中文摘要：

提出了一种基于图正则化的半监督非负矩阵分解算法（GSNMF），克服了非负矩阵分解（NMF）、约束非负矩阵分解（CNMF）和图正则化非负矩阵分解（GNMF）方法忽略样本数据的局部几何结构或标签信息不足的缺陷，且NMF、CNMF和GNMF均为GSNMF的特例。也从理论上证明了GSNMF算法的收敛性。该算法对样本数据进行低维非负分解时，在图框架下既保持数据的几何结构，又利用已知样本的标签信息，在进行半监督学习时，同类样本能更好地聚集而类间距离尽可能大。在人脸数据库ORL、FERET和手写体数据库USPS上的仿真结果表明，相对于NMF及其一些改进算法，GSNMF均具有更高的聚类精度。

英文摘要：

This paper presents a novel algorithm called Graph regularized-based Semi-supervised NMF （GSNMF）. It overcomes the shortcomings which ignore the geometric structure and the label information of the data for Non-negative Matrix F actorization （NMF）, Constrained NMF （CNMF） and Graphed regularized NMF （GNMF）. Moreover, those algorithms are special case of GSNMF. The convergence proof of this algorithm is provided. GSNMF preserves the intrinsic geometry of data and uses the label information as semi-supervised learning. It makes nearby samples with the same class-label more compact, and nearby classes separated. Compared with NMF, LNMF, PNMF, GNMF and CNMF, experiment results on ORL face database, FERET face database and USPS handwrite database have shown that the proposed method achieves better clustering results.