Regularization parameters for the SFM fit using Elastic Net.

We used regularization and cross-validation to (a) prefer solutions that minimize the number of fascicles and (b) prevent over-fitting. To find the appropriate setting of the regularization parameters λ and α, we used a cross-validation approach. The SFM was fit on one set of data for a range of λ and α values. For each combination the SFM was fit to one data set and the prediction error was calculated using the other data set. We choose λ and α that minimize the median rRMSE across white matter voxels. We explore the effects of regularization and the trade-off of different sets of constraints on the accuracy of the fit. The best setting of these parameters is to a relatively low degree of regularization (λ = 0.0005) and relatively L1-weighted constraint (α = 0.2). These are the parameters used in all the SFM model fits.

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