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Low-Rank Matrix Approximation with Manifold Regularization
July 2013 (vol. 35 no. 7)
pp. 1717-1729
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.
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 and Machine Intelligence, vol. 35, no. 7, pp. 1717-1729, July 2013, doi:10.1109/TPAMI.2012.274
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