Graphe de connectivité cérébrale et longue dépendance

Florent Chatelain (1) , Sophie Achard (2) , Cedric Gouy-Pailler (3) , Olivier J.J. Michel (2) , Pierre-Olivier Amblard (2)

1 GIPSA-SAIGA - GIPSA - Signal et Automatique pour la surveillance, le diagnostic et la biomécanique
2 GIPSA-CICS - GIPSA - Communication Information and Complex Systems
3 LIST (CEA) - Laboratoire d'Intégration des Systèmes et des Technologies

In this communication, a decomposable graph based partial correlation matrix estimator is proposed for the analysis of time series exhibiting long memory properties. The estimator is derived from the set of wavelet coefficients computed at a given scale; the obtained coefficient are asymptotically uncorrelated, thus avoiding to introduce bias in the estimation. Decomposability of the graph leads to derive an explicit formulation of the maximum likelihood estimation of the partial correlation matrix; however, some spurious links must be introduced in order to insure graph decomposability. Surrogate data that mimik fMRI records are used to illustrate the pertinence and accuracy of the proposed approach. The simulations show that even for small size samples, the proposed methods outperforms the classical approaches. Furthermore, the added links do not affect the quality of the estimation. An appealing feature of decomposabilty resides in the possibility to account for conditional dependences through a clique based approach.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Florent Chatelain, Sophie Achard, Cedric Gouy-Pailler, Olivier J.J. Michel, Pierre-Olivier Amblard. Graphe de connectivité cérébrale et longue dépendance. GRETSI 2011 - XXIIIème Colloque francophone de traitement du signal et des images, Sep 2011, Bordeaux, France. ⟨hal-00639898⟩