Globality constrained adaptive graph regularized non‐negative matrix factorization for data representation

Abstract

Benefiting from the good physical interpretations and low computational complexity, non-negative matrix factorization (NMF) has attracted wide attentions in data representation learning tasks. Some graph-based NMF approaches make the learned representation encode the topological structure by the local graph Laplacian regularizer, which improves the discriminant ability of data representation. However, the performance of graph-based NMF methods depend heavily on the quality of the predefined graph and the complexity of models is high. Here, a globality constrained adaptive graph regularized non-negative matrix factorization for data representation (GCAG-NMF) model is proposed, which not only uses the self-representation characteristics of data to learn an adaptive graph to describe the sample relationship more accurately, but also proposes a graph factorization technique to reduce the complexity of the model and improve the discriminative ability of data representation. Then, an iterative optimizing strategy with low complexity and strict convergence guarantee is developed to optimize the objective function. Experimental results on some databases demonstrate the effectiveness of the proposed model.