关键词: 非负矩阵分解方法（NMF）, 低秩结构, 图嵌入, 鲁棒性

Abstract:

The existing non-negative matrix factorization (NMF) algorithms still have some shortcomings. On one hand, the NMF method calculates its low-dimensional representation directly on the high-dimensional original image data set, but in fact the effective information of the original image data set is often hidden in its low-rank structure; on the other hand, the NMF method also has the shortcomings of being sensitive to noise data and unreliable graphs and poor robustness. In order to solve these problems, a non-negative low rank graph embedding (NLGE) algorithm is proposed, which takes into account both the geometric information of the original image data and the effective low-rank structure, and further improves its robustness. In addition, an iteration rule for solving NLGE algorithm is given, and the convergence of the algorithm is further proven. Finally, the experimental results on ORL, CMU PIE, YaleB and USPS databases show the effectiveness of NLGE algorithm.

Key words: non-negative matrix factorization (NMF), low rank structure, graph embedding, robustness