Department of Mathematics and the State Key Laboratory of CAD&CG, Zhejiang University, Yuquan Campus, Hangzhou 310027, China.
IEEE Trans Pattern Anal Mach Intell. 2013 Jul;35(7):1717-29. doi: 10.1109/TPAMI.2012.274.
This paper proposes a new model of low-rank matrix factorization that incorporates manifold regularization to the matrix factorization. Superior to the graph-regularized nonnegative matrix factorization, this new regularization model has globally optimal and closed-form solutions. A direct algorithm (for data with small number of points) and an alternate iterative algorithm with inexact inner iteration (for large scale data) are proposed to solve the new model. A convergence analysis establishes the global convergence of the iterative algorithm. The efficiency and precision of the algorithm are demonstrated numerically through applications to six real-world datasets on clustering and classification. Performance comparison with existing algorithms shows the effectiveness of the proposed method for low-rank factorization in general.
本文提出了一种新的低秩矩阵分解模型，将流形正则化纳入矩阵分解中。与图正则化的非负矩阵分解相比，这种新的正则化模型具有全局最优和闭式解。提出了一种直接算法（用于点数较少的数据）和一种带有不精确内迭代的交替迭代算法（用于大规模数据）来解决新模型。通过对六个真实数据集在聚类和分类上的应用，数值分析证明了迭代算法的全局收敛性。算法的效率和精度通过在六个真实数据集上的聚类和分类任务的数值实验进行了验证。与现有算法的性能比较表明了该方法在低秩分解方面的有效性。
