Cognitive Computation

, Volume 10, Issue 6, pp 991–1005 | Cite as

Combining Non-negative Matrix Factorization and Sparse Coding for Functional Brain Overlapping Community Detection

  • X. Li
  • Z. Hu
  • H. WangEmail author


The functional system of the human brain can be viewed as a complex network. Among various features of the brain functional network, community structure has raised significant interest in recent years. Increasing evidence has revealed that most realistic complex networks have an overlapping community structure. However, the overlapping community structure of the brain functional network has not been adequately studied. In this paper, we propose a novel method called sparse symmetric non-negative matrix factorization (ssNMF) to detect the overlapping community structure of the brain functional network. Specifically, it is formulated by combining the effective techniques of non-negative matrix factorization and sparse coding. Besides, the non-negative adaptive sparse representation is applied to construct the whole-brain functional network, based on which ssNMF is performed to detect the community structure. Both simulated and real functional magnetic resonance imaging data are used to evaluate ssNMF. The experimental results demonstrate that the proposed ssNMF method is capable of accurately and stably detecting the underlying overlapping community structure. Moreover, the physiological interpretation of the overlapping community structure detected by ssNMF is straightforward. This novel framework, we think, provides an effective tool to study overlapping community structure and facilitates the understanding of the network organization of the functional human brain.


Overlapping community detection Non-negative matrix factorization Sparse coding Brain functional network Functional magnetic resonance imaging 



The authors wish to thank the editors and reviewers for the comments and recommendations, which have helped improve the paper substantially.

Funding Information

This work was supported in part by the National Natural Science Foundation of China under grants 61773114 and 61472089, the Joint Fund of the National Natural Science Foundation of China and Guangdong Province under grant U1501254, the Science and Technology Planning Project of Guangdong Province under grants 2015B010131015 and 2015B010108006, Key Project of Internation as well as Hongkong, Macao & Taiwan Innovation Platform and International Cooperation by Universities in Guangdong Province under grant 2015KGJHZ023, and the China Scholarship Council Fund under Grant 201603780037.

Compliance with Ethical Standards

Ethical approval: All the procedures performed in the studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee as well as with the 1964 Helsinki declaration and its later amendments, or comparable ethical standards.

Conflict of interests

The authors declare that they have no conflict of interest.

Informed Consent

Informed consent was obtained from all the individual participants included in the study.


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Authors and Affiliations

  1. 1.School of Mathematics and Big DataFoshan UniversityFoshanPeople’s Republic of China
  2. 2.Research Center for Learning ScienceSoutheast UniversityNanjingPeople’s Republic of China
  3. 3.School of Mathematics and PhysicsAnhui University of TechnologyMaanshanPeople’s Republic of China

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