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In this paper, we use the complex multi-task Bayesian compressive sensing (CMT-BCS) algorithm [29], which is based on the Bayesian framework that exploits the statistical relationship between multiple measurements or sensing tasks and exploit the group sparsity between real and imaginary parts of the sparse entries.
The CMT-BCS algorithm exploits the group sparsity between the real and imaginary parts of the sparse entries, ℜ u(n)) and I u(n)), and the solution of u(n)= ℜ (u(n)) + j I u(n)) converges to a K-sparse solution, whose indices correspond to estimates of acceleration of the K ground moving targets, a ̂ ( k ) = â x ( k ), â y ( k ), 0 T, where k = 1,⋯,K.
Results are presented for white matter connectomes that show plausible cortico-cortical sparsity (between 11 and 17%).
Since the ℓ2,1-norm regularizer impose the sparsity between all features and non-sparsity between tasks, the features that are discriminative for all tasks will get large weights.
The sparse group lasso encourages sparsity between and within groups, and has been previously applied to GWAS for variants with frequencies [Zhou et al., 44].
The Sparse Group Lasso method is a combination of Lasso and Group Lasso, which can achieve sparsity between groups and within the group.
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For simplification, M ij of each subject is thresholded to create a binarized matrix A ij in a range of sparsity, comprising between 5% and 10% of the 4,005 possible edges in a network with 90 nodes [ 28].
The sparsity of the between-community connectivity is the basis for community separation quality measures such as the modularity index, [10].
Sometimes the predictors can be naturally grouped where pursuing the between-group sparsity is desired.
Firstly, we look at the relations between sparsity and recovery success ratio.
Hoyer [20] has the same conclusion about the trade-off between sparsity, localization and data representation sufficiency.
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