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Table 1 Sparse approaches

From: A flexible framework for sparse simultaneous component based data integration

Norm Properties Sparse approach
   Lasso Elastic net Group lasso Sparse group lasso Elitist lasso
l 1 selection and shrinkage at the level of the concatenated data YES YES NO YES NO
l 2 2 shrinkage, groups correlated variables NO YES NO NO NO
l 2,1 selection and shrinkage of entire blocks NO NO YES YES NO
L 1,2 selection and shrinkage within each block NO NO NO NO YES
  1. Different norms used in the context of sparse approaches, their properties, and specific sparse approaches based on particular combinations of the penalties. A 'YES' indicates that the norm is active in the approach.