Adaptive structure learning for low-rank supervised feature selection

Previous Spectral Feature Selection (SFS) methods output promising feature selection results in many real-world applications, which deeply depend on the preservation of the local or global structures of the data via learning a graph matrix. However, current SFS methods 1) learn the graph matrix in the original data which may contain a number of noise to affect the results of feature selection, 2) conduct the learning of a low-dimensional feature space and the graph matrix individually, thus hard achieve the optimal results of feature selection even though both of these two steps achieve their individual optimization, and 3) consider either the local or global structure of data to difficult provide complementary information for feature selection. To address the above issues, this paper proposes a novel supervised feature selection algorithm to simultaneously preserve the local structure (via adaptive structure learning in a low-dimensional feature space of the original data) and the global structure (via a low-rank constraint) of the data. Moreover, we also propose a new optimization method to fast optimize the resulting objective function. We finally verify the proposed method on eight real-word and benchmark datasets, by comparing with the state-of-the-art feature selection methods, and experimental results show that our proposed method achieves competitive results in term of classification performance.