基于图正则化和稀疏约束的半监督非负矩阵分解

非负矩阵分解是在矩阵非负约束下的分解算法。为了提高识别率,提出了一种基于稀疏约束和图正则化的半监督非负矩阵分解方法。该方法对样本数据进行低维非负分解时,既保持数据的几何结构,又利用已知样本的标签信息进行半监督学习,而且对基矩阵施加稀疏性约束,最后将它们整合于单个目标函数中。构造了一个有效的更新算法,并且在理论上证明了该算法的收敛性。在多个人脸数据库上的仿真结果表明,相对于NMF、GNMF、CNMF等算法,GCNMFS具有更好的聚类精度和稀疏性。

Semi-supervised Nonnegative Matrix Factorization Based on Graph Regularization and Sparseness Constraints

Nonnegative matrix factorization (NMF) is a kind of matrix factorization algorithm under non-negative constraints .With the aim to enhance the recognition rate,a method called graph regularized and constrained non-negative matrix factorization with sparseness (GCNMFS) was proposed.It not only preserves the intrinsic geometry of data,but also uses the label information for semi-supervised learning and introduces sparseness constraint into base matrix.Finally,they are integrated into a single objective function.An efficient updating approach was produced and the convergence of this algorithm was also proved.Compared with NMF,GNMF and CNMF,experiments on some face databases show that the proposed method can achieve better clustering results and sparseness.