非负矩阵低秩分解的交替二次规划算法

摘要

非负矩阵分解算法有多种，但都存在着各自的缺陷。在现有工作的基础上，将非负矩阵分解(NMF)模型转化为一组(两个)二次凸规划模型，利用二次凸规划有解的充分必要条件推导出迭代公式，进行交替迭代，可求出问题的解。得到的解不仅具有某种最优性、稀疏性，还避免了约束非线性规划求解的复杂过程和大量的计算。证明了迭代的收敛性，且收敛速度快于已知的方法，对于大规模数据模型尤能显示出其优越性。%Many algorithms are available for solving the problem of non-negative matrix factorization (NMF)despite respective shortcomings.Based on existing works,NMF model is transformed into one group of (two ) convex quadratic programming model. Using the sufficient and necessary conditions for quadratic programming problems,iteration formula for NMF is obtained by which the problem is solved after alternative iteration process.The obtained solution reaches its optimality and sparseness while avoiding computational burden and complexity for solving constrained nonlinear programming problems.The iteration convergence can be proved easily and its speed is faster than that of existing approaches.The proposed approach has its superority for large-scale data model.