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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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MD5: 7F93D36B4C49F56A8A4D9EB43F3F19D0
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https://www.mdpi.com/2227-7390/9/5/540
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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
Typology:
1.01 - Original Scientific Article
Organization:
FS - Faculty of Mechanical Engineering
Publication status:
Published
Publication version:
Version of Record
Year:
2021
Number of pages:
22 str.
Numbering:
Vol. 9, iss. 5, art. 540
PID:
20.500.12556/RUL-125500
UDC:
519.61(045)
ISSN on article:
2227-7390
DOI:
10.3390/math9050540
COBISS.SI-ID:
56467971
Publication date in RUL:
19.03.2021
Views:
937
Downloads:
220
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Record is a part of a journal
Title:
Mathematics
Shortened title:
Mathematics
Publisher:
MDPI AG
ISSN:
2227-7390
COBISS.SI-ID:
523267865
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
Projects
Funder:
Other - Other funder or multiple funders
Funding programme:
Swiss Government Excellence Scholarships
Project number:
ESKAS-2019.0147
Funder:
ARRS - Slovenian Research Agency
Project number:
P2-0162
Name:
Tranzientni dvofazni tokovi
Funder:
ARRS - Slovenian Research Agency
Project number:
J1-2453
Name:
Matrično konveksne množice in realna algebraična geometrija
Funder:
ARRS - Slovenian Research Agency
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 - Slovenian Research Agency
Project number:
J5-2552
Name:
Napovedovanje sodelovanja med raziskovalci s pomočjo odkrivanja zakonitosti iz literature
Funder:
ARRS - Slovenian Research Agency
Project number:
J2-2512
Name:
Stohastični modeli za logistiko proizvodnih procesov
Funder:
ARRS - Slovenian Research Agency
Project number:
J1-1691
Name:
Weissova domneva in posplošitve
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