Nonlinear Joint Unsupervised Feature Selection

In the era of big data, one is often confronted with the problem of high dimensional data for many machine learning or data mining tasks. Feature selection, as a dimension reduction technique, is useful for alleviating the curse of dimensionality while preserving interpretability. In this paper, we focus on unsupervised feature selection, as class labels are usually expensive to obtain. Unsupervised feature selection is typically more challenging than its supervised counterpart due to the lack of guidance from class labels. Recently, regression-based methods with L2,1 norms have gained much popularity as they are able to evaluate features jointly which, however, consider only linear correlations between features and pseudo-labels. In this paper, we propose a novel nonlinear joint unsupervised feature selection method based on kernel alignment. The aim is to find a succinct set of features that best aligns with the original features in the kernel space. It can evaluate features jointly in a nonlinear manner and provides a good ‘0/1’ approximation for the selection indicator vector. We formulate it as a constrained optimization problem and develop a Spectral Projected Gradient (SPG) method to solve the optimization problem. Experimental results on several real-world datasets demonstrate that our proposed method outperforms the state-of-the-art approaches significantly.