Graph-Regularized, Sparsity-Constrained Non-Negative Matrix Factorization with Earth Mover’s Distance Metric

Abstract

Non-negative matrix factorization (NMF) is widely used as a powerful matrix factorization tool in data representation. However, the traditional NMF, measured by Euclidean distance or Kullback–Leibler distance, does not take into account the internal implied geometric information of the dataset and cannot measure the distance between samples as well as possible. To remedy the defects, in this paper, we propose the NMF method with Earth mover’s distance as a metric, for short GSNMF-EMD. It combines graph regularization and L1/2 smooth constraints. The GSNMF-EMD method takes into account the intrinsic implied geometric information of the dataset and can produce more sparse and stable local solutions. Experiments on two specific image datasets showed that the proposed method outperforms related state-of-the-art methods.

Keywords

• non-negative matrix factorization (NMF)
• Earth mover’s distance (EMD)
• graph regularized
• <i>L</i>_1/2 sparsity-constrained