[Eeglablist] AMICA lrate gets stuck
Jason Palmer
japalmer29 at gmail.com
Tue Aug 18 23:14:55 PDT 2015
Hi Kevin,
Yes, the doPCA flag is definitely not supported! ;-) You should just use the pcakeep flag for pca dimensionalit reduction. In this case amica will keep the number of pca dimensions you specify. Even though a full S sphering matrix is output, the actual sphering matrix used is just the first pcakeep rows. So icaact = W * S(1:pcakeep,:) * EEG.data; And icawinv = pinv(W*S(1:pcakeep)).
If you don’t specify pcakeep less than nchan, then it will still do the sphering decorrelation to get the starting point, but there will be no dimensionality reduction.
You can also do the sphering separately if you want. The amica reduced dimension sphering matrix is actually an attempted rotation of the first pcakeep eigenvectors back to a more data-like space, similar to the advantage of the sqrt covariance sphering over eigenvector sphering, as this starting point seems to be better (resulting in faster convergence) than using the eigenvectors, which produce starting components that are relatively more dependent. So the Amica S output in the reduced pcakeep case won’t be the eigenvectors exactly, but a rotation of that space.
Best,
Jason
From: Kevin Tan [mailto:kevintan at cmu.edu]
Sent: Tuesday, August 18, 2015 10:52 PM
To: japalmer at ucsd.edu; EEGLAB List
Subject: Re: AMICA lrate gets stuck
Hi Jason,
I have some PCA-related questions for you.
Using the 'doPCA' flag (either 0 or 1) in runamica12.m results in this error:
runamica(): unknown flag: dopca
Error in runamica12 (line 100)
if ~isempty(strfind(computer,'64'))
Output argument "weights" (and maybe others) not assigned during call to
"/home/kevinalt/MATLAB/eeglab13_4_4b/plugins/amica/runamica12.m>runamica12".
Not using 'doPCA' flag still results in "doPCA = 1" in the config file. Not using 'pcakeep' flag results in "pcakeep = chans" in config file.
Is PCA still being performed if pcakeep = chans? Does it matter whether I use command arguments ('pcakeep', chans) vs. just not using the 'pcakeep' flag?
If I do want dimension reduction, is it best to use arguments ('pcakeep', comps) or to perform PCA beforehand then combine PCA eigenvector & ICA matrices? Like this:
[eigenvectors, eigenvalues, PCAdata] = pcsquash(EEG.data(:, :), nmIC);
[weights, sphere, mods] = runamica12(PCAdata);
weights = weights * sphere * eigenvectors(:, 1:nmIC)';
sphere = eye(chans);
Many thanks for the continued help, I really appreciate it!
--Kevin
--
Kevin Alastair M. Tan
Lab Manager/Research Assistant
Department of Psychology & Center for the Neural Basis of Cognition
Carnegie Mellon University
Baker Hall 434 <https://www.google.com/maps/place/40%C2%B026%2729.5%22N+79%C2%B056%2744.0%22W/@40.4414869,-79.9455701,61m/data=!3m1!1e3!4m2!3m1!1s0x0:0x0> | kevintan at cmu.edu | tarrlab.org/kevintan <http://tarrlabwiki.cnbc.cmu.edu/index.php/KevinTan>
On Mon, Aug 17, 2015 at 10:12 PM, Jason Palmer <japalmer29 at gmail.com> wrote:
Yes single channel sources are common for ICA of EEG with over 100 channels. Single-channel artifacts are probably responsible for them. Cleaning the data more intensely can reduce their number. But the number of “good” components, i.e. detectable, instantaneously independent, relatively large, synchronous patch brain sources, seems to be limited to about to 20-30, with additional degrees of freedom (additional number of channels) being used to deal with non-stationarity and artifacts, so you shouldn’t expect all “good” components.
Best,
Jason
From: Kevin Tan [mailto:kevintan at cmu.edu]
Sent: Monday, August 17, 2015 6:51 PM
To: japalmer at ucsd.edu; EEGLAB List
Subject: Re: AMICA lrate gets stuck
Ah ok, did not know the wchange output in Infomax is calculated in that way, thanks for clearing that up.
My data is 136ch (but usually 125-130 after PREP) with ~700,000 samples (depending on epoch rejection). Is 10^-5 still a good nd weight change to shoot for?
Also, is it common to see some single-channel weighted ICs (usually weak ones) even after ensuring the rank is correct? This also occurs with Infomax, wanted to see if AMICA can get rid of it.
Thanks again,
Kevin
--
Kevin Alastair M. Tan
Lab Manager/Research Assistant
Department of Psychology & Center for the Neural Basis of Cognition
Carnegie Mellon University
Baker Hall 434 <https://www.google.com/maps/place/40%C2%B026%2729.5%22N+79%C2%B056%2744.0%22W/@40.4414869,-79.9455701,61m/data=!3m1!1e3!4m2!3m1!1s0x0:0x0> | kevintan at cmu.edu | tarrlab.org/kevintan <http://tarrlabwiki.cnbc.cmu.edu/index.php/KevinTan>
On Mon, Aug 17, 2015 at 7:35 PM, Jason Palmer <japalmer29 at gmail.com> wrote:
Hi Kevin,
The Infomax wchange is actually the weight change TIMES the lrate, which is going to 1e-7. So the actual final wchange for extended infomax is 1e7 * wchange.
For Amica, if the nd weight change gets down to the 10^-5 magnitude, that is usually about the best you can expect with the large number of parameters being estimated and the finite computer precision. How small it can get depends on the number of samples you have compared to the number of channels. More channels = more parameters (nchan^2) = relatively little data = “noisier” convergence. More data = better determined optimum = less noisy convergence = smaller nd. For 64 channels with 100,000 samples, an nd of 10^-5 sounds appropriate.
However you can change “maxiter” from the default 2000, using the ‘maxiter’ keyword. This LL should continue to increase and the nd decrease (or at least not increase) beyond 2000 iterations, but not significantly. There should be a weight change “noise floor” reached, where the LL continues to increase by less and less, with possible reductions in lrate, and the nd hovers around the “noise floor”.
Best,
Jason
From: Kevin Tan [mailto:kevintan at cmu.edu]
Sent: Monday, August 17, 2015 4:21 PM
To: japalmer at ucsd.edu; EEGLAB List
Subject: Re: AMICA lrate gets stuck
Hi Jason,
Thanks so much for the detailed response, really helps clarify what drives the lrate changes between the two implementations.
However, for the same dataset processed the same way, AMICA yields higher wchange at last iteration (0.0000464763) versus extended Infomax (0.000000).
What are some reasons for this discrepancy, and what can I do improve it? Or is weight change between the two implementations not comparable? The entire AMICA log is linked in original post if that helps.
Thanks again,
Kevin
--
Kevin Alastair M. Tan
Lab Manager/Research Assistant
Department of Psychology & Center for the Neural Basis of Cognition
Carnegie Mellon University
Baker Hall 434 <https://www.google.com/maps/place/40%C2%B026%2729.5%22N+79%C2%B056%2744.0%22W/@40.4414869,-79.9455701,61m/data=!3m1!1e3!4m2!3m1!1s0x0:0x0> | kevintan at cmu.edu | tarrlab.org/kevintan <http://tarrlabwiki.cnbc.cmu.edu/index.php/KevinTan>
On Mon, Aug 17, 2015 at 7:06 PM, Jason Palmer <japalmer29 at gmail.com> wrote:
Hi Kevin,
The Amica lrate is not supposed to decrease. The algorithm is a more typical gradient descent / Newton optimization algorithm, as opposed to the Infomax implementation in runica.m, which uses a type of simulated annealing, deciding whether to reduce the learning rate based on the angle between recent update directions. The idea there is that this angle will be small when the algorithm is near an optimum, as though it is “heading right for it”, so the lrate gets reduced if the algorithm is moving “erratically” with a large angle between consecutive directions, and doesn’t get reduced if the estimate is “moving smoothly”. In practice, this annealing method usually ends up in fact reducing the learning rate continuously until it reaches the preset minimum, which usually happens at around 500 iterations (500 reductions). I.e. the angle is never actually small, so the stopping condition is essentially a maximum number of iterations, with the updates being of smaller and smaller magnitude due to the lrate decreasing.
Amica only reduces the lrate if the likelihood decreases. In theory, with a reasonable optimum, an optimization algorithm should be able to converge without reducing the learning rate. The convergence is measured by the weight change (the nd in the amica output) independently of the lrate. That is, the weight change should theoretically decrease to zero with a constant (sufficiently small) lrate—the higher the better since higher lrate means faster convergence. A potential issue with the runica Infomax is early convergence if you are starting far from the optimum. Fortunately the optimum is usually not far from the “sphering” starting point, so 500 iterations is usually enough to converge (even with decreasing lrate).
So in Amica, the convergence is judged by the “nd”, not the lrate. The lrate should be ideally be 0.5 or 1.0, and the LL should be increasing, and the nd should be decreasing to zero.
Hope that is helpful.
Best,
Jason
From: Kevin Tan [mailto:kevintan at cmu.edu]
Sent: Monday, August 17, 2015 2:31 PM
To: jason at sccn.ucsd.edu; EEGLAB List
Subject: AMICA lrate gets stuck
Hi Dr. Palmer & EEGLAB list,
I'm trying out AMICA for artifact rejection and DIPFIT. In my tests, the lrate consistently gets stuck at 0.5, stopping only due to max iteration limit. This does not happen with extended Infomax.
This happens whether I use the cluster (128 threads) or a normal PC (4 threads). I run AMICA 'locally' as it's called within a matlab script already run via PBS, not sure if that makes a difference.
Here's the AMICA test stream:
- PREP pipeline
- Remove PREP-interpolated channels
- Remove 1 additional channel for rank consistency
- 1hz FIR hi-pass
- Epoch -500 to 1000ms no baseline correction
- Epoch rejection
- AMICA (using EEG(:,:) -- is it ok to concatenate epochs like this?)
Here's the output log (using the cluster):
https://cmu.box.com/s/t7j3shmwjj1wj8to80au8mdm6b5676rh
Many thanks,
Kevin
--
Kevin Alastair M. Tan
Lab Manager/Research Assistant
Department of Psychology & Center for the Neural Basis of Cognition
Carnegie Mellon University
Baker Hall 434 <https://www.google.com/maps/place/40%C2%B026%2729.5%22N+79%C2%B056%2744.0%22W/@40.4414869,-79.9455701,61m/data=!3m1!1e3!4m2!3m1!1s0x0:0x0> | kevintan at cmu.edu | tarrlab.org/kevintan <http://tarrlabwiki.cnbc.cmu.edu/index.php/KevinTan>
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