Accelerated multiplicative updates and hierarchical ALS algorithms for nonnegative matrix factorization

Neural Computation

Volumn 24, Issue 4, 2012, Pages 1085-1105

  Gillis, Nicolas ^a   Glineur, François ^b  

^a UNIVERSITY OF WATERLOO   (Canada)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; BIOLOGY; IMAGE PROCESSING; INFORMATION PROCESSING; LETTER; REGRESSION ANALYSIS;

ALGORITHMS; AUTOMATIC DATA PROCESSING; COMPUTATIONAL BIOLOGY; IMAGE PROCESSING, COMPUTER-ASSISTED; LEAST-SQUARES ANALYSIS;

DATA HANDLING; DATA MINING; GRADIENT METHODS; IMAGE PROCESSING; MATRIX FACTORIZATION;

ALTERNATING LEAST SQUARES; CLUSTERINGS; COMPUTATIONAL BIOLOGY; DATA ANALYSIS TECHNIQUES; HYPERSPECTRAL DATA ANALYSIS; IMAGES PROCESSING; MULTIPLICATIVE UPDATES; NONNEGATIVE MATRIX FACTORIZATION; SIMPLE++; TEXT-MINING;

MATRIX ALGEBRA;

EID: 84861111031     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/NECO_a_00256     Document Type: Letter

References (27)

1. Berry, M. W., Browne, M., Langville, A. N., Pauca, V. P., & Plemmons, R. J. (2007). Algorithms and applications for approximate nonnegative matrix factorization. Computational Statistics and Data Analysis, 52, 155-173.
2. Bertsekas, D. P. (1999a). Nonlinear programming (2nd ed.). Belmont, MA: Athena Scientific.
3. Bertsekas, D. P. (1999b). Corrections for the book nonlinear programming (2nd ed.). Available online at http://www.athenasc.com/nlperrata.pdf.
4. Cichocki, A., Amari, S., Zdunek, R., & Phan, A. H. (2009). Non-negative matrix and tensor factorizations: Applications to exploratory multi-way data analysis and blind source separation. Hoboken, NJ: Wiley/Blackwell.
5. Cichocki, A., & Phan, A. H. (2009). Fast local algorithms for large scale nonnegative matrix and tensor factorizations. IEICE Transactions on Fundamentals of Electronics, E92-A, 708-721.
6. Cichocki, A., Zdunek, R., & Amari, S. (2006). Non-negativematrix factorizationwith quasi-newton optimization. In Lecture Notes in Artificial Intelligence, 4029 (pp. 870-879). Berlin: Springer.
7. Cichocki, A., Zdunek, R., & Amari, S. (2007). Hierarchical ALS algorithms for nonnegative matrix and 3D tensor factorization. In Lecture Notes in Computer Science, 4666 (pp. 169-176). Berlin: Springer.
8. Daube-Witherspoon, M. E., & Muehllehner, G. (1986). An iterative image space reconstruction algorithm suitable for volume ECT. IEEE Trans. Med. Imaging, 5, 61-66.
9. Devarajan, K. (2008). Nonnegative matrix factorization: An analytical and interpretive tool in computational biology. PLoS Computational Biology, 4(7), e1000029.
10. Dhillon, I. S., Kim, D., & Sra, S. (2007). Fast Newton-type methods for the least squares nonnegative matrix approximation problem. In Proc. of SIAM Conf. on Data Mining (pp. 343-354). Philadelphia: SIAM.
11. Ding, C., He, X., & Simon, H. D. (2005). On the equivalence of nonnegative matrix factorization and spectral clustering. In Proc. of SIAM Conf. on Data Mining (pp. 606-610). Philadelphia: SIAM.
12. Gillis, N. (2011). Nonnegative matrix factorization: Complexity, algorithms and applications. Unpublished doctoral dissertation, Universit́e catholique de Louvain. Louvain-La-Neuve: CORE.
13. Gillis, N., & Glineur, F. (2008). Nonnegative factorization and the maximum edge biclique problem. CORE discussion paper 2008/64.
14. Gonzales, E. F.,&Zhang, Y. (2005). Accelerating the Lee-Seung algorithm for non-negative matrix factorization (Tech. Rep.). Houston, TX: Department of Computational and Applied Mathematics, Rice University.
15. Han, J., Han, L., Neumann, M., & Prasad, U. (2009). On the rate of convergence of the image space reconstruction algorithm. Operators and Matrices, 3(1), 41-58.
16. Ho, N.-D. (2008). Nonnegative matrix factorization: Algorithms and applications. Unpublished docotral dissertation, Universit́e catholique de Louvain.
17. Kim, H., & Park, K. (2008). Non-negative matrix factorization based on alternating non-negativity constrained least squares and active set method. SIAM J. Matrix Anal. Appl., 30, 713-730.
18. Kim, J., & Park, H. (2008). Toward faster nonnegative matrix factorization: A new algorithm and comparisons. In Proc. of IEEE Int. Conf. on Data Mining (pp. 353-362). Piscataway, NJ: IEEE.
19. Lee, D. D., & Seung, H. S. (1999). Learning the parts of objects by nonnegative matrix factorization. Nature, 401, 788-791.
20. Lee, D. D., & Seung, H. S. (2001). Algorithms for non-negative matrix factorization. In T. K. Leen, T. G. Dietterich, & V. Tresp (Eds.), Advances in neural information processing, systems, 13. Cambridge, MA: MIT Press.
21. Li, L., & Zhang, Y.-J. (2009). FastNMF: Highly efficient monotonic fixed-point nonnegative matrix factorization algorithm with good applicability. J. Electron. Imaging, 18, 033004.
22. Lin, C.-J. (2007a). Projected gradient methods for nonnegative matrix factorization. Neural Computation, 19, 2756-2779.
23. Lin, C.-J. (2007b). On the convergence of multiplicative update algorithms for nonnegative matrix factorization. IEEE Trans. on Neural Networks, 18, 1589-1596.
24. Pauca, P. V., Piper, J., & Plemmons, R. J. (2006). Nonnegative matrix factorization for spectral data analysis. Linear Algebra and Its Applications, 406, 29-47.
25. Shahnaz, F., Berry, M. W., Langville, A. N., Pauca, V. P., & Plemmons, R. J. (2006). Document clustering using nonnegative matrix factorization. Information Processing and Management, 42, 373-386.
26. Vavasis, S. A. (2009). On the complexity of nonnegative matrix factorization. SIAM Journal on Optimization, 20, 1364-1377.
27. Zhong, S., & Ghosh, J. (2005). Generativemodel-based document clustering: A comparative study. Knowledge and Information Systems, 8, 374-384.