Semi-Supervised Non-Negative Matrix Factorization With Dissimilarity and Similarity Regularization

Yuheng JIA, Sam KWONG, Junhui HOU, Wenhui WU

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

61 Citations (Scopus)


In this article, we propose a semi-supervised non-negative matrix factorization (NMF) model by means of elegantly modeling the label information. The proposed model is capable of generating discriminable low-dimensional representations to improve clustering performance. Specifically, a pair of complementary regularizers, i.e., similarity and dissimilarity regularizers, is incorporated into the conventional NMF to guide the factorization. And, they impose restrictions on both the similarity and dissimilarity of the low-dimensional representations of data samples with labels as well as a small number of unlabeled ones. The proposed model is formulated as a well-posed constrained optimization problem and further solved with an efficient alternating iterative algorithm. Moreover, we theoretically prove that the proposed algorithm can converge to a limiting point that meets the Karush-Kuhn-Tucker conditions. Extensive experiments as well as comprehensive analysis demonstrate that the proposed model outperforms the state-of-the-art NMF methods to a large extent over five benchmark data sets, i.e., the clustering accuracy increases to 82.2% from 57.0%.
Original languageEnglish
Pages (from-to)2510-2521
Number of pages12
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number7
Early online date30 Aug 2019
Publication statusPublished - Jul 2020
Externally publishedYes

Bibliographical note

This work was supported in part by the Natural Science Foundation of China under Grant 61672443, Grant 61871342 and Grant 61772344, in part by Hong Kong RGC General Research Funds under Grant 9042489 (CityU 11206317) and Grant 9042322 (CityU 11200116), and in part by the Early Career Scheme under Grant 9048123 (CityU 21211518).


  • Dimensionality reduction
  • Karush-Kuhn-Tucker (KKT) conditions
  • non-negative matrix factorization (NMF)
  • semi-supervised


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