Regularized nonnegative matrix factorization with adaptive local structure learning

Abstract

Due to the effectiveness of Nonnegative Matrix Factorization (NMF) and its graph regularized extensions, these methods have been received much attention from various researchers. Generally, these methods are performed in two separate steps including Laplacian graph construction and the subsequent matrix decomposition.However, the similarity measurement for Laplacian graph is challenging since it’s often affected by several factors such as the neighborhood size, choice of similarity metric, etc. As a result, the learned graph may be not suitable, let alone the subsequent matrix decomposition. In this paper, we propose adaptive graph regularized NMF. Different from existing methods, the similarity matrix is automatically learned from the data. The proposed model can simultaneously performs matrix decomposition and similarity learning. By balancing the interactions between both of the two subtasks in our model, each subtask is improved iteratively based on the result of another. Experimental results on benchmark data sets illustrate the effectiveness of our model.