Fig 1.
Schematic of the group-lasso settling disputes.
The true areas are shaded pink and green. The blue region is stronger than green in subject 1, but pink and green still get chosen over the blue because of their aggregate strength across the other 5 subjects; in effect, a majority vote. In the group-lasso solution, the blue ROI activation would be set to zero.
Fig 2.
Localization of the visual ROIs used for the simulations.
V2v is in green and V4 is in purple. A) Shows left and ventral views of one typical subject. B) Shows the ventral views of 4 other subjects.
Fig 3.
Performance of the group-lasso and minimum norm.
Performance of the group-lasso (in red) and minimum-norm (in blue) on one instance of simulated data for one (left column) and five subjects (right column). Vertical lines correspond to the solutions chosen by optimizing the GCV error curve for each method, with the asterisks indicating the results from the minimum norm. The values obtained for the MSE, AUC close and far and energy and energy metrics are provided on the four first rows. Because there is no left and right subspace reduction with the minimum-norm, the GCV curve for this approach has a different scale than the one obtained with group-lasso. We therefore displays these curves separately on the fifth and sixth rows.
Fig 4.
MSE from dimension reduction by principal components (in red) and temporal smoothing (in blue) with right singular vectors of Y, averaged over 100 simulations.
A large portion of the MSE in our model is due to the dimension reduction from taking the first 5 principal components for each ROI, and a negligible portion is due to the temporal smoothing.
Fig 5.
Performance of the group-lasso and minimum norma as a function of the number of subjects.
Performance of the group-lasso is shown in red and the minimum norm in blue as a function of the number of subjects. Plots are of averages from 50 simulations with different subsets of subjects. Vertical lines are standard error bars. The group lasso performance improves with increasing numbers of subjects for the AUC and energy metric, but the minimum norm does not. MSE does not vary systematically with number of subjects for either inverse type.
Fig 6.
AUC obtained after post-processing the recovered activity by averaging across subjects.
Plots are of average values over the same 50 data instances from before, along with standard error bars. Notice that the group-lasso with 4 subjects often outperforms the minimum norm with 25 subjects. Minimum norm in blue, group lasso in red.
Fig 7.
SSVEP to alternations between coherent and incoherent motion.
Panel A is the group-average (n = 9) waveforms from all 128 EEG sensors. The inset shows the group-average scalp topography. Panel B shows the individual participant topographies for all 9 participants that went into to group average. The topography is shown for the same time as in panel A.
Fig 8.
Representative cortical surface reconstructions.
Visual ROIs V1, V2, V3, V3A, V4, MT and LOC are shown (see color bar for labeling convention). Top panel shows ventral surface view, bottom panel posterior view. Note that while there is a general pattern of agreement in the relative location of the visual areas, there is considerable variability in the detailed shape, size and location of the ROIs across subjects.
Fig 9.
(A) Minimum norm solutions for coherent/incoherent motion SSVEP responses in visual ROIs. With the minimum norm all visual ROIs contain some level of activation. With left and right ROIs showing differences. (B) group Lasso solutions for coherent motion SSVEP responses in visual ROIs. With the group Lasso only a few of the visual ROIs contain some level of activation. With left and right ROIs showing similar waveforms. Group lasso solution produces stronger distinctions between MT and V3A ROI activations and the other ROIs than does the minimum norm.
Fig 10.
Scalp topographies from measured data and reconstructed from inverse solutions.
(Top) The top row is the original SSVEP data demonstrating cross-participant heterogeniety. (Middle) Reconstructed topographies from the minimum norm solution. (Bottom) Reconstructed topographies from the group Lasso solution. Even though the group lasso solution utilizes fewer cortical areas than the minimum norm it is still able to capture the cross-participant heterogeniety.