Adaptive dual graphs and non-convex constraint based embedded feature selection

Abstract

In traditional feature selection methods, to guarantee the sparsity of the rows, ${l}_1$-norm or ${l}_{2,1}$-norm is often used to constrain the evaluation matrix. As convex regularization terms, they work well in most cases. However, when dealing with redundant features, some non-convex regularization terms tend to show better performance. With the advantages of adaptive manifold learning and non-convex constraints, a novel algorithm is proposed in this paper, called adaptive dual graphs and non-convex constraint based embedded feature selection (DNEFS). With the framework of sparse regression, DNEFS preserves the manifold structure information of both data space and feature space, simultaneously. Meanwhile, by using the principle of information entropy, the local manifold information in dual graphs can be learned and updated adaptively, resulting in a better feature selection effect. Different from traditional convex constraints, a novel non-convex regularization term is introduced in this paper. This regularization term consists of the difference between ${l}_{2,1}$-norm and Frobenius norm, and is written as ${l}_{2,1-2}$-norm. By using this novel regularization term, DNEFS can handle redundant features more efficiently. Then, an alternating iterative updating method is used in this paper to optimize the objective function, and six benchmark datasets are used to test the performance of DNEFS. By comparing with six comparison algorithms, the experimental results show that DNEFS can achieve better performance.