title: Low-rank matrix approximation with manifold regularization.
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.
authors.affiliation: Department of Mathematics and the State Key Laboratory of CAD&CG, Zhejiang University, Yuquan Campus, Hangzhou 310027, China. zyzhang@zju.edu.cn
authors.forename: Zhenyue
authors.initials: Z
authors.lastname: Zhang
authors.forename: Keke
authors.initials: K
authors.lastname: Zhao
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D016000:Cluster Analysis; D003198:Computer Simulation; D016208:Databases, Factual; D005145:Face / Q000033:anatomy & histology; D006801:Humans; D007091:Image Processing, Computer-Assisted; D008962:Models, Theoretical; D010363:Pattern Recognition, Automated / Q000379:methods*