Soft Label Guided Unsupervised Discriminative Sparse Subspace Feature Selection

Feature selection and subspace learning are two primary methods to achieve data dimensionality reduction and discriminability enhancement. However, data label information is unavailable in unsupervised learning to guide the dimensionality reduction process. To this end, we propose a soft label guided unsupervised discriminative sparse subspace feature selection (UDS\(^2\)FS) model in this paper, which consists of two superiorities in comparison with the existing studies. On the one hand, UDS\(^2\)FS aims to find a discriminative subspace to simultaneously maximize the between-class data scatter and minimize the within-class scatter. On the other hand, UDS\(^2\)FS estimates the data label information in the learned subspace, which further serves as the soft labels to guide the discriminative subspace learning process. Moreover, the \(\ell _{2,0}\)-norm is imposed to achieve row sparsity of the subspace projection matrix, which is parameter-free and more stable compared to the \(\ell _{2,1}\)-norm. Experimental studies to evaluate the performance of UDS\(^2\)FS are performed from three aspects, i.e., a synthetic data set to check its iterative optimization process, several toy data sets to visualize the feature selection effect, and some benchmark data sets to examine the clustering performance of UDS\(^2\)FS. From the obtained results, UDS\(^2\)FS exhibits competitive performance in joint subspace learning and feature selection in comparison with some related models.