<html><head><meta http-equiv="Content-Type" content="text/html charset=windows-1252"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div>Dear Nick et al.,</div><div><br></div><div>it is also important to consider alternative possibilities to reduce the degrees of freedom based on the existing knowledge about the data. For example:</div><div>Case 1- The research question.</div><div>Consider the case of mid-frontal theta in the context of error related design. Base on what we already know from the existing literature it is probably save to reduce the 128x128x70x50 matrix to a 128x128 where the time-freq tile of interest will be something from .3 to 1 seconds ~6 Hz. </div><div>Case 2- The data itself.</div><div>Consider continuous resting state recording and long-range connectivity as a research question. The time dimension doesn’t really make sense and from what we know, or believe to know about long range communication, this is likely to happen in the lower frequency bands. With a peak in the power spectrum as an additional including criterion it is likely that the frequency dimension would be reduced to ~ 10 Hz. </div><div>Case 3- The preceding analysis</div><div>Admittedly not always yet more often than not connectivity analysis follows extensive analysis on sensor level where most likely relevant time-frequency tiles were already defined while controlling for MCP. In that case one will go for the connectivity patterns concerning these preceding findings thereby reducing the time-freq dimension again.</div><div><br></div><div>These are just a few examples where you will have a chan x chan matrix to begin with. Whether you are interested in the mean connective value of a given channel or channel(seed) to all other channels both approaches will give a 128 x 1 matrix that can be further evaluated in the context of a permutation approach or whatever preferred method.</div><div><br></div><div>Tzvetan</div><div> </div><div><br class="Apple-interchange-newline"><blockquote type="cite">
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<div class="moz-cite-prefix">Hi Tom and Jake, thanks very much for
adding momentum to this. I haven't yet looked into spectral graph
clustering, and really haven't been thinking of it terms of graph
theory but it now seems silly that I haven't. <br>
<br>
If I'm understanding the suggestions correctly, the idea is to use
the eigenvectors of the connectivity measure (WPLI in this case)
to determine which nodes/voxels to cluster together. So nodes
with similar graphs will be clustered together. This would be
analogous to the graph bisection problem where k=2. 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. <br>
<br>
<br>
Jake thanks for the resources, I'm beginning to dig into them and
they seem promising. My understanding is that graph bisection
divides the graph into two groups that have the minimum number of
connections between them. So this could be used to cluster nodes
that have similar topographies together, but it's not clear the
best division would occur in the first bisection, instead possibly
in subsequent bisections. Is this where the recursive algorithm
comes in? I found this paper of yours '
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Spectral Techniques for Graph Bisection in Genetic
Algorithms', but it doesn't seem to get past the initial
bisection. <br>
<br>
<br>
As I said, I haven't really been thinking of the problem in graph
theory terms, but if my understanding is correct the current data
set I'm working with could have an adjacency matrix as large as
128x128x70x50 (chan x chan x time x frequency), and as small as
128x128 for a single time x frequency bin. <br>
<br>
<br>
Nick<br>
<br>
<br>
On 6/2/15 12:38 PM, Jacob Martin wrote:<br>
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<blockquote cite="mid:4529C3E1-8A08-4558-B79C-B7E426233AD4@gmail.com" type="cite">
<pre wrap="">Hi Tom and Nick,
Here's a paper i wrote which may help give some background on spectral clustering:
"Ranks and representations for spectral graph bisection"
I also have a genetic algorithm which uses recursive spectral graph bisection to cluster graphs using the ideas from the above paper. It is written in Java and is quite competitive and fast compared to other algorithms. Nick, perhaps i could lend a hand.
I suggest looking up Chris Walshaw's partition archive for lots of examples of algorithms. I had a few minimum bisection records in there a while back with an older algorithm, but haven't looked at it in years or tried with my new algorithms yet.
How big are your adjacency matrices? Note that the minimum bisection problem is NP complete.
Best
Jake
--
Jacob Martin, PhD
Center for Brain and Cognition
CerCo CNRS
Toulouse, France
On 02 Jun 2015, at 13:33, Tom Holroyd <a class="moz-txt-link-rfc2396E" href="mailto:tomh@kurage.nimh.nih.gov"><tomh@kurage.nimh.nih.gov></a> wrote:
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 <a class="moz-txt-link-rfc2396E" href="mailto:nick.ketz@gmail.com"><nick.ketz@gmail.com></a> wrote:
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<pre wrap="">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
</pre>
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<pre wrap="">On 6/2/15 4:00 AM, <a class="moz-txt-link-abbreviated" href="mailto:fieldtrip-request@science.ru.nl">fieldtrip-request@science.ru.nl</a> 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
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<pre wrap="">Dear Fieldtrip Users,
I am a first-year PhD student and have been lurking here for a
long time (finding lots of useful answers), it's about time I ask
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
(<a href="seehttp://mailman.science.ru.nl/pipermail/fieldtrip/2014-February/007620.html">seehttp://mailman.science.ru.nl/pipermail/fieldtrip/2014-February/007620.html</a>)
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
adjacent cells are not necessarily spatially adjacent. I suspect
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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