1. Spatio-Temporal Clustering
Will Penny
Karl Friston
Acknowledgments: Stefan Kiebel and John Ashburner
The Wellcome Department of Imaging Neuroscience, UCL
http//:

2. 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.

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

4. 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

5. Generative Model
Scan 9

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

7. 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

8. Auditory Data
SPM
MGLM (K=4)

9. Face Data
SPM
MGLM (K=2)

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