Deep semi-nonnegative matrix factorization with elastic preserving for data representation

Deep matrix factorization methods can automatically learn the hidden representation of high dimensional data. However, they neglect the intrinsic geometric structure information of data. In this paper, we propose a Deep Semi-Nonnegative Matrix Factorization with Elastic Preserving (Deep Semi-NMF-EP) method by adding two graph regularizers in each layer. Therefore, the proposed Deep Semi-NMF-EP method effectively preserves the elasticity of data and thus can learn a better representation of high-dimensional data. In addition, we present an effective algorithm to optimize the proposed model and then provide its complexity analysis. The experimental results on the benchmark datasets show the excellent performance of our proposed method compared with other state-of-the-art methods.