A Discrete-Time Neurodynamic Approach to Sparsity-Constrained Nonnegative Matrix Factorization

Xinqi LI, Jun WANG, Sam KWONG

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

11 Citations (Scopus)


Sparsity is a desirable property in many nonnegative matrix factorization (NMF) applications. Although some level of sparseness of NMF solutions can be achieved by using regularization, the resulting sparsity depends highly on the regularization parameter to be valued in an ad hoc way. In this letter we formulate sparse NMF as a mixed-integer optimization problem with sparsity as binary constraints. A discrete-time projection neural network is developed for solving the formulated problem. Sufficient conditions for its stability and convergence are analytically characterized by using Lyapunov's method. Experimental results on sparse feature extraction are discussed to substantiate the superiority of this approach to extracting highly sparse features.
Original languageEnglish
Pages (from-to)1531-1562
Number of pages32
JournalNeural Computation
Issue number8
Early online date15 Jul 2020
Publication statusPublished - Aug 2020
Externally publishedYes

Bibliographical note

This work was supported in part by the Research Grants Council of the Hong Kong Special Administrative Region of China under grants 11208517, 11202318, 11202019, 11200116 (9042322), 11206317 (9042489), and 11209819 (9042816); and by the National Natural Science Foundation of China under grant 61673330; and by the Key Project of Science and Technology Innovation 2030 supported by the Ministry of Science and Technology of China (grant 2018AAA0101301).


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