  There exist many high-dimensional data in real-world applications such as
biology, computer vision, and social networks. Feature selection approaches are
devised to confront with high-dimensional data challenges with the aim of
efficient learning technologies as well as reduction of models complexity. Due
to the hardship of labeling on these datasets, there are a variety of
approaches on feature selection process in an unsupervised setting by
considering some important characteristics of data. In this paper, we introduce
a novel unsupervised feature selection approach by applying dictionary learning
ideas in a low-rank representation. Dictionary learning in a low-rank
representation not only enables us to provide a new representation, but it also
maintains feature correlation. Then, spectral analysis is employed to preserve
sample similarities. Finally, a unified objective function for unsupervised
feature selection is proposed in a sparse way by an $\ell_{2,1}$-norm
regularization. Furthermore, an efficient numerical algorithm is designed to
solve the corresponding optimization problem. We demonstrate the performance of
the proposed method based on a variety of standard datasets from different
applied domains. Our experimental findings reveal that the proposed method
outperforms the state-of-the-art algorithm.
