We used sparsity/parsimony enforcing regularization techniques in a nested cross validation grid search to select features for 17 unique supervised learning models, encoding missing values as additional indicator features.
In the first extension, we use group-sparsity enforcing regularization term to impose the sparse structure.
The innovative idea of this paper is to aggregate the DEDR-optimal fixed-point iterative reconstruction/enhancement procedures developed in the previous studies [7, 8, 10] with the multi-level robustness and convergence enforcing regularization via constructing the proper projections onto convex sets (POCS) in the solution domain.
Functions Φ are chosen in such a way to enforce a global regularization constraint on the cross-spectra.
For example in the uniform law of large numbers view, regularization enforces small capacity, while in the stability view we see that regularization ensures that the output hypothesis is not too brittle (this was covered in some details in the previous notes).
Therefore, a nuclear norm regularization is enforced to capture that sparse prior.
In the present approach, the necessity of regularization is enforced by means of the trust region approach.
Thus, in the experiments, when (i.e., no spatial regularization is enforced), we obtain the same results as in Table 1.
Sparsity is enforced through L1-norm regularization, which inherently removes outliers and irrelevant associations.
Finally, through enforcing the ℓ2,1-norm regularization, the imaging feature selection across most SNPs are coupled (Argyriou et al., 2007; Obozinski et al., 2006), so that the identified imaging phenotypes have common influence on all the SNPs.
