RRNMF-MAGL: Robust regularization non-negative matrix factorization with multi-constraint adaptive graph learning for dimensionality reduction.

In this paper, a new unsupervised dimensionality reduction method named robust regularization non-negative matrix factorization with multi-constraint adaptive graph learning (RRNMF-MAGL) is developed. Compared with the existing methods, RRNMF-MAGL can extract robust low-dimensional features and adaptively learn a manifold structure to well reflect the data distribution. Specifically, to alleviate the influence of outliers and noises, a robust non-negative matrix factorization (RNMF) approach with L21-norm loss function is first constructed. Then, a multi-constraint adaptive graph learning (MAGL) model is designed based on low-dimensional features to reduce the computational complexity and avoid the adverse influence of redundant information. Moreover, multiple constraints (i.e., sparsity and locality) are incorporated into graph learning for enhancing the discrimination ability of graph structure. Next, to make the learned low-dimensional features well maintain the local geometric structure information of data, a graph Laplacian regularization (GLR) is designed. Finally, an iterative update strategy is proposed to optimize RRNMF-MAGL and its convergence is verified by numerical experiments. The superior effectiveness and robustness of RRNMF-MAGL is demonstrated by extensive experiments on eight publicly available datasets.