基于稀疏约束的半监督非负矩阵分解算法

矩阵分解因可以实现大规模数据处理而具有十分广泛的应用。非负矩阵分解(Nonnegative Matrix Factorization,NMF)是一种在约束矩阵元素为非负的条件下进行的分解方法。利用少量已知样本的标注信息和大量未标注样本,并施加稀疏性约束,构造了一种新的算法——基于稀疏约束的半监督非负矩阵分解算法。推导了其有效的更新算法,并证明了该算法的收敛性。在常见的人脸数据库上进行了验证,实验结果表明CNMFS算法相对于NMF和CNMF等算法具有较好的稀疏性和聚类精度。

Constrained Nonnegative Matrix Factorization with Sparseness for Image Representation

Matrix decomposition is widely applied in many domains since it is exploited to process the large-scale data.To the best of our knowledge,nonnegative matrix factorization (NMF) is a non-negative decomposition method under the condition that constraint matrix elements are non-negative.By using the informati on provided by a few known labeled examples and large number of unlabeled examples as well as imposing a certain sparseness constraint on NMF, this paper put forward a method called constraint nonnegative matrix factorization with sparseness (CNMFS).In the algorithm,an effective update approach is constructed,whose convergence is proved subsequently.Extensive experiments were conducted on common face databases,and the comparisons with two state-of-the-art algorithms including CNMF and NMF demonstrate that CNMFS has superiority in both sparseness and clustering.