Two algorithms for orthogonal nonnegative matrix factorization with application to clustering

Neurocomputing

Volumn 141, Issue , 2014, Pages 15-25

  Pompili, Filippo ^a   Gillis, Nicolas ^b   Absil, P A ^c   Glineur, François ^c  

^a UNIVERSITY OF PERUGIA   (Italy)

^b UNIVERSITY OF MONS   (Belgium)

^c UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Clustering; Document classification; Hyperspectral images; Nonnegative matrix factorization; Orthogonality

Indexed keywords

CONSTRAINED OPTIMIZATION; INFORMATION RETRIEVAL SYSTEMS; LAGRANGE MULTIPLIERS; SPECTROSCOPY;

CLUSTERING; DOCUMENT CLASSIFICATION; HYPER-SPECTRAL IMAGES; NONNEGATIVE MATRIX FACTORIZATION; ORTHOGONALITY;

CLUSTERING ALGORITHMS;

ACCURACY; ALGORITHM; ARTICLE; CLUSTER ANALYSIS; COMPARATIVE STUDY; DATA ANALYSIS; EM LIKE ALGORITHM; LINEAR SYSTEM; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MATHEMATICAL PARAMETERS; ORTHOGONAL NONNEGATIVE MATRIX FACTORIZATION; ORTHOGONAL NONNEGATIVE MATRIX FACTORIZATION ALGORITHM; PRIORITY JOURNAL; QUANTITATIVE ANALYSIS; RELIABILITY; SIGNAL NOISE RATIO;

EID: 84901628210     PISSN: 09252312     EISSN: 18728286     Source Type: Journal    
DOI: 10.1016/j.neucom.2014.02.018     Document Type: Article

References (21)

1. Absil P.-A., Malick JérÔme Projection-like retractions on matrix manifolds. SIAM J. Optim. 2012, 22:135-158.
2. A. Banerjee, I. Dhillon, J. Ghosh, S. Sra,Generative model-based clustering of directional data, in: Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD-03), ACM Press, 2003, pp. 19-28.
3. Blei D.M., Ng A.Y., Jordan M.I. Latent dirichlet allocation. J. Mach. Learn. Res. 2003, 3:993-1022.
4. Bottou L. Online Algorithms and Stochastic Approximations. Online learning and neural networks 1998, Cambridge University Press, Cambridge. D. Saad (Ed.).
5. Boutsidis C., Gallopoulos E. Svd based initialization. a head start for nonnegative matrix factorization. Pattern Recognit. 2008, 41(4):1350-1362.
6. Chi E.C., Kolda T.G. On tensors, sparsity, and nonnegative factorizations. SIAM J. Matrix Anal. Appl. 2012, 33:1272-1299.
7. S. Choi, Algorithms for orthogonal nonnegative matrix factorization, in: Proceedings of the International Joint Conference on Neural Networks, 2008, pp. 1828-1832.
8. Dhillon I.S., Guan Y., Kulis B. Weighted graph cuts without eigenvectors. a multilevel approach. IEEE Trans. Pattern Anal. Mach. Intell. 2007, 29(11):1944-1957.
9. C. Ding, X. He, On the equivalence of nonnegative matrix factorization and spectral clustering, in: Proceedings of the Fifth SIAM Conference on Data Mining, 2005, pp. 606-610.
10. C. Ding, T. Li, W. Peng, H. Park,Orthogonal nonnegative matrix tri-factorizations for clustering, in: Proceedings of the Twelfth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Philadelphia, PA, USA, August 20-23, 2006, 2006, pp. 126-135.
11. Gillis N., Plemmons R.J. Dimensionality reduction, classification, and spectral mixture analysis using nonnegative underapproximation. Opt. Eng. 2011, 50:027001.
12. Z. Guo, T. Wittman, S. Osher, L1 unmixing and its application to hyperspectral image enhancement, in: Proceedings of SPIE Conference on Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XV, 2009.
13. Horn R.A., Johnson C. Matrix Analysis 1990, Cambridge University Press, Cambridge.
14. Kim J., Park H. Fast nonnegative matrix factorization. an active-set-like method and comparisons. SIAM J. Sci. Comput. 2011, 6:3261-3281.
15. Lin C.-J. Projected gradient methods for nonnegative matrix factorization. Neural Comput. 2007, 19:2756-2779.
16. Nocedal J., Wright S.J. Numerical Optimization 2006, Springer, New York. Second Ed.
17. Pauca V.P., Piper J., Plemmons R.J. Nonnegative matrix factorization for spectral data analysis. Linear Algebra Appl. 2006, 406(1):29-47.
18. F. Pompili, N. gillis, P.-A. Absil, F. Glineur, Onp-mf: An orthogonal nonnegative matrix factorization algorithm with application to clustering, in: 21st European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, 2013.
19. M. Winter, N-findr: an algorithm for fast autonomous spectral end-member determination in hyperspectral data, in: Proceedings of SPIE Conference on Imaging Spectrometry V, 1999.
20. Yang Z., Oja E. Linear and nonlinear projective nonnegative matrix factorization. Trans. Neural Netw. 2010, 21:734-749.
21. Zhong S., Ghosh J. Generative model-based document clustering. a comparative study. Knowl. Inf. Syst. 2005, 8(3):374-384.