Pairwise Constraint Propagation-Induced Symmetric Nonnegative Matrix Factorization

Wenhui WU, Yuheng JIA, Sam KWONG, Junhui HOU

Research output: Journal PublicationsJournal Article (refereed)peer-review

58 Citations (Scopus)


As a variant of nonnegative matrix factorization (NMF), symmetric NMF (SNMF) has shown to be effective for capturing the cluster structure embedded in the graph representation. In contrast to the existing SNMF-based clustering methods that empirically construct the similarity matrix and rigidly introduce the supervisory information to the assignment matrix, in this paper, we propose a novel SNMF-based semisupervised clustering method, namely, pairwise constraint propagation-induced SNMF (PCPSNMF). By formulating a single-constrained optimization problem, PCPSNMF is capable of learning the similarity and assignment matrices adaptively and simultaneously, in which a small amount of supervisory information in the form of pairwise constraints is introduced in a flexible way to guide the construction of the similarity matrix, and the two matrices communicate with each other to achieve mutual refinement until convergence. In addition, we propose an efficient alternating iterative algorithm to solve the optimization problem, whose convergence is theoretically proven. Experimental results over several benchmark image data sets demonstrate that PCPSNMF is less sensitive to initialization and produces higher clustering performance, compared with the state-of-the-art methods.
Original languageEnglish
Pages (from-to)6348-6361
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number12
Early online date18 May 2018
Publication statusPublished - Dec 2018
Externally publishedYes

Bibliographical note

This work was supported in part by the Natural Science Foundation of China under Grant 61672443 and in part by Hong Kong RGC General Research Funds under Grant 9042038 (CityU 11205314) and Grant 9042322 (CityU 11200116).


  • Pairwise constraint propagation (PCP)
  • semisupervised clustering
  • symmetric nonnegative matrix factorization (SNMF)


Dive into the research topics of 'Pairwise Constraint Propagation-Induced Symmetric Nonnegative Matrix Factorization'. Together they form a unique fingerprint.

Cite this