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Issue No.07 - July (2013 vol.35)
pp: 1717-1729
Zhenyue Zhang , Dept. of Math., Zhejiang Univ., Hangzhou, China
Keke Zhao , Dept. of Math., Zhejiang Univ., Hangzhou, China
ABSTRACT
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.
INDEX TERMS
Approximation methods, Sparse matrices, Manifolds, Symmetric matrices, Vectors, Matrix decomposition, Algorithm design and analysis,manifold learning, Matrix factorization, graph regularization, classification, clustering
CITATION
Zhenyue Zhang, Keke Zhao, "Low-Rank Matrix Approximation with Manifold Regularization", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.35, no. 7, pp. 1717-1729, July 2013, doi:10.1109/TPAMI.2012.274
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