A Novel Sparse Group Gaussian Graphical Model for Functional Connectivity Estimation

  • Bernard Ng
  • Gaël Varoquaux
  • Jean Baptiste Poline
  • Bertrand Thirion
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7917)


The estimation of intra-subject functional connectivity is greatly complicated by the small sample size and complex noise structure in functional magnetic resonance imaging (fMRI) data. Pooling samples across subjects improves the conditioning of the estimation, but loses subject-specific connectivity information. In this paper, we propose a new sparse group Gaussian graphical model (SGGGM) that facilitates joint estimation of intra-subject and group-level connectivity. This is achieved by casting functional connectivity estimation as a regularized consensus optimization problem, in which information across subjects is aggregated in learning group-level connectivity and group information is propagated back in estimating intra-subject connectivity. On synthetic data, we show that incorporating group information using SGGGM significantly enhances intra-subject connectivity estimation over existing techniques. More accurate group-level connectivity is also obtained. On real data from a cohort of 60 subjects, we show that integrating intra-subject connectivity estimated with SGGGM significantly improves brain activation detection over connectivity priors derived from other graphical modeling approaches.


brain connectivity fMRI Gaussian graphical model regularized consensus optimization sparse inverse covariance estimation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Huang, S., Li, J., Sun, L., Ye, J., Fleisher, A., Wu, T., Chen, K., Reiman, E.: Learning Brain Connectivity of Alzheimer’s Disease by Sparse Inverse Covariance Estimation. Neuroimage 50, 935–949 (2010)CrossRefGoogle Scholar
  2. 2.
    Delbeuck, X., Van der Linden, M., Collette, F.: Alzheimer’s Disease as a Disconnection Syndrome? Neuropsychol. Rev. 13, 79–92 (2003)CrossRefGoogle Scholar
  3. 3.
    Fox, M.D., Raichle, M.E.: Spontaneous Fluctuations in Brain Activity Observed with Functional Magnetic Resonance Imaging. Nat. Rev. Neurosci. 8, 700–711 (2007)CrossRefGoogle Scholar
  4. 4.
    Smith, S.M., Fox, P.T., Miller, K.L., Glahn, D.C., Fox, P.M., Mackay, C.E., Filippini, N., Watkins, K.E., Toro, R., Laird, A.R., Beckmann, C.F.: Correspondence of the Brain’s Functional Architecture During Activation and Rest. Proc. Natl. Acad. Sci. 106, 13040–13045 (2009)CrossRefGoogle Scholar
  5. 5.
    Varoquaux, G., Gramfort, A., Poline, J.B., Thirion, B.: Brain Covariance Selection: Better Individual Functional Connectivity Models Using Population Prior. In: Advances in Neural Information Processing Systems, vol. 23, pp. 2334–2342 (2010)Google Scholar
  6. 6.
    Smith, S.: The Future of fMRI Connectivity. NeuroImage 62, 1257–1266 (2012)CrossRefGoogle Scholar
  7. 7.
    Chen, Y., Wiesel, A., Eldar, Y.C., Hero, A.O.: Shrinkage Algorithms for MMSE Covariance Estimation. IEEE Trans. Sig. Proc. 58, 5016–5029 (2010)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Ng, B., Varoquaux, G., Poline, J.-B., Thirion, B.: A Novel Sparse Graphical Approach for Multimodal Brain Connectivity Inference. In: Ayache, N., Delingette, H., Golland, P., Mori, K. (eds.) MICCAI 2012, Part I. LNCS, vol. 7510, pp. 707–714. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  9. 9.
    Venkataraman, A., Rathi, Y., Kubicki, M., Westin, C.F., Golland, P.: Joint Modeling of Anatomical and Functional Connectivity for Population Studies. IEEE Trans. Med. Imaging 31, 164–182 (2012)CrossRefGoogle Scholar
  10. 10.
    Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers. Found. Trend Mach. Learn. 3, 1–122 (2010)zbMATHCrossRefGoogle Scholar
  11. 11.
    Hsieh, C.J., Sustik, M.A., Dhillon, I.S., Ravikumar, P.: Sparse Invers Covariance Matrix Estimation Using Quadratic Approximation. In: Advances in Neural Information Processing Systems, vol. 24, pp. 2330–2338 (2011)Google Scholar
  12. 12.
    Ng, B., Abugharbieh, R., Varoquaux, G., Poline, J.B., Thirion, B.: Connectivity-Informed fMRI Activation Detection. In: Fichtinger, G., Martel, A., Peters, T. (eds.) MICCAI 2011, Part II. LNCS, vol. 6892, pp. 285–292. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  13. 13.
    Friston, K.J., Holmes, A.P., Worsley, K.J., Poline, J.B., Frith, C.D., Frackowiak, R.S.J.: Statistical Parametric Maps in Functional Imaging: A General Linear Approach. Hum. Brain Mapp. 2, 189–210 (1995)CrossRefGoogle Scholar
  14. 14.
    Pinel, P., Thirion, B., Meriaux, S., Jober, A., Serres, J., Le Bihan, D., Poline, J.B., Dehaene, S.: Fast Reproducible Identification and Large-scale Databasing of Individual Functional Cognitive Networks. BioMed. Central Neurosci. 8, 91 (2007)Google Scholar
  15. 15.
    Michel, V., Gramfort, A., Varoquaux, G., Eger, E., Keribin, C., Thirion, B.: A Supervised Clustering Approach for fMRI-based Inference of Brain States. Patt. Recog. 45, 2041–2049 (2012)zbMATHCrossRefGoogle Scholar
  16. 16.
    Arsigny, V., Fillard, P., Pennec, X., Ayache, N.: Fast and Simple Calculus on Tensors in the Log-Euclidean Framework. In: Duncan, J., Gerig, G. (eds.) MICCAI 2005, Part I. LNCS, vol. 3749, pp. 115–122. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Nichols, T., Hayasaka, S.: Controlling the Familywise Error Rate in Functional Neuroimaging: a Comparative Review. Stat. Methods Med. Research 12, 419–446 (2003)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Bernard Ng
    • 1
    • 2
  • Gaël Varoquaux
    • 1
  • Jean Baptiste Poline
    • 1
  • Bertrand Thirion
    • 1
  1. 1.Parietal TeamNeurospin, INRIA SaclayFrance
  2. 2.FIND LabStanford UniversityUnited States

Personalised recommendations