Analysis of Dynamic Brain Connectivity Through Geodesic Clustering

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11752)


Analysis of dynamic functional connectivity allows for studying the time variant behavior of brain connectivity during specific tasks or at rest. There is, however, a debate around the significance of studies analyzing the dynamic connectivity, as it is usually estimated using short subsequences of the entire time-series. Therefore, a question that naturally arises is whether the dynamic connectivity information is robust enough to compare connectivity matrices. In this paper we investigate the importance of the choice of metric on the space of graphs to answer this question, using a dataset of twins under the assumption that twins connectivity is more similar than in any other pair of unrelated subjects. Specifically, the problem was formulated as a classification task between twin and non-twin pairs. The approach described in the paper relies on geodesic clustering of dynamic connectivity matrices to find a subset of brain states, which were then used to encode the pairwise connectivity similarities between subjects. Experiments were performed to compare the use of Euclidean distance in a vectorial space and a geodesic distance in the Riemannian space of symmetric positive definite matrices. We showed that the geodesic distance provided a better classification of twins subjects, suggesting this use of this distance can robustly compare dynamic connectivity matrices.


Dynamic functional connectivity Geodesic clustering Connectomes Task-based fMRI SVM Symmetric positive definite matrices 



The authors acknowledge Cigdem Beyan and Muhammad Shahid for the helpful discussions.


  1. 1.
    Friston, K.J., Frith, C.D., Liddle, P.F., Frackowiak, R.S.J.: Functional connectivity: the principal-component analysis of large (PET) data sets. J. Cereb. Blood Flow Metab. 13, 5 (1993). Scholar
  2. 2.
    Allen, E.A., Damaraju, E., Plis, S.M., Erhardt, E.B., Eichele, T., Calhoun, V.D.: Tracking whole-brain connectivity dynamics in the resting state. Cereb. Cortex 24(3), 663–676 (2014)CrossRefGoogle Scholar
  3. 3.
    Chang, C., Liu, Z., Chen, M.C., Liu, X., Duyn, J.H.: EEG correlates of time-varying BOLD functional connectivity. NeuroImage 72(15), 227–236 (2013)CrossRefGoogle Scholar
  4. 4.
    Sakoǧlu, Ü., Pearlson, G.D., Kiehl, K.A., Wang, Y.M., Michael, A.M., Calhoun, V.D.: A method for evaluating dynamic functional network connectivity and task-modulation: application to schizophrenia. MAGMA 23, 351–366 (2010). Scholar
  5. 5.
    Leonardi, N., et al.: Principal components of functional connectivity: a new approach to study dynamic brain connectivity during rest. NeuroImage 83, 937–950 (2013)CrossRefGoogle Scholar
  6. 6.
    Leonardi, N., Shirer, W., Greicius, M., Van De Ville, D.: Disentangling dynamic networks: separated and joint expressions of functional connectivity patterns in time. Hum. Brain Mapp. 35(12), 5984–5995 (2014)CrossRefGoogle Scholar
  7. 7.
    Yaesoubi, M., Miller, R.L., Calhoun, V.D.: Mutually temporally independent connectivity patterns: a new framework to study the dynamics of brain connectivity at rest with application to explain group difference based on gender. NeuroImage 107, 85–94 (2015)CrossRefGoogle Scholar
  8. 8.
    Li, X., et al.: Dynamic functional connectomics signatures for characterization and differentiation of PTSD patients. Hum. Brain Mapp. 35, 1761–1778 (2014)CrossRefGoogle Scholar
  9. 9.
    Chiang, S., et al.: Time-dependence of graph theory metrics in functional connectivity analysis. NeuroImage 125, 601–615 (2016)CrossRefGoogle Scholar
  10. 10.
    Ma, S., Calhoun, V.D., Phlypo, R., Adal, T.: Dynamic changes of spatial functional network connectivity in healthy individuals and schizophrenia patients using independent vector analysis. NeuroImage 90, 196–206 (2014)CrossRefGoogle Scholar
  11. 11.
    Varoquaux, G., Craddock, R.C.: Learning and comparing functional connectomes across subjects. NeuroImage 80, 405–415 (2013)CrossRefGoogle Scholar
  12. 12.
    Richiardi, J., Eryilmaz, H.I., Schwartz, S., Vuilleumier, P.: Decoding brain states from fMRI connectivity graphs. NeuroImage 56(2), 616–626 (2011)CrossRefGoogle Scholar
  13. 13.
    Yamin, A., et al.: Comparison of brain connectomes using geodesic distance on manifold: a twin’s study. In: International Symposium on Biomedical Imaging 2019, Venice, 8–11 April 2019Google Scholar
  14. 14.
    Li, K., Guo, L., Nie, J., Li, G., Liu, T.: Review of methods for functional brain connectivity detection using fMRI. Comput. Med. Imaging Graph. 33(2), 131–139 (2009)CrossRefGoogle Scholar
  15. 15.
    Yamin, A., et al.: Investigating the impact of genetic background on brain dynamic functional connectivity through machine learning: a twins study. In: IEEE-EMBS International Conference on Biomedical and Health Informatics, Chicago, IL, USA, 19–22 May 2019Google Scholar
  16. 16.
    Victor, M.V., Andrew, R.M., Kent, A.K., Vince, D.C.: Dynamic functional network connectivity discriminates mild traumatic brain injury through machine learning. Neuroimage: Clin. 19, 30–37 (2018)CrossRefGoogle Scholar
  17. 17.
    Tejwani, R., Liska, A., You, H.: Autism Classification Using Brain Functional Connectivity Dynamics and Machine Learning (2019).
  18. 18.
    Poffenberger, A.T.: Reaction Time to Retinal Stimulation, with Special Reference to the Time Lost in Conduction Through Nerve Centers. The Science Press, New York (1912)Google Scholar
  19. 19.
    Tzourio-Mazoyer, N., et al.: Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. Neuroimage 15, 273–289 (2002)CrossRefGoogle Scholar
  20. 20.
    Marrelec, G., et al.: Partial correlation for functional brain interactivity investigation in functional MRI. Neuroimage 32, 228–237 (2006)CrossRefGoogle Scholar
  21. 21.
    Varoquaux, G., Gramfort, A., Poline, J.B., Thirion, B., Zemel, R, Shawe-Taylor, J.: Brain covariance selection: better individual functional connectivity models using population prior. In: Advances in Neural Information Processing Systems, Vancouver, Canada (2010)Google Scholar
  22. 22.
    Smith, S.M., et al.: Network modelling methods for FMRI. Neuroimage 54, 875–891 (2011)CrossRefGoogle Scholar
  23. 23.
    Friedman, J., Hastie, T., Tibshirani, R.: Sparse inverse covariance estimation with the graphical lasso. Biostatistics 9(3), 432–441 (2008). Scholar
  24. 24.
    Rashid, B., Damaraju, E., Pearlson, G.D., Calhoun, V.D.: Dynamic connectivity states estimated from resting fMRI identify differences among Schizophrenia, bipolar disorder, and healthy control subjects. Front. Hum. Neurosci. 8, 897 (2014). Scholar
  25. 25.
    Dodero, L., Minh, H.Q., Biagio, M.S., Murino, V., Sona, D.: Kernel-based classification for brain connectivity graphs on the Riemannian manifold of positive definite matrices. In: ISBI 2015, 16–19 April 2015Google Scholar
  26. 26.
    Dodero, L., Sambataro, F., Murino, V., Sona, D.: Kernel-based analysis of functional brain connectivity on Grassmann manifold. In: Navab, N., Hornegger, J., Wells, W., Frangi, A. (eds.) MICCAI 2015. LNCS, vol. 9351, pp. 604–611. Springer, Cham (2015). Scholar
  27. 27.
    Dryden, I.L., Koloydenko, A., Zhou, D.: Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging. Ann. Appl. Stat. 3(3), 1102–1123 (2009)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Lee, H., Ahn, H.-J., Kim, K.-R., Kim, P., Koo, J.-Y.: Geodesic clustering for covariance matrices. Commun. Stat. Appl. Methods 22, 321–331 (2015). Scholar
  29. 29.
    Yang, X., Song, Q., Cao, A.: Weighted support vector machine for data classification. In: Proceedings of 2005 IEEE International Joint Conference on Neural Networks, Montreal, Quebec, vol. 2, pp. 859–864 (2005).

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Pattern Analysis and Computer VisionIstituto Italiano di TecnologiaGenovaItaly
  2. 2.Department of Electrical, Electronics and Telecommunication Engineering and Naval ArchitectureUniversità degli Studi di GenovaGenovaItaly
  3. 3.Human Neuroscience PlatformFoundation Campus Biotech GenevaGenevaSwitzerland
  4. 4.Scientific Institute IRCCS “E. Medea”Bosisio PariniItaly
  5. 5.Fondazione IRCCS Ca’ Granda Ospedale Maggiore PoliclinicoUniversità di MilanoMilanItaly
  6. 6.Department of Computer ScienceUniversità di VeronaVeronaItaly
  7. 7.Department of Psychiatry and Behavioral NeuroscienceWayne State UniversityDetroitUSA
  8. 8.Neuroinformatics LaboratoryFondazione Bruno KesslerTrentoItaly

Personalised recommendations