Inexact block coordinate descent methods for symmetric nonnegative matrix factorization

Qingjiang Shi, Haoran Sun, Songtao Lu, Mingyi Hong, Meisam Razaviyayn

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Symmetric nonnegativematrix factorization (SNMF) is equivalent to computing a symmetric nonnegative low rank approximation of a data similarity matrix. It inherits the good data interpretability of the well-known nonnegative matrix factorization technique and has better ability of clustering nonlinearly separable data. In this paper, we focus on the algorithmic aspect of the SNMF problem and propose simple inexact block coordinate decentmethods to address the problem, leading to both serial and parallel algorithms. The proposed algorithms have guaranteed convergence to stationary solutions and can efficiently handle large-scale and/or sparse SNMF problems. Extensive simulations verify the effectiveness of the proposed algorithms compared to recent state-of-the-art algorithms.

Original languageEnglish (US)
Article number7990154
Pages (from-to)5995-6008
Number of pages14
JournalIEEE Transactions on Signal Processing
Issue number22
StatePublished - Nov 15 2017

Bibliographical note

Funding Information:
Manuscript received March 11, 2017; revised June 21, 2017; accepted June 21, 2017. Date of publication July 24, 2017; date of current version September 19, 2017. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Mats Bengtsson. The work of Q. Shi is supported by NSFC under grant 61671411 and 61631020. The work of H. Sun and M. Hong was supported in part by NSF under Grant CCF-1526078 and in part by AFOSR under Grant 15RT0767. (Corresponding author: Qingjiang Shi.) Q. Shi was with the Department of Industrial and Manufacturing Systems Engineering, Iowa State University, Ames, IA 50011 USA. He is now with the College of Electronic Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China (e-mail:

Publisher Copyright:
© 2017 IEEE.


  • Block coordinate decent
  • Block successive upper-bounding minimization
  • Parallel algorithm
  • Stationary solution
  • Symmetric nonnegative matrix factorization


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