Low-Rank Matrix Approximation with Manifold Regularization
Low-Rank Matrix Approximation with Manifold Regularization
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DOI：
10.1109/tpami.2012.274
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发表时间：
2013-07
影响因子：
23.6
通讯作者：
Zhenyue Zhang;Keke Zhao
中科院分区：
文献类型：
--
作者：
Zhenyue Zhang;Keke Zhao
本文提出了一种新的低秩矩阵分解模型，它将流形正则化结合到矩阵分解中。与图正则化非负矩阵分解相比，该正则化模型具有上级的全局最优解和封闭解。提出了一种直接算法（适用于少量数据）和一种非精确内迭代交替迭代算法（适用于大规模数据）。收敛性分析建立了全局收敛的迭代算法。通过对六个真实数据集的聚类和分类实验，验证了该算法的有效性和准确性。与现有算法的性能比较表明，所提出的方法的有效性低秩分解一般。
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.