title: Transport on Riemannian manifold for functional connectivity-based classification.
abstract: 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.
authors.forename: Bernard
authors.initials: B
authors.lastname: Ng
authors.forename: Martin
authors.initials: M
authors.lastname: Dressler
authors.forename: Gaël
authors.initials: G
authors.lastname: Varoquaux
authors.forename: Jean Baptiste
authors.initials: JB
authors.lastname: Poline
authors.forename: Michael
authors.initials: M
authors.lastname: Greicius
authors.forename: Bertrand
authors.initials: B
authors.lastname: Thirion
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D001921:Brain / Q000502:physiology*; D063132:Connectome / Q000379:methods*; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D011939:Mental Recall / Q000502:physiology*; D009415:Nerve Net / Q000502:physiology*; D010363:Pattern Recognition, Automated / Q000379:methods*; D021641:Recognition, Psychology / Q000502:physiology; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity