A block coordinate descent-based projected gradient algorithm for orthogonal non-negative matrix factorization

Asadi, Soodabeh (author), Povh, Janez (author)

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

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