Robust Exponential Graph Regularization Non-Negative Matrix Factorization Technology for Feature Extraction

Abstract

Graph regularized non-negative matrix factorization (GNMF) is widely used in feature extraction. In the process of dimensionality reduction, GNMF can retain the internal manifold structure of data by adding a regularizer to non-negative matrix factorization (NMF). Because Ga NMF regularizer is implemented by local preserving projections (LPP), there are small sample size problems (SSS). In view of the above problems, a new algorithm named robust exponential graph regularized non-negative matrix factorization (REGNMF) is proposed in this paper. By adding a matrix exponent to the regularizer of GNMF, the possible existing singular matrix will change into a non-singular matrix. This model successfully solves the problems in the above algorithm. For the optimization problem of the REGNMF algorithm, we use a multiplicative non-negative updating rule to iteratively solve the REGNMF method. Finally, this method is applied to AR, COIL database, Yale noise set, and AR occlusion dataset for performance test, and the experimental results are compared with some existing methods. The results indicate that the proposed method is more significant.

Keywords

• graph regularization non-negative matrix factorization (GNMF)
• non-negative matrix factorization (NMF)
• local preserving projections (LPP)
• feature extraction
• SSS problems