Nonnegative matrix factorization with manifold regularization and maximum discriminant information
- PDF / 530,772 Bytes
- 10 Pages / 595.276 x 790.866 pts Page_size
- 19 Downloads / 246 Views
ORIGINAL ARTICLE
Nonnegative matrix factorization with manifold regularization and maximum discriminant information Wenjun Hu1,2,3 • Kup-Sze Choi3 • Jianwen Tao4 • Yunliang Jiang1 Shitong Wang2
•
Received: 1 February 2015 / Accepted: 27 June 2015 Springer-Verlag Berlin Heidelberg 2015
Abstract Nonnegative matrix factorization (NMF) has been successfully used in different applications including computer vision, pattern recognition and text mining. NMF aims to decompose a data matrix into the product of two matrices (respectively denoted as the basis vectors and the encoding vectors), whose entries are constrained to be nonnegative. Unlike the ordinary NMF, we propose a novel NMF, denoted as MMNMF, which considers both geometrical information and discriminative information hidden in the data. The geometrical information is discovered by minimizing the distance among the encoding vectors, while the discriminative information is uncovered by maximizing the distance among base vectors. Clustering experiments are performed on the real-world data sets of faces, images, and documents to demonstrate the effectiveness of the proposed algorithm. Keywords Nonnegative matrix factorization Manifold regularization Maximum information Clustering
& Wenjun Hu [email protected] 1
School of Information Engineering, Huzhou University, Huzhou, Zhejiang, China
2
School of Digital Media, Jiangnan University, Wuxi, Jiangsu, China
3
School of Nursing, Centre for Smart Health, Hong Kong Polytechnic University, Hong Kong, China
4
School of Information Science and Engineering, Ningbo Institute of Technology, Zhejiang University, Ningbo, Zhejiang, China
1 Introduction Nonnegative matrix factorization (NMF) [1, 2] is a popular matrix factorization technique, which decomposes a data matrix into the product of two matrices whose entries are constrained to be nonnegative. With this nonnegative constraint, NMF can be interpreted as a parts-based representation of the data that only allows additive combination but not subtractive, which makes it distinct from other matrix factorization methods, such as singular value decomposition (SVD), principal component analysis (PCA) and independent component analysis (ICA) [3, 4]. A number of studies have shown that NMF has been successfully applied in various application fields, including computer vision, text mining [5, 6], pattern recognition [7]. And the performance of NMF is especially remarkable in applications concerning face recognition, document representation and brain electromagnetic tomography [8–11]. Research effort has been devoted to further improve NMF. Ding et al. proposed semi-NMF and convex-NMF to extend the applicability of NMF [11]. The semi-NMF also strengthens the connections between NMF and K-means clustering. By introducing the manifold regularization and the margin maximization to NMF, Guan et al. [12] proposed the manifold regularized discriminative NMF (MDNMF). In MD-NMF, the data geometric structure is retained through an adjacent graph constructed by the sa
Data Loading...
