Issue No. 07 - July (2013 vol. 35)
Zhenyue Zhang , Dept. of Math., Zhejiang Univ., Hangzhou, China
Keke Zhao , Dept. of Math., Zhejiang Univ., Hangzhou, China
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.
Approximation methods, Sparse matrices, Manifolds, Symmetric matrices, Vectors, Matrix decomposition, Algorithm design and analysis
Zhenyue Zhang and Keke Zhao, "Low-Rank Matrix Approximation with Manifold Regularization," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 35, no. 7, pp. 1717-1729, 2013.