Accelerated Multiplicative Updates and Hierarchical ALS Algorithms for Nonnegative Matrix Factorization
Publication date :
01 January 2012
Journal title :
Neural Computation
ISSN :
0899-7667
Publisher :
MIT Press, Morocco
Volume :
24
Issue :
4
Pages :
1085-1105
Peer reviewed :
Peer Reviewed verified by ORBi
Research unit :
F151 - Mathématique et Recherche opérationnelle
Research institute :
R300 - Institut de Recherche en Technologies de l'Information et Sciences de l'Informatique R450 - Institut NUMEDIART pour les Technologies des Arts Numériques
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.
Bertsekas, D. P. (1999a). Nonlinear programming (2nd ed.). Belmont, MA: Athena Scientific.
Bertsekas, D. P. (1999b). Corrections for the book nonlinear programming (2nd ed.). Available online at http://www.athenasc.com/nlperrata.pdf.
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.
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.
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.
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.
Daube-Witherspoon, M. E., & Muehllehner, G. (1986). An iterative image space reconstruction algorithm suitable for volume ECT. IEEE Trans. Med. Imaging, 5, 61-66.
Devarajan, K. (2008). Nonnegative matrix factorization: An analytical and interpretive tool in computational biology. PLoS Computational Biology, 4(7), e1000029.
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.
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.
Gillis, N. (2011). Nonnegative matrix factorization: Complexity, algorithms and applications. Unpublished doctoral dissertation, Universit́e catholique de Louvain. Louvain-La-Neuve: CORE.
Gillis, N., & Glineur, F. (2008). Nonnegative factorization and the maximum edge biclique problem. CORE discussion paper 2008/64.
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.
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.
Ho, N.-D. (2008). Nonnegative matrix factorization: Algorithms and applications. Unpublished docotral dissertation, Universit́e catholique de Louvain.
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.
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.
Lee, D. D., & Seung, H. S. (1999). Learning the parts of objects by nonnegative matrix factorization. Nature, 401, 788-791.
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.
Li, L., & Zhang, Y.-J. (2009). FastNMF: Highly efficient monotonic fixed-point nonnegative matrix factorization algorithm with good applicability. J. Electron. Imaging, 18, 033004.
Lin, C.-J. (2007b). On the convergence of multiplicative update algorithms for nonnegative matrix factorization. IEEE Trans. on Neural Networks, 18, 1589-1596.
Pauca, P. V., Piper, J., & Plemmons, R. J. (2006). Nonnegative matrix factorization for spectral data analysis. Linear Algebra and Its Applications, 406, 29-47.
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.
Vavasis, S. A. (2009). On the complexity of nonnegative matrix factorization. SIAM Journal on Optimization, 20, 1364-1377.
Zhong, S., & Ghosh, J. (2005). Generativemodel-based document clustering: A comparative study. Knowledge and Information Systems, 8, 374-384.
