Robust semi non-negative low-rank graph embedding algorithm via the L21 norm

摘要

The non-negative matrix factorization (NMF) method is applied in many fields, including pattern recognition, visual analysis, and biomedicine. However, existing NMF methods acquire low dimensional representation directly from high dimensional data, and the low-rank part of the data contains the most useful information. Furthermore, the NMF method is vulnerable to noise interference and is not adequately robust. Therefore, a robust semi non-negative low-rank graph embedding algorithm via the L21 norm (RSNLGEL21) is proposed to address the stated problems. The algorithm considers the effective low-rank structure and geometric information of the original data and constrains the coefficient matrix to be non-negative; however, it does not impose a non-negative constraint on the base matrix. In addition, the L21 norm is introduced into the graph embedding and data reconstruction functions slightly to improve its recognition ability and robustness. Moreover, this paper also provides an iterative formula to the RSNLGEL21 algorithm and the corresponding proof of convergence and to analyze its computational complexity. Experiments on the ORL, FEI, AR, and FERET image datasets shows that the RSNLGEL21 algorithm has certain advantages in clustering performance.