Spatio-Temporal Clustering Will Penny Karl Friston Acknowledgments: Stefan Kiebel and John Ashburner The Wellcome Department of Imaging Neuroscience, UCL http//:www.fil.ion.ucl.ac.uk/~wpenny

Generative Model We have ACTIVE components which describe spatially localised clusters of activity with a temporal signature correlated with the activation paradigm. We have NULL components which describe spatially distributed background activity temporally uncorrelated with the paradigm. At each voxel and time point fMRI data is a mixture of ACTIVE and NULL components.

Generative Model S1 r0 m1 S2 r1 m2 r2 The fundamental quantities of interest are the properties of spatial clusters of activation

Generative Model At each voxel i and time point t 1. Select component k with probability Spatial Prior 2. Draw a sample from component k’s temporal model General Linear Model

Generative Model Scan 9

Expectation-Maximisation (EM) algorithm Parameter Estimation Expectation-Maximisation (EM) algorithm Temporal E-Step Spatial Posterior Normalizer

Parameter Estimation Expectation-Maximisation (EM) algorithm M-Step Prototype time series for component k Variant of Iteratively Reweighted Least Squares mk and Sk updated using line search

Auditory Data SPM MGLM (K=4)

Face Data SPM MGLM (K=2)

Prototype time series for cluster Face Data Prototype time series for cluster (dotted line) GLM Estimate (solid line) 60 secs