Locality and similarity preserving embedding for feature selection

Feature selection (FS) methods have commonly been used as a main way to select the relevant features. In this paper, we propose a novel unsupervised FS method, i.e., locality and similarity preserving embedding (LSPE) for feature selection. Specifically, the nearest neighbor graph is firstly constructed to preserve the locality structure of data points, and then this locality structure is mapped to the reconstruction coefficients such that the similarity among these data points is preserved. Moreover, the sparsity derived by the locality is also preserved. Finally, the low dimensional embedding of the sparse reconstruction is evaluated to best preserve the locality and similarity. We impose ℓ_2,1-norm on the transformation matrix to achieve row-sparsity, which allows us to select relevant features and learn the embedding simultaneously. The selected features have good stability due to the locality and similarity preserving, and more importantly, they contain natural discriminating information even if no class labels are provided. We present the optimization algorithm and analysis of convergence of the proposed method. The extensive experimental results show the effectiveness of the proposed method.