稀疏限制的增量式鲁棒非负矩阵分解及其应用

Incremental robust non-negative matrix factorization with sparseness constraints and its application

针对鲁棒非负矩阵分解(RNMF)的运算规模随训练样本数量逐渐增多而不断增大的问题,提出一种稀疏限制的增量式鲁棒非负矩阵分解算法。首先,对初始数据进行鲁棒非负矩阵分解;然后,将其分解结果参与到后续迭代运算;最后,在对系数矩阵增加稀疏限制的情况下与增量式学习相结合,使目标函数值在迭代求解时下降地更快。该算法在节省运算时间的同时提高了分解后数据的稀疏度。在数值实验中,将所提算法与鲁棒非负矩阵分解算法、稀疏限制的鲁棒非负矩阵分解(RNMFSC)算法进行了比较。在ORL和YALE人脸数据库上的实验结果表明,所提算法在运算时间和分解后数据的稀疏度等方面均优于其他两个算法,并且还具有较好的聚类效果,尤其在YALE人脸数据库上当聚类类别数为3时该算法的聚类准确率达到了91.67%。

Aiming at the problem that the operation scale of Robust Non-negative Matrix Factorization(RNMF) increases with the number of training samples, an incremental robust non-negative matrix factorization algorithm with sparseness constraints was proposed. Firstly, robust non-negative matrix factorization was performed on initial data. Then, the factorized result participated in the subsequent iterative operation. Finally, with sparseness constraints, the coefficient matrix was combined with incremental learning, which made the objective function value fall faster in the iterative solution. The cost of computation was reduced and the sparseness of data after factorization was improved. In the numerical experiments, the proposed algorithm was compared with RNMF algorithm and RNMF with Sparseness Constraints(RNMFSC) algorithm. The experimental results on ORL and YALE face databases show that the proposed algorithm is superior to the other two algorithms in terms of operation time and sparseness of factorized data, and has better clustering effect, especially in YALE face database, when the clustering number is 3, the clustering accuracy of the proposed algorithm reaches 91.67%.