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

摘要：

现有的非负矩阵分解方法（NMF）还存在一些不足之处。一方面，NMF方法直接在高维原始图像数据集上计算它的低维表示，而实际上原始图像数据集的有效信息常常隐藏在它的低秩结构中；另一方面，NMF方法还存在对噪声数据和不可靠图敏感以及鲁棒性差的缺点。为了解决这些问题，提出了一种非负低秩图嵌入算法（NLGE），该算法同时考虑了原始图像数据的几何信息和有效低秩结构，使得其鲁棒性有了进一步的提高。此外，还给出了一种求解NLGE算法的迭代规则，并进一步证明了该求解算法的收敛性。最后，在ORL、CMU PIE、YaleB和USPS数据库上的实验结果表明了NLGE算法的有效性。

关键词: 非负矩阵分解方法（NMF）, 低秩结构, 图嵌入, 鲁棒性