# [FieldTrip] fieldtrip Digest, Vol 55, Issue 2

Tom Holroyd tomh at kurage.nimh.nih.gov
Tue Jun 2 19:33:23 CEST 2015

```Several people have been doing things with spectral clustering,
involving the graph Laplacian, wherein we say that each voxel of the
brain is a node in a graph, and various connectivity measures connect
the nodes. The Laplacian of the graph has many interesting properties,
and the first K eigenvalues can be used to create clusters.

I'm afraid I don't know how to do permutation stats on that, but
k-means clustering of the graph eigenvectors can have random starting
points ...

On Tue, 02 Jun 2015 09:53:42 -0600
Nick Ketz <nick.ketz at gmail.com> wrote:

> Mathis, you have hit on a much larger problem.  Tzvetan is right to
> suggest calculating each grid-point's connectivity with all other
> grid-points, which gives you a connectivity topography map for each
> grid-point.  The next logical step, which I've been struggling with,
> is to somehow cluster these topographies together, giving you
> clusters of neighboring grid-point topographies that are similar.  Is
> there any work being done to solve this problem?
>
> I have been struggling with this problem for some time, that is: how
> to do cluster based permutation statistics in chan x chan bins of
> connectivity  measures.  Ideally I want to do this in a full chan x
> chan x freq x time cluster analysis.  I've searched on the list for
> related topics; posted, probably incoherently, my own issues; and
> generally scanned the list and the literature for any sort of
> relevant topics trying to broach this problem, but am still stuck.
>
> The standard 3d chan x freq x time clustering uses a neighborhood
> structure to define what channels are considered neighbors, and uses
> numeric adjacency to cluster time and frequency. With chan x chan
> data however, there unfortunately isn't an intuitive way to think
> about neighborhood for the pairwise connectivity.  There are
> neighbors surrounding the reference grid-point, and there are
> neighbors in each grid-point's connectivity topography, i.e.
> neighboring grid-points that have similar/significant connectivity
> values.  How do you combine the two in a sensible way?  And even more
> challenging how do you do statistics on them?
>
> I have been considering several approaches, including
> multi-dimensional scaling of these grid-point connectivity
> topographies, or just a correlation between topographies, and then
> using those values to select which reference grid-points to consider
> as similar enough to average together.  This then gives you a
> reference cluster of grid-points and allows you to do standard
> cluster permutation statistics on the average of the reference
> grid-points.  How exactly to determine which reference grid-points
> are 'similar enough' to be consider clusters is the tricky part, i.e.
> how can you statistically test if they should be considered a cluster
> or not?
>
> I've been working in isolation on this problem for some time, and
> would love a discussion on the topic.  I'm hoping this message spurs
> other list lurkers to at least commiserate with me, but if possible
> to also post whatever approaches they have taken to solve the problem
> of clustering pairwise connectivity data.
>
>
>
> Nick
>
>
>
> On 6/2/15 4:00 AM, fieldtrip-request at science.ru.nl wrote:
> > Hi Mathis, alternatively you could use ft_sourcestatistics. For
> > this you should reduce your 600 x 600 x freq matrix to freq of
> > interest first. Next, the resulting 600 x 600 matrix you?d reduce
> > to 600 x 1 where each grid point has a mean connectivity value to
> > all possible grid points. >From then on you could use
> > ft_sourcestatistics and ft_sourceinterpolate to visualize. Good
> > luck, Tzvetan
> >> >Dear Fieldtrip Users,
> >> >
> >> >I am a first-year PhD student and have been lurking here for a
> >> >my first question:
> >> >
> >> >I am trying to compare connectivity in source space (~25
> >> >subjects, between two conditions, ~600 virtual channels on a
> >> >1.5cm grid) using ft_freqstatistics with a cluster-based
> >> >permutation test (see code below).
> >> >
> >> >The original input datasets have the dimensions: chan x chan x
> >> >freq. I tried restructuring them to chancmb x freq
> >> >(seehttp://mailman.science.ru.nl/pipermail/fieldtrip/2014-February/007620.html)
> >> >before doing ft_freqstatistics, but the function then takes
> >> >forever appending the (admittedly big) datasets.
> >> >
> >> >I then tried feeding them to ft_freqstatistics without
> >> >restructuring, which didn't throw any errors. However, I noticed
> >> >that the resulting clusters consist of adjacent cells in the chan
> >> >x chan matrix, which doesn't make much sense since channels in
> >> >that ft_freqstatistic assumes the 3-D input to contain a temporal
> >> >dimension and therefore tries to build temporally adjacent
> >> >clusters. Could any of the fieldtrip developers comment on this?
> >> >Does anyone in the FT-community have any advice on how to
> >> >statistically evaluate connectivity data using the permutation
> >> >approach?
> >> >
> >> >Thanks for any input, best wishes,
> >> >Mathis Kaiser
>
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--
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

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