基于图正则化的受限非负矩阵分解算法及在图像表示中的应用

非负矩阵分解(NMF)是一种非常有效的图像表示方法，已被广泛应用到模式识别领域.针对NMF算法是无监督学习算法，无法同时考虑样本类别信息和固有几何结构信息的缺点，提出一种基于图正则化的受限非负矩阵分解(GRCNMF)的算法.该算法利用硬约束保持样本的类别信息，增强算法的鉴别能力，同时还利用近邻图来保持样本间固有的几何结构.通过在COIL20和ORL图像库中的聚类实验结果表明GRCNMF优于其它几种算法，说明GRCNMF的有效性.

Graph-Regularized Constrained Non-Negative Matrix Factorization Algorithm and Its Application to Image Representation

Non-negative matrix factorization (NMF) is an effective image representation method and has considerable attention in pattern recognition. The NMF is an unsupervised learning algorithm which can not take into account the label information and the intrinsic geometry structure simultaneously. In this paper,a matrix decomposition method called graph-regularized constrained non-negative matrix factorization (GRCNMF) is proposed,which preserves the label information with resorting to hard constraints,and hence the discriminating ability is improved. Meanwhile,a neighbors graph preserves the intrinsic geometrical structure of the data. The clustering experiments on the COIL20 and ORL image database demonstrate the effectiveness of the GRCNMF compared to other approaches.