1. June 18th, 2013 OHBM morning workshop 1
Data-driven brain parcellations:
A statistical perspective
Bertrand Thirion
INRIA Saclay–Ile de France, PARIETAL team,
Neurospin
bertrand.thirion@inria.fr

2. June 18th, 2013 OHBM morning workshop 2
Rationale for parcel-based data analysis

K parcels rather than 105
voxels
− Multiple comparisons
− Connectivity studies
− Brain-level MVPA

Local physiological parameters [Chaari et
al MICCAI 2012]
[Thirion et al HBM 2006, Compstat 2010]
[Craddock et al. HBM 2012]
[Varoquaux et al. Nimg 2013]
[Yeo et al. J. neurosphys. 2011]
parcel voxel cluster

3. June 18th, 2013 OHBM morning workshop 3
Atlases or data-driven parcellations ?

Atlases (AAL, Harvard-Oxford...) can be
used to define ROIs:
 A priori definition and labels
 Limited resolution

Data-driven Parcellations:
 Flexible description, better data fit
 Do not fit a priori with current knowledge

Lack of consistency: [Bohland et al. Plos One
2009]

4. June 18th, 2013 OHBM morning workshop 4
Data-driven parcellations: how ?
Any kind of data...

Cyto-architecture

Sulco-gyral anatomy

Anatomical connectivity

Functional data:
− Resting-state fMRI
− Activation fMRI
− Meta-analysis / co-
activation)
… many possible methods

K-means, mixture models

Spectral clustering

Agglomerative clustering

Decompositions approaches:
− ICA, sparse PCA and variants

5. June 18th, 2013 OHBM morning workshop 5
Model selection for brain parcellations
Low K: parcels
represent
functional
signals poorly
Large K:
parcels are not
reproducible
See also [Craddock et al. HBM 2012]
Model selection is an ill-posed problem
- A model is not good in itself, but in view of a given objective
- the data dot not conform well to models
?

6. June 18th, 2013 OHBM morning workshop 6
Criteria for model evaluation

(Penalized) goodness of fit
− BIC criterion: penalized log-likelihood
− Cross validation: log-likelihood on left-out data (CVLL)

Reproducibility across bootstrap samples
− Estimate parcellation on different subgroups and compare
co-labelling statistics (mutual information, rand index)
Voxel
signal
Parcel
mean
signal
random
subject effect
noise

7. June 18th, 2013 OHBM morning workshop 7
Impact of changing K on the variance
00
1.6
Variance (a.u.)
σ1
2
σ2
2

The allocation of variance into inter- and
intra-subject components depends on K
− σ1
2
= within subject variance
− σ2
2
= between subject variance

8. June 18th, 2013 OHBM morning workshop 8
Results: goodness of fit

Kopt
~ 4000 to 7000

Wards > K-means > spectral clustering
For a good summary of the activation values, use a (very)
large number of parcels
BIC CV-
LL

9. June 18th, 2013 OHBM morning workshop 9
Results: reproducibility

Kopt
~ 200

Spectral clustering > Wards > K-means
To reproduce well the parcels, use ~ 200 parcels
Accuracy
Reproducibility

10. June 18th, 2013 OHBM morning workshop 10
Hints from simulations

Poor between subject registration might artificially
inflate the number of parcels required to fit the
signal
 Functional registration should improve the estimation
[Sabuncu et al. Cerb. Cortex 2009, Robinson et al. IPMI
2013 ]

Smoothing also inflates the number of parcels

11. June 18th, 2013 OHBM morning workshop 11
Discussion

Current atlases are too coarse to yield reliable
averages of fMRI data

Goodness of fit is different from stability /
reproducibility [Strother et al. 2002]

Wards' methods better suited than alternatives

12. June 18th, 2013 OHBM morning workshop 12
What about resting state

Consider linear decompositions and clustering

The signal cannot be easily modeled probabilistically

Cross-validation of the R2
of resting-state signals, AMI

Smaller number of regions (~80) [Abraham et al MICCAI 2013]
Accuracy Reproducibility

13. June 18th, 2013 OHBM morning workshop 13
Resting-state parcellations
[Abraham et al MICCAI 2013]

14. June 18th, 2013 OHBM morning workshop 14
Conclusion

Usefulness of brain parcellations
− A good model depends on the context
− Reproducibility and accuracy yields different responses

Need (more) multi-modal data to properly define regions

Winners:
− Ward's clustering (large K)
− Dictionary learning (small K)

Might be worth combining results from different parcellations
[Varoquaux et al. ICML 2012, da Mota et al. MICCAI 2013, Poster
#1275]

15. June 18th, 2013 OHBM morning workshop 15
Acknowledgements

Gaël Varoquaux, Alexandre Abraham, Alan
Tucholka, Benoit da Mota, Virgile Fritsch, Vincent
Michel

JB Poline, Guillaume Flandin, Philippe Pinel