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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
Article
  • 107 Downloads

Abstract

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.

Keywords

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

Notes

Acknowledgements

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.

References

  1. 1.
    Bullmore E, Sporns O. Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci 2009;10(3):186–198.PubMedGoogle Scholar
  2. 2.
    Girvan M, Newman M. Community structure in social and biological networks. Proc Natl Acad Sci 2002; 99(12):7821–7826.PubMedGoogle Scholar
  3. 3.
    Sporns O. Contributions and challenges for network models in cognitive neuroscience. Nat Neurosci 2014;17(5): 652–660.PubMedGoogle Scholar
  4. 4.
    Meunier D, Lambiotte R, Bullmore E. Modular and hierarchically modular organization of brain networks. Front Neurosci 2010;4:200.PubMedPubMedCentralGoogle Scholar
  5. 5.
    Sporns O, Betzel R. Modular brain networks. Annu Rev Psychol 2016;67:613–640.PubMedGoogle Scholar
  6. 6.
    Ziemke T, Lowe R. On the role of emotion in embodied cognitive architectures: From organisms to robots. Cogn Comput 2009;1(1):104–117.Google Scholar
  7. 7.
    Yan X. Dissociated emergent response system and fine-processing system in human neural network and a heuristic neural architecture for autonomous humanoid robots. Cogn Comput 2011;3(2):367–373.Google Scholar
  8. 8.
    Mohan V, Morasso P, Sandini G, Kasderidis S. Inference through embodied simulation in cognitive robots. Cogn Comput 2013;5(3):355–382.Google Scholar
  9. 9.
    Power JD, Cohen AL, Nelson SM, Wig GS, Barnes KA, Church JA, et al. Functional network organization of the human brain. Neuron 2011;72(4):665–678.PubMedPubMedCentralGoogle Scholar
  10. 10.
    Alexander-Bloch A, Lambiotte R, Roberts B, Giedd J, Gogtay N, Bullmore E. The discovery of population differences in network community structure: new methods and applications to brain functional networks in schizophrenia. Neuroimage 2012;59(4):3889–3900.PubMedGoogle Scholar
  11. 11.
    Thirion B, Dodel S, Poline JB. Detection of signal synchronizations in resting-state fMRI datasets. Neuroimage 2006;29(1):321–327.PubMedGoogle Scholar
  12. 12.
    van Den Heuvel M, Mandl R, Pol HH. Normalized cut group clustering of resting-state fMRI data. PloS ONE 2008;3(4):e2001.Google Scholar
  13. 13.
    Newman ME. Modularity and community structure in networks. Proc Natl Acad Sci 2006;103(23):8577–8582.PubMedGoogle Scholar
  14. 14.
    Von Luxburg U. A tutorial on spectral clustering. Stat Comput 2007;17(4):395–416.Google Scholar
  15. 15.
    Fortunato S, Hric D. Community detection in networks: a user guide. Phys Rep 2016;659:1–44.Google Scholar
  16. 16.
    Palla G, Derényi I, Farkas I, Vicsek T. Uncovering the overlapping community structure of complex networks in nature and society. Nature 2005;435(7043):814.PubMedGoogle Scholar
  17. 17.
    Tao D, Li X, Wu X, Maybank S. Geometric mean for subspace selection. IEEE Trans Pattern Anal Mach Intell 2009;31(2):260–274.PubMedGoogle Scholar
  18. 18.
    Xu C, Tao D, Xu C. Multi-view learning with incomplete views. IEEE Trans Image Process 2015;24 (12):5812–5825.PubMedGoogle Scholar
  19. 19.
    Liu W, Yang X, Tao D, Cheng J, Tang Y. Multiview dimension reduction via Hessian multiset canonical correlations. Inf Fusion 2018;41:119–128.Google Scholar
  20. 20.
    Ding C, He X, Simon HD. On the equivalence of non-negative matrix factorization and spectral clustering. In: Proceedings of the 2005 SIAM International Conference on Data Mining; 2005. p. 606–610.Google Scholar
  21. 21.
    Xie J, Kelley S, Szymanski BK. Overlapping community detection in networks: the state-of-the-art and comparative study. ACM Comput Surv 2013;45(4):43.Google Scholar
  22. 22.
    Zarei M, Izadi D, Samani KA. Detecting overlapping community structure of networks based on vertex–vertex correlations. J Stat Mech-Theory Exp 2009;11:P11013.Google Scholar
  23. 23.
    Psorakis I, Roberts S, Ebden M, Sheldon B. Overlapping community detection using bayesian non-negative matrix factorization. Phys Rev E 2011;83(6):066114.Google Scholar
  24. 24.
    Yang J, Leskovec J. Overlapping community detection at scale: a non-negative matrix factorization approach. In: Proceedings of the sixth ACM International Conference on Web Search and Data Mining; 2013. p. 587–596.Google Scholar
  25. 25.
    Wang F, Li T, Wang X, Zhu S, Ding C. Community discovery using non-negative matrix factorization. Data Min Knowl Discov 2011;22(3):493–521.Google Scholar
  26. 26.
    Li X, Hu Z, Wang H. Overlapping community structure detection of brain functional network using non-negative matrix factorization. In: International Conference on Neural Information Processing (ICONIP); 2016. p. 140–147.Google Scholar
  27. 27.
    Chen S, Xin Y, Luo B. Action-based pedestrian identification via hierarchical matching pursuit and order preserving sparse coding. Cogn Comput 2016;8(5):797–805.Google Scholar
  28. 28.
    Lv L, Zhao D, Deng Q. A semi-supervised predictive sparse decomposition based on task-driven dictionary learning. Cogn Comput 2017;9(1):115–124.Google Scholar
  29. 29.
    Liu M, Xu C, Luo Y, Xu C, Wen Y, Tao D. Cost-sensitive feature selection by optimizing F-measures. IEEE Trans Image Process 2018;27(3):1323–1335.Google Scholar
  30. 30.
    Li Y, Yu Z, Bi N, Xu Y, Gu Z, Amari S. Sparse representation for brain signal processing: a tutorial on methods and applications. IEEE Signal Process Mag 2014;31(3):96–106.Google Scholar
  31. 31.
    Xie J, Douglas PK, Wu YN, Brody AL, Anderson AE. Decoding the encoding of functional brain networks: an fMRI classification comparison of non-negative matrix factorization (NMF), independent component analysis (ICA), and sparse coding algorithms. J Neurosci Method 2017;282:81–94.Google Scholar
  32. 32.
    Biswal B, Yetkin FZ, Haughton VM, Hyde JS. Functional connectivity in the motor cortex of resting human brain using echo-planar MRI. Magn Reson Med 1995;34(4):537–541.PubMedGoogle Scholar
  33. 33.
    Li X, Hu Z, Wang H. Sparse-network based framework for detecting the overlapping community structure of brain functional network. In: Advances in Brain Inspired Cognitive Systems; 2016. p. 355–365.Google Scholar
  34. 34.
    Lee D, Seung H. Learning the parts of objects by non-negative matrix factorization. Nature 1999;401(6755): 788–791.PubMedGoogle Scholar
  35. 35.
    Guan N, Tao D, Luo Z, Shawe-Taylor J. 2012. MahNMF: Manhattan non-negative matrix factorization. arXiv:1207.3438.
  36. 36.
    Liu T, Gong M, Tao D. Large-cone non-negative matrix factorization. IEEE Trans Neural Netw Learn Syst 2017;28(9):2129– 2142.PubMedGoogle Scholar
  37. 37.
    Shan D, Xu X, Liang T, Ding S. Rank-adaptive non-negative matrix factorization. Cogn Comput. 2018;10(3):506–515.Google Scholar
  38. 38.
    Padilla P, López M, Górriz J M, Ramirez J, Salas-Gonzalez D, Álvarez I. NMF-SVM based CAD tool applied to functional brain images for the diagnosis of Alzheimer’s disease. IEEE Trans Med Imaging 2012; 31(2):207–216.PubMedGoogle Scholar
  39. 39.
    Wang Y, Zhang Y. Non-negative matrix factorization: A comprehensive review. IEEE Trans Knowl Data Eng 2013;25(6):1336–1353.Google Scholar
  40. 40.
    Zhang Z, Wang Y, Ahn YY. Overlapping community detection in complex networks using symmetric binary matrix factorization. Phys Rev E 2013;87(6):062803.Google Scholar
  41. 41.
    Zhang Y, Yeung DY. Overlapping community detection via bounded non-negative matrix tri-factorization. In: Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining; 2012. p. 606–614.Google Scholar
  42. 42.
    Zhang Z, Xu Y, Yang J, Li X, Zhang D. A survey of sparse representation: algorithms and applications. IEEE Access 2015;3:490–530.Google Scholar
  43. 43.
    Donoho DL, Elad M. Optimally sparse representation in general (non-orthogonal) dictionaries via 1 minimization. Proc Natl Acad Sci 2003;100(5):2197–2202.PubMedGoogle Scholar
  44. 44.
    Guo S, Wang Z, Ruan Q. Enhancing sparsity via p(0 < p < 1) minimization for robust face recognition. Neurocomputing 2013;99:592–602.Google Scholar
  45. 45.
    Bengio S, Pereira F, Singer Y, Strelow D. Group sparse coding. In: Advances in Neural Information Processing Systems; 2009. p. 82–89.Google Scholar
  46. 46.
    Liu W, Zha Z, Wang Y, Lu K, Tao D. P-Laplacian regularized sparse coding for human activity recognition. IEEE Trans Ind Electron 2016;63(8):5120–5129.Google Scholar
  47. 47.
    Hoyer PO. Non-negative sparse coding. In: Proceedings of the 12th IEEE Workshop on Neural Networks for Signal Processing; 2002. p. 557–565.Google Scholar
  48. 48.
    Hoyer PO. Non-negative matrix factorization with sparseness constraints. J Mach Learn Res 2004;5(Nov): 1457–1469.Google Scholar
  49. 49.
    Gao Y, Church G. Improving molecular cancer class discovery through sparse non-negative matrix factorization. Bioinformatics 2005;21(21):3970–3975.PubMedGoogle Scholar
  50. 50.
    Grave E, Obozinski GR. Bach FR. Trace lasso: a trace norm regularization for correlated designs. In: Advances in Neural Information Processing Systems; 2011. p. 2187–2195.Google Scholar
  51. 51.
    Lu C, Feng J, Lin Z, Yan S. Correlation adaptive subspace segmentation by trace lasso. In: IEEE International Conference on Computer Vision; 2013. p. 1345–1352.Google Scholar
  52. 52.
    Li X, Wang H. Identification of functional networks in resting state fMRI data using adaptive sparse representation and affinity propagation clustering. Front Neurosci 2015;9:383.PubMedPubMedCentralGoogle Scholar
  53. 53.
    Lin CJ. On the convergence of multiplicative update algorithms for non-negative matrix factorization. IEEE Trans Neural Netw 2007;18(6):1589–1596.Google Scholar
  54. 54.
    Rosvall M, Bergstrom CT. Maps of random walks on complex networks reveal community structure. Proc Natl Acad Sci 2008;105(4):1118–1123.PubMedGoogle Scholar
  55. 55.
    Blondel VD, Guillaume JL, Lambiotte R, Lefebvre E. Fast unfolding of communities in large networks. J Stat Mech 2008;2008(10):P10008.Google Scholar
  56. 56.
    Shi J, Malik J. Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 2000;22(8): 888–905.Google Scholar
  57. 57.
    Frey BJ, Dueck D. Clustering by passing messages between data points. Science 2007;315(5814):972–976.PubMedPubMedCentralGoogle Scholar
  58. 58.
    Eavani H, Satterthwaite TD, Filipovych R, Gur RE, Gur RC, Davatzikos C. Identifying sparse connectivity patterns in the brain using resting-state fMRI. Neuroimage 2015;105:286– 299.PubMedGoogle Scholar
  59. 59.
    Smith SM, Miller KL, Salimi-Khorshidi G, Webster M, Beckmann CF, Nichols TE, Ramsey JD, Woolrich MW. Network modelling methods for fMRI. Neuroimage 2011;54(2):875–891.PubMedGoogle Scholar
  60. 60.
    Lovász L, Plummer MD. Matching theory. Ann Discret Math. 1986;29:1–543.Google Scholar
  61. 61.
    Yang J, Leskovec J. Overlapping community detection at scale: a nonnegative matrix factorization approach. In: Proceedings of the 6th ACM International Conference on Web Search and Data Mining; 2013. p. 587–596.Google Scholar
  62. 62.
    McDaid AF, Greene D, Hurley N. 2011. Normalized mutual information to evaluate overlapping community finding algorithms. arXiv:1110.2515.
  63. 63.
    Gregory S. Fuzzy overlapping communities in networks. J Stat Mech: Theory Exp 2011;2011(02):P02017.Google Scholar
  64. 64.
    Biswal BB, Mennes M, Zuo XN, Gohel S, Kelly C, Smith SM, et al. Toward discovery science of human brain function. Proc Natl Acad Sci 2010;107(10):4734–4739.PubMedGoogle Scholar
  65. 65.
    Zuo XN, Anderson JS, Bellec P, Birn RM, Biswal BB, Blautzik J, et al. An open science resource for establishing reliability and reproducibility in functional connectomics. Sci Data 2014;1:140049.PubMedPubMedCentralGoogle Scholar
  66. 66.
    Chen B, Xu T, Zhou C, Wang L, Yang N, Wang Z. Individual variability and test–retest reliability revealed by ten repeated resting-state brain scans over one month. PloS ONE 2015;10:e0144963.PubMedPubMedCentralGoogle Scholar
  67. 67.
    Yan C, Zang Y. DPARSF: A matlab toolbox for “pipeline” data analysis of resting-state fMRI. Front Syst Neurosci 2010;4:13.Google Scholar
  68. 68.
    Tzourio-Mazoyer N, Landeau B, Papathanassiou D, Crivello F, Etard O, Delcroix N, et al. Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. Neuroimage 2002;15(1):273–289.PubMedGoogle Scholar
  69. 69.
    Campello RJGB, Hruschka ER. A fuzzy extension of the silhouette width criterion for cluster analysis. Fuzzy Set Syst 2006;157(21):2858–2875.Google Scholar
  70. 70.
    Fransson P, Marrelec G. The precuneus/posterior cingulate cortex plays a pivotal role in the default mode network: evidence from a partial correlation network analysis. Neuroimage 2008;42:1178–1184.PubMedGoogle Scholar
  71. 71.
    van den Heuvel MP, Pol HEH. Exploring the brain network: a review on resting-state fMRI functional connectivity. Eur Neuropsychopharmacol 2010;20(8):519–534.Google Scholar
  72. 72.
    Isaacson R. The limbic system. Berlin: Springer Science & Business Media; 2013.Google Scholar
  73. 73.
    Cole MW, Reynolds JR, Power JD, Repovs G, Anticevic A, Braver TS. Multi-task connectivity reveals flexible hubs for adaptive task control. Nature Neurosci 2013;16(9):1348– 1355.PubMedGoogle Scholar
  74. 74.
    Mazoyer B, Zago L, Mellet E, Bricogne S, Etard O, Houdé O, et al. Cortical networks for working memory and executive functions sustain the conscious resting state in man. Brain Res Bull 2001;54(3):287–298.PubMedGoogle Scholar
  75. 75.
    Yeo BTT, Krienen FM, Chee MWL, Buckner RL. Estimates of segregation and overlap of functional connectivity networks in the human cerebral cortex. Neuroimage 2014;88:212–227.PubMedGoogle Scholar
  76. 76.
    van den Heuvel MP, Sporns O. Network hubs in the human brain. Trends Cogn Sci 2013;17:683–696.Google Scholar
  77. 77.
    Peharz R, Pernkopf F. Sparse nonnegative matrix factorization with 0-constraints. Neurocomputing 2012;80:38–46.PubMedPubMedCentralGoogle Scholar
  78. 78.
    Kong D, Fujimaki R, Liu J, Nie F, Ding C. Exclusive feature learning on arbitrary structures via 1,2-norm. In: Advances in Neural Information Processing Systems; 2014. p. 1655–1663.Google Scholar
  79. 79.
    He Z, Xie S, Zdunek R, Zhou G, Cichocki A. Symmetric nonnegative matrix factorization: Algorithms and applications to probabilistic clustering. IEEE Trans Neural Netw 2011;22(12):2117–2131.PubMedGoogle Scholar
  80. 80.
    Kuang D, Ding C, Park H. Symmetric nonnegative matrix factorization for graph clustering. In: Proceedings of the 2012 SIAM International Conference on Data Mining; 2012. p. 106–117.Google Scholar
  81. 81.
    Huang K, Sidiropoulos ND, Swami A. Non-negative matrix factorization revisited: Uniqueness and algorithm for symmetric decomposition. IEEE Trans Signal Process 2014; 62 (1): 211– 224.Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

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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