A probabilistic derivation of LASSO and L12-norm feature selections

LASSO and `2,1-norm based feature selection had achieved success in many application areas. In this paper, we first derive LASSO and `1,2-norm feature selection from a probabilistic framework, which provides an independent point of view from the usual sparse coding point of view. From here, we further propose a feature selection approach based on the probability-derived `1,2-norm. We point out some inflexibility in the standard feature selection that the feature selected for all different classes are enforced to be exactly the same using the widely used `2,1-norm, which enforces the joint sparsity across all the data instances. Using the probability-derived `1,2-norm feature selection, allowing certain flexibility that the selected features do not have to be exactly same for all classes, the resulting features lead to better classification on six benchmark datasets.