Sparse feature selection via fast embedding spectral analysis. (July 2023) - Wang, Jingyu; Wang, Hongmei; Nie, Feiping; Li, Xuelong
Highlights: Adaptive anchor neighbor graph is learned to attenuate the influence of the mismatch between the neighbor structure and the category relationship in the high-dimensional data manifold structure. A sparse constraint via ℓ 2, 0 -norm is adopted to guarantee the sparsity of spectral analysis model;, and the orthogonal constraint of projection matrix guarantees subspace orthogonality to improve model performance. An equivalent form of the original model is proposed, an iterative optimization algorithm is presented to deal with the non-convex optimization problem in fewer iterations and less time. Abstract: Feature selection has been a research hotspot in many fields. Models based on graph learning are currently the most popular approaches. However, the sparsity of most models is not strong, and graph learning for pair-sample evaluation takes a lot of time. ℓ 2, 1 -norm regularization is the sparsity strategy adopted in most sparse models at present since the convex function is easy to solve. Nevertheless, the sparsity of ℓ 2, 1 -norm is insufficient, and there exist parameter adjustment problems. ℓ 2, 0 -norm is a better choice, which can strengthen the sparse constraints of the subspace. In this paper, the Sparse feature selection via Fast Embedding Spectral Analysis (SFESA) is proposed. Firstly, an adaptive anchor nearest neighbor graph is constructed to avoid the high time cost of learning pairwise nearest neighbor graphs to a certain extent. The low-dimensional embedding of data manifold structure is maintained by performing spectral analysis for the constructed graph. Secondly, the projected data is approximated to the low-dimensional embedding structure via a regularization term. Finally, ℓ 2, 0 -norm is employed to constrain the projection matrix to enhance the subspace sparsity. Furthermore, a fast iterative algorithm is presented to solve this non-convex optimization problem. Extensive experiments on multiple public datasets show that SFESA can obtain excellent performance in less time.