求解正则化非负低秩逼近问题的交替最小二乘算法

The alternating least squares method for solving the regularized low rank approximation of nonegative matrix

针对正则化非负矩阵低秩逼近问题,利用满秩分解刻画问题的可行集,将非负矩阵的正则化低秩逼近问题转化为等价的非负矩阵分解问题。通过构造交替最小二乘法求解转化后的非负矩阵分解问题,并采用投影梯度法求解相关子问题。数值实验验证了算法的可行性。

The regularized low rank approximation problem of the nonnegative matrix is studied.By making use of full rank decomposition,the feasible set is characterized and the regularized low rank approximation problem of the nonnegative matrix is transformed into an equivalent nonnegative matrix factorization problem.The alternating least squares method is designed to solve the equivalent problem,and we proposed projected gradient method to solve the corresponding subproblems.Numerical experiments show that this method is feasible.