[FieldTrip] Cluster-Statistics on wPLI data

[Tom Holroyd]

> The problem with mixture
> models is the arbitrary nature of how many clusters to use, and
> without a way to determine the statistical likelihood of a given
> cluster this is a real problem for determining the validity of a
> given cluster.

Yea. Given the nature of MEG, with ~300 channels, you look at the
eigenvalue spectrum of a typical channel covariance matrix and see that
it typically starts to flatten out at around 50 or so, and then figure
maybe K=20~25 clusters, so you take the top K (or K-1*) eigenvectors of
the Laplacian matrix and use K-means clustering to relabel the nodes
(voxels) according to which subnetwork they are in. I tend to sort them
by size, and see how they change over conditions. The results are
"interesting", but that's different from "publishable". It's a real
problem, as you say, to determine the likelihood of a cluster. One
approach is to start with random MEG data. Note that passing random MEG
data through a beamformer results in almost the same thing as passing
real MEG data through a beamformer. Quite a lot of structure is in the
weights. So you need to shuffle the beamformers as well. Then do the
spectral clustering and look at how things change.

This is an open area and I'd welcome any insights anyone may have about
how to visualize or work with distributions of clusters in 3D.

It is also worth pointing out that all of this depends highly on what
your connectivity measure is. Beamformed virtual channels can be quite
noisy ... many books have been written about how to estimate spectra,
coherence, and the like. This paper is fairly interesting:

"A Generalized MVDR Spectrum" Benesty, Chen, and Huang

http://externe.emt.inrs.ca/users/benesty/papers/spl_dec2005.pdf

* This post is too short to talk about that.

-- 
Dr. Tom
--
"There are not more than five musical notes,
yet the combinations of these five give rise to
more melodies than can ever be heard." -- Sun Tzu