非负矩阵分解的一个约束稀疏算法

针对非负矩阵分解中系数矩阵不够稀疏的问题,提出一个新的约束非负矩阵分解算法。在经典非负矩阵分解的优化函数中施加稀疏性约束,并对分解系数矩阵施加最小相关约束,与此同时对基矩阵施加2-范数约束,在保证非负约束和分解精度的基础上,使分解后得到的矩阵尽可能稀疏,这样可以更加节省存储空间,分解结果更优。对比实验表明,提出的算法具有更好的稀疏性,且实验误差更小。

A Constrained Sparse Algorithm for Nonnegative Matrix Factorization

Non-negative matrix factorization provides a new way for large-scale data processing, the non-negative constraint applies to a large number of experimental data in the real world, so it is widely used. Adding a sparseness constraint to the original NMF algorithm is an improvement, which can ensure the non-negative constraint and accurate decomposition, make the decomposed matrix sparse as far as possible, so as to save more storage space. A new constrained non-negative matrix factorization algorithm is proposed, which makes the decomposition results better by imposing the minimum correlation constraints on the coefficient matrices and the 2-norm constraints on the basis matrix at the same time. Comparison experiment shows that the propose algorithm has the better sparseness and smaller error than both the original NMF algorithm and the SNMF algorithm.