Discriminative feature selection via a structured sparse subspace learning module

In this paper, we first propose a novel Structured Sparse Subspace Learning (S³L) module to address the long-standing subspace sparsity issue. Elicited by proposed module, we design a new discriminative feature selection method, named Subspace Sparsity Discriminant Feature Selection (S²DFS) which enables the following new functionalities: 1) Proposed S²DFS method directly joints trace ratio objective and structured sparse subspace constraint via `<sub>2,0</sub>-norm to learn a row-sparsity subspace, which improves the discriminability of model and overcomes the parameter-tuning trouble with comparison to the methods used `_2,1-norm regularization; 2) An alternative iterative optimization algorithm based on the proposed S³L module is presented to explicitly solve the proposed problem with a closed-form solution and strict convergence proof. To our best knowledge, such objective function and solver are first proposed in this paper, which provides a new though for the development of feature selection methods. Extensive experiments conducted on several high-dimensional datasets demonstrate the discriminability of selected features via S²DFS with comparison to several related SOTA feature selection methods. Source matlab code: https://github.com/StevenWangNPU/L20-FS.