title: Convex nonnegative matrix factorization with manifold regularization.
abstract: Nonnegative Matrix Factorization (NMF) has been extensively applied in many areas, including computer vision, pattern recognition, text mining, and signal processing. However, nonnegative entries are usually required for the data matrix in NMF, which limits its application. Besides, while the basis and encoding vectors obtained by NMF can represent the original data in low dimension, the representations do not always reflect the intrinsic geometric structure embedded in the data. Motivated by manifold learning and Convex NMF (CNMF), we propose a novel matrix factorization method called Graph Regularized and Convex Nonnegative Matrix Factorization (GCNMF) by introducing a graph regularized term into CNMF. The proposed matrix factorization technique not only inherits the intrinsic low-dimensional manifold structure, but also allows the processing of mixed-sign data matrix. Clustering experiments on nonnegative and mixed-sign real-world data sets are conducted to demonstrate the effectiveness of the proposed method.
authors.affiliation: School of Information Engineering, Huzhou University, Huzhou, Zhejiang, China; Centre for Smart Heath, School of Nursing, Hong Kong Polytechnic University, Hong Kong, China. Electronic address: hoowenjun@foxmail.com.
authors.forename: Wenjun
authors.initials: W
authors.lastname: Hu
authors.affiliation: Centre for Smart Heath, School of Nursing, Hong Kong Polytechnic University, Hong Kong, China.
authors.forename: Kup-Sze
authors.initials: KS
authors.lastname: Choi
authors.affiliation: School of Information Engineering, Huzhou University, Huzhou, Zhejiang, China.
authors.forename: Peiliang
authors.initials: P
authors.lastname: Wang
authors.affiliation: School of Information Engineering, Huzhou University, Huzhou, Zhejiang, China.
authors.forename: Yunliang
authors.initials: Y
authors.lastname: Jiang
authors.affiliation: School of Digital Media, Jiangnan University, Wuxi, Jiangsu, China.
authors.forename: Shitong
authors.initials: S
authors.lastname: Wang
mesh_terms: D000465:Algorithms; D016000:Cluster Analysis; D016571:Neural Networks, Computer; D010363:Pattern Recognition, Automated / Q000379:methods
keywords: Clustering; Convex nonnegative matrix factorization; Manifold regularization; Nonnegative matrix factorization