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.

Hierarchical Object Part Learning Using Deep Lp Smooth Symmetric Non-Negative Matrix Factorization

“…In order to improve feature extraction and data compression, researchers have developed several variants of NMF. These variants introduce different constraints on the basis matrix U and the coefficient matrices V. Some examples of these constraints include non-negativity [8], sparsity [10], manifold constraints [4], non-smoothness [5], and orthogonality [11]. When the matrix X represents the similarity values between two data points and exhibits symmetry (i.e., X = X ⊤ ∈ R n×n and V = U ⊤ ), symmetric non-negative matrix factorization [12] is proposed as a suitable approach.…”