Low-rank adaptive graph embedding for unsupervised feature extraction

Abstract

Abstract Most of manifold learning based feature extraction methods are two-step methods, which first construct a weighted neighborhood graph and then use the pre-constructed graph to perform subspace learning. As a result, these methods fail to use the underlying correlation structure of data to learn an adaptive graph to preciously characterize the similarity relationship between samples. To address this problem, we propose a novel unsupervised feature extraction method called low-rank adaptive graph embedding (LRAGE), which can perform subspace learning and adaptive probabilistic neighborhood graph embedding simultaneously based on reconstruction error minimization. The proposed LRAGE is imposed with low-rank constraint for the sake of exploring the underlying correlation structure of data and learning more informative projection. Moreover, the L 2 , 1 -norm penalty is imposed on the regularization to further enhance the robustness of LRAGE. Since the resulting objective function has no closed-form solutions, an iterative optimization algorithm is elaborately designed. The convergence of the proposed algorithm is proved and the corresponding computational complexity analysis is also presented. In addition, we explore the potential properties of the proposed LRAGE by comparing it with several similar models on both synthetic and real-world data sets. Extensive experiments on five well-known face data sets and three non-face data sets demonstrate the superiority of the proposed LRAGE.