Graph non-negative matrix factorization with alternative smoothed L0 regularizations

Graph non-negative matrix factorization (GNMF) can discover the data’s intrinsic low-dimensional structure embedded in the high-dimensional space. So, it has superior performance for data representation and clustering. Unfortunately, it is sensitive to noise and outliers. In this paper, to improve the robustness of GNMF, l0 norm is introduced to enhance the sparsity of factorized matrices. As the discontinuity of l0 norm and minimizing it is a NP-hard problem, five functions approximating l0 norm are used to transform the problem of the sparse graph non-negative matrix factorization (SGNMF) to a global optimization problem. Finally, the multiplicative updating rules (MUR) are designed to solve the problem and the convergence of algorithm is proven. In the experiment, the accuracy and normalized mutual information of clustering results show the superior performance of SGNMF on five public datasets.