An interior point trust region method for nonnegative matrix factorization

Neurocomputing

Volumn 97, Issue , 2012, Pages 309-316

  Jiang, Jiao Jiao ^a   Zhanga, Hai Bin ^a   Yu, Shui ^b  

^a BEIJING UNIVERSITY OF TECHNOLOGY   (China)

^b DEAKIN UNIVERSITY   (Australia)

Author keywords

Active set method; Blind source separation; Interior point trust region method; Nonnegative Matrix Factorization

Indexed keywords

ACTIVE-SET METHOD; DIMENSION REDUCTION; GLOBAL REGIONS; INTERIOR POINT; KL-DIVERGENCE; LOGARITHMIC BARRIER FUNCTION; MATHEMATICAL CALCULATIONS; NONNEGATIVE MATRIX FACTORIZATION; NUMERICAL EXPERIMENTS; PARAMETERIZED; SUFFICIENT CONDITIONS; TRUST REGION; TRUST-REGION METHODS;

BLIND SOURCE SEPARATION; COST FUNCTIONS; FEATURE EXTRACTION; LINEAR SYSTEMS;

NUMERICAL METHODS;

ACCURACY; ALGORITHM; ARITHMETIC; ARTICLE; CALCULATION; INTERIOR POINT TRUST REGION METHOD; LINEAR SYSTEM; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; PREDICTION; PRIORITY JOURNAL; REGRESSION ANALYSIS; SENSITIVITY AND SPECIFICITY; SIGNAL NOISE RATIO; UNCERTAINTY;

EID: 84865327519     PISSN: 09252312     EISSN: 18728286     Source Type: Journal    
DOI: 10.1016/j.neucom.2012.05.008     Document Type: Article

References (22)

1. Cichocki A., Zdunek R. Multilayer nonnegative matrix factorization. Electron. Lett. 2006, 42:947-948.
2. A. Cichocki, R. Zdunek, S. Amari, S.Csiszar's divergences for non-negative matrix factorization: family of new algorithms, in: Proceedings of the Sixth International Conference on Independent Component Analysis and Blind Signal Separation, Charleston, SC, 2006.
3. Lee D.D., Seung H.S. Learning the parts of objects by nonnegative matrix factorization. J. Nat. 1999, 401:788-791.
4. D.D. Lee, H.S. Seung, Algorithms for nonnegative matrix factorization, in: Proceedings of the Advances in Neural Information Processing Systems (NIPS), 2000, pp. 556-562.
5. D. Guillamet, J. Vitrià, Classifying faces with nonnegative matrix factorization, in: Proceedings of the Fifth Catalan Conference for Artificial Intelligence, Castello de la Plana, Spain, 2002.
6. Guillamet D., Vitrià J., Schiele B. Introducing a weighted nonnegative matrix factorization for image classification. J. Pattern Recogn. Lett. 2003, 24:2447-2454.
7. Shahnaz F., Berry M., Pauca P., Plemmons R. Document clustering using non-negative matrix factorization. J. Inf. Process. Manage. 2006, 42:373-386.
8. I. Dhillon, S. Sra, Generalized nonnegative matrix approximations with Bregman divergences, in: Proceedings of the Neural Information Processing Systems (NIPS) Conference, Vancouver, BC, 2005.
9. J.S. Lee, D.D. Lee, S. Choi, D.S. Lee, Application of nonnegative matrix factorization to dynamic positron emission tomography, in: Proceedings of the Third International Conference on Independent Component Analysis and Blind Signal Separation, San Diego, CA, 2001, pp. 556-562.
10. C.-J. Lin, Projected Gradient Methods for Non-negative Matrix Factorization, Technical Report, Information and Support Services Technical Report ISSTECH-95-013, Department of Computer Science, National Taiwan University, 2005.
11. Rojas M., Steihaug T. An interior-point trust-region-based method for large-scale non-negative regularization. J. Inverse Probl. 2002, 18:1291-1307.
12. Zdunek R., Cichocki A. Nonnegative matrix factorization with constrained second-order optimization. J. Signal Process. 2007, 878:1904-1916.
13. Zdenuk R., Cichocki A. Nonnegative matrix factorization with quadratic programming. J. Neurocomput. 2007, 71:2309-2320.
14. R. Zdunek, A. Cichocki, Non-negative matrix factorization with quasi-newton optimization, in: Proceedings of the Eighth International Conference on Artificial Intelligence and Soft Computing, ICAISC, Zakopane, Poland, 2006.
15. Rojas M., Santos S.A., Sorensen D.C. A new matrix-free algorithm for the large-scale trust-region subproblem. SIAM J. Optim. 2000, 11:611-646.
16. J. Jiang, H. Zhang, Multiplicative Update for Projective Nonnegative Matrix Factorization with Bregman Divergence, in: Proceedings of the Third International Symposium on Information Processing, 2010, pp. 233-301.
17. Nocedal J., Wright S.J. Numerical Optimization. Springer Series in Operations Research 1999, Springer, New York.
18. Wild S., Curry J., Dougherty A. Improving non-negative matrix factorizations through structured initialization. Pattern Recogn. 2004, 37:2217-2232.
19. A. Lefevre, F. Bach, C. Févotte, Itakura-Saito nonnegative matrix factorization with group sparsity, in: Proceedings of the 36th International Conference on Acoustics, Speech, and Signal Processing, 2011.
20. Cichocki A., Cruces S., Amari S. Generalized alpha-beta divergences and their application to robust nonnegative matrix factorization. Entropy 2011, 13:134-170.
21. Paninski L. Estimation of entropy and mutual information. Neural Comput. 2003, 15:1191-1253.
22. S.A. Vavasis, On the Complexity of Nonnegative Matrix Factorization, eprint arXiv, 2007, 0708.4149.