Non-negative matrix factorization (NMF) is a recently popularized technique for learning parts-based, linear representations of non-negative data. Although the decomposition rate of NMF is very fast, it still suffers from the following deficiency: It only revealed the local geometry structure; global geometric information of data set is ignored. This paper proposes a manifold ranking graph regularization non-negative matrix factorization with local and global geometric structure (MRLGNMF) to overcome the above deficiency. In particular, MRLGNMF induces manifold ranking to the non-negative matrix factorization with Sinkhorn distance. Numerical results show that the new algorithm is superior to the existing algorithm.

中文翻译：

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具有全局和局部结构的流形排序图正则化非负矩阵分解

非负矩阵分解（NMF）是一种最近流行的技术，用于学习基于零件的非负数据的线性表示。尽管NMF的分解速度非常快，但仍然存在以下不足：仅显示局部几何结构； NMF分解不充分。数据集的全局几何信息将被忽略。本文提出了一种具有局部和全局几何结构（MRLGNMF）的流形排序图正则化非负矩阵分解，以克服上述缺陷。尤其是，MRLGNMF可以利用Sinkhorn距离对非负矩阵分解进行流形排序。数值结果表明，新算法优于现有算法。