanje sodelovanja med raziskovalci s pomočjo odkrivanja zakonitosti iz literature

Funder:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS)
Project number:J2-2512
Name:Stohastični modeli za logistiko proizvodnih procesov

Funder:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS)
Project number:J1-1691
Name:Weissova domneva in posplošitve

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