稀疏性正则化非负矩阵分解的在线学习方法

Sparse Regularized Non-Negative Matrix Factorization through Online Learning

针对非负矩阵分解效率低的不足,提出一种基于在线学习的稀疏性非负矩阵分解的快速方法.通过对目标函数添加正则化项来控制分解后系数矩阵的稀疏性,将问题转化成稀疏表示的字典学习问题,利用在线字典学习算法求解目标函数,并对迭代过程的矩阵更新进行转换,采取块坐标下降法进行矩阵更新,提高算法收敛速度.实验结果表明,该方法在有效保持图像特征信息的同时,运行效率得到提高.

In order to overcome the inefficiency of non-negative matrix factorization, a fast approach based on online learning for sparse regularized non-negative matrix factorization is proposed. Firstly, the objective function is defined by imposing the regularization term to control the sparsity of the coefficient matrix, and the problem is transformed into the dictionary learning problem of sparse representation. Therefore, the object function can be solved by the online dictionary learning algorithm. Then, the block-coordinate descent algorithm is used to update the matrix in every iterative process, consequently, the convergence rate is improved. The experimental results show that the proposed method effectively preserves structure information of images and simultaneously enhances the running efficiency evidently.