Generalized Graph Regularized Non-negative Matrix Factorization for Data Representation

In this paper, a novel method called Generalized Graph Regularized Non-Negative Matrix Factorization (GGNMF) for data representation is proposed. GGNMF is a part-based data representation which incorporates generalized geometrically-based regularizer. New updating rules are adopted for this method, and the new method convergence is proved under some specific conditions. In our experiments, we evaluated the performance of GGNMF on image clustering problems. The results show that, with the guarantee of the convergence, the proposed updating rules can achieve even better performance.

[1]  Stan Z. Li,et al.  Learning spatially localized, parts-based representation , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[2]  Xin Liu,et al.  Document clustering based on non-negative matrix factorization , 2003, SIGIR.

[3]  Victoria Stodden,et al.  When Does Non-Negative Matrix Factorization Give a Correct Decomposition into Parts? , 2003, NIPS.

[4]  Yunde Jia,et al.  FISHER NON-NEGATIVE MATRIX FACTORIZATION FOR LEARNING LOCAL FEATURES , 2004 .

[5]  Patrik O. Hoyer,et al.  Non-negative Matrix Factorization with Sparseness Constraints , 2004, J. Mach. Learn. Res..

[6]  Daoqiang Zhang,et al.  Two-Dimensional Non-negative Matrix Factorization for Face Representation and Recognition , 2005, AMFG.

[7]  Jiawei Han,et al.  Document clustering using locality preserving indexing , 2005, IEEE Transactions on Knowledge and Data Engineering.

[8]  Michael W. Berry,et al.  Document clustering using nonnegative matrix factorization , 2006, Inf. Process. Manag..

[9]  Anastasios Tefas,et al.  Exploiting discriminant information in nonnegative matrix factorization with application to frontal face verification , 2006, IEEE Transactions on Neural Networks.

[10]  Chih-Jen Lin,et al.  On the Convergence of Multiplicative Update Algorithms for Nonnegative Matrix Factorization , 2007, IEEE Transactions on Neural Networks.

[11]  Jiawei Han,et al.  Non-negative Matrix Factorization on Manifold , 2008, 2008 Eighth IEEE International Conference on Data Mining.

[12]  Chris H. Q. Ding,et al.  Convex and Semi-Nonnegative Matrix Factorizations , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Thomas S. Huang,et al.  Graph Regularized Nonnegative Matrix Factorization for Data Representation. , 2011, IEEE transactions on pattern analysis and machine intelligence.