[Mne_analysis] Elastic Net Inverse Solutions

[Liu, Feng]

Hi Emily,


I think for the spatial extents estimation, you can choose to use an L1 norm of total variation (TV) term defined using cortex spatial information.

Please check the papers from Dr. Lei Ding "Reconstructing cortical current density by exploring sparseness in the transform domain" or you can check "s-SMOOTH: Sparsity and Smoothness Enhanced EEG Brain Tomography" which has a higher order of smoothness definition.


Best regards,

Feng Liu

________________________________
From: mne_analysis-bounces at nmr.mgh.harvard.edu <mne_analysis-bounces at nmr.mgh.harvard.edu> on behalf of Emily Stephen <emilyps14 at gmail.com>
Sent: Tuesday, September 19, 2017 3:29:36 PM
To: Discussion and support forum for the users of MNE Software
Subject: Re: [Mne_analysis] Elastic Net Inverse Solutions

OK, one more question:

My ultimate goal *is* to estimate the spatial extent of the sources, and I'm thinking very carefully about ways to approach the problem. Elastic nets by themselves won't do it, but I'm hoping that I can make progress by (1) choosing the tuning parameters in a data-driven way and (2) rigorously describing the uncertainty in the resulting estimates.

Are you aware of other/better ways of doing spatial extent estimation?

Thanks,
Emily



On Tue, Sep 19, 2017 at 4:21 PM, Emily Stephen <emilyps14 at gmail.com<mailto:emilyps14 at gmail.com>> wrote:
Thanks, Alex! I'll keep thinking carefully about my options.

Emily

On Tue, Sep 19, 2017 at 4:11 PM, Alexandre Gramfort <alexandre.gramfort at inria.fr<mailto:alexandre.gramfort at inria.fr>> wrote:
hi,

I was drawn to Elastic Nets because I'm dealing with a dataset that is unlikely to be strictly sparse spatially, and I expect a large-ish region to have quite highly correlated activity. My understanding and experience with L1 regularization is that it chooses a small subset of these correlated sources, rather than selecting a set of them (I woudl like the solution to capture all of the correlated active sources). L2 regularization, of course, has the opposite problem, allowing all of the sources to be nonzero.

this is correct for ENet vs L1 but my reaction is that it then boils down to the problem of interpretation of an activation foci. ENet will not give you the extent of the course and it's just a "proxy" towards a region of confidence / uncertainty around the localized focal dipolar foci the L1 solver will give you.

In an ideal world I would like an inverse solution that can have a large contiguous region of highly correlated active sources, and the rest of the brain as zero or close to zero.

careful not to interpret this as source extension.

I should be able to do this with elastic nets by tuning the two regularization parameters. Is there a configuration of mixed norm solvers that can do it?

we never implemented E-Net with MxNE in MNE sorry.

I'll deal with the time dimension later, although I'm open to the idea of doing the whole thing in the frequency domain, since I have a long stretch of stationary data and the interesting effects are all in one frequency band.

if it's stationary you can use MxNE after filtering the data in the band of interest.

HTH
Alex

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