Symmetric nonnegative matrix factorization: Algorithms and applications to probabilistic clustering

Zhaoshui He, Shengli Xie, Rafal Zdunek, Guoxu Zhou, Andrzej Cichocki

Research output: Contribution to journalArticlepeer-review

139 Citations (Scopus)


Nonnegative matrix factorization (NMF) is an unsupervised learning method useful in various applications including image processing and semantic analysis of documents. This paper focuses on symmetric NMF (SNMF), which is a special case of NMF decomposition. Three parallel multiplicative update algorithms using level 3 basic linear algebra subprograms directly are developed for this problem. First, by minimizing the Euclidean distance, a multiplicative update algorithm is proposed, and its convergence under mild conditions is proved. Based on it, we further propose another two fast parallel methods: α-SNMF and β-SNMF algorithms. All of them are easy to implement. These algorithms are applied to probabilistic clustering. We demonstrate their effectiveness for facial image clustering, document categorization, and pattern clustering in gene expression.

Original languageEnglish
Article number6061964
Pages (from-to)2117-2131
Number of pages15
JournalIEEE Transactions on Neural Networks
Issue number12 PART 1
Publication statusPublished - Dec 2011
Externally publishedYes


  • Basic linear algebra subprograms
  • completely positive
  • coordinate update
  • multiplicative update
  • nonnegative matrix factorization
  • parallel update
  • probabilistic clustering
  • symmetric nonnegative matrix factorization


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