一种受限非负矩阵分解方法

Constrained factorization method for non-negative matrix

提出一种获取潜在语义的受限非负矩阵分解方法 .通过在非负矩阵分解方法的目标函数上增加 3个约束条件来定义受限非负矩阵分解方法的目标函数 ,给出求解受限非负矩阵分解方法目标函数的迭代规则 ,并证明迭代规则的收敛性 .与非负矩阵分解方法相比 ,受限非负矩阵分解方法能获取尽可能正交的潜在语义 .实验表明 ,受限非负矩阵分解方法在信息检索上的精度优于非负矩阵分解方法 .

A novel method, constrained non-negative matrix factorization, is presented to capture the latent semantic relations. The objective function of constrained non-negative matrix factorization is defined by imposing three additional constraints, in addition to the non-negativity constraint in the standard non-negative matrix factorization. The update rules to solve the objective function with these constraints are presented, and its convergence is proved. In contrast to the standard non-negative matrix factorization, the constrained non-negative matrix factorization can capture the semantic relations as orthogonal as possible. The experiments indicate that the constrained non-negative matrix factorization has better precision than the standard non-negative matrix factorization in information retrieval.