Semisupervised Feature Selection With Sparse Discriminative Least Squares Regression
Chen Wang, Xiaojun Chen, Guowen Yuan, Feiping Nie, Min Yang
Abstract
In big data time, selecting informative features has become an urgent need. However, due to the huge cost of obtaining enough labeled data for supervised tasks, researchers have turned their attention to semisupervised learning, which exploits both labeled and unlabeled data. In this article, we propose a sparse discriminative semisupervised feature selection (SDSSFS) method. In this method, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula> -dragging technique for the supervised task is extended to the semisupervised task, which is used to enlarge the distance between classes in order to obtain a discriminative solution. The flexible <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{2,p}$ </tex-math></inline-formula> norm is implicitly used as regularization in the new model. Therefore, we can obtain a more sparse solution by setting smaller <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> . An iterative method is proposed to simultaneously learn the regression coefficients and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula> -dragging matrix and predicting the unknown class labels. Experimental results on ten real-world datasets show the superiority of our proposed method.