Adaptive Graph Regularized Deep Semi-nonnegative Matrix Factorization for Data Representation

Recently, matrix factorization-based data representation methods exhibit excellent performance in many real applications. However, traditional deep semi-nonnegative matrix factorization (DSNMF) models the relationship between samples by predefining a fixed graph, which is not optimal and thus cannot exploit the intrinsic local structure among data effectively. In this work, an adaptive graph regularized deep semi-nonnegative matrix factorization (AGRDSNMF) algorithm is proposed for data representation. This proposed AGRDSNMF method can construct an adaptive optimal graph in each layer, whose weights are automatically determined by the probabilities between neighborhood samples. Then the adaptive graph regularizer of each layer is adopted to constrain the corresponding coefficient matrix during decomposition. Therefore, AGRDSNMF can capture the geometric structure of the representation in each layer. Experiments are conducted on COIL20, PIE, and TDT2 datasets, and our AGRDNSMF algorithm can achieve encouraging clustering performance.