Transport on Riemannian Manifold for Functional Connectivity-Based Classification

  • Bernard Ng
  • Martin Dressler
  • Gaël Varoquaux
  • Jean Baptiste Poline
  • Michael Greicius
  • Bertrand Thirion
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8674)


We present a Riemannian approach for classifying fMRI connectivity patterns before and after intervention in longitudinal studies. A fundamental difficulty with using connectivity as features is that covariance matrices live on the positive semi-definite cone, which renders their elements inter-related. The implicit independent feature assumption in most classifier learning algorithms is thus violated. In this paper, we propose a matrix whitening transport for projecting the covariance estimates onto a common tangent space to reduce the statistical dependencies between their elements. We show on real data that our approach provides significantly higher classification accuracy than directly using Pearson’s correlation. We further propose a non-parametric scheme for identifying significantly discriminative connections from classifier weights. Using this scheme, a number of neuroanatomically meaningful connections are found, whereas no significant connections are detected with pure permutation testing.


Classification Connectivity fMRI Riemannian manifold 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Bernard Ng
    • 1
    • 2
  • Martin Dressler
    • 3
  • Gaël Varoquaux
    • 1
  • Jean Baptiste Poline
    • 1
  • Michael Greicius
    • 2
  • Bertrand Thirion
    • 1
  1. 1.Parietal team, NeurospinINRIA SaclayFrance
  2. 2.FIND LabStanford UniversityUSA
  3. 3.Cognition and BehaviourDonders Institute for BrainNijmegenThe Netherlands

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