A full algorithm to compute the constrained positive matrix factorization and its application in unsupervised unmixing of hyperspectral imagery

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 6966, Issue , 2008, Pages

  Masalmah, Yahya M ^a   Veléz Reyes, Miguel ^b  

^a University of Turabo   (Puerto Rico)

^b UNIVERSITY OF PUERTO RICO   (Puerto Rico)

Author keywords

Abundance estimation; Endmember determination; Hyperspectral imagery; Initialization; Iterative methods; Positive matrix factorization; Spectral unmixing

Indexed keywords

ALGORITHMS; BOOLEAN FUNCTIONS; COMPUTATIONAL METHODS; FACTORIZATION; FIBER OPTIC SENSORS; LIGHT MEASUREMENT; MATRIX ALGEBRA; NUMERICAL METHODS; REMOTE SENSING; SCHEDULING ALGORITHMS; SPACE OPTICS; TECHNOLOGY; TURBULENT FLOW;

ENDMEMBERS; ENVIRONMENTAL REMOTE SENSING; HYPER-SPECTRAL; HYPERSPECTRAL IMAGERY (HSI); INITIALIZATION STAGE; MULTI-SPECTRAL (MS); POSITIVE MATRIX FACTORIZATION (PMF); PROBLEM BASED; SIMULATED DATA; SUBSET SELECTION; ULTRASPECTRAL; UN-MIXING;

EVOLUTIONARY ALGORITHMS;

EID: 44949129922     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.779444     Document Type: Conference Paper

References (26)

1. N. Keshava and J.F. Mustrad. "A Survey of Spectral Unmixing." In Lincoln Laboratory Journal, Vol. 14, No.1, pp. 55-78, 2003.
2. C. L. Lawson and R. J. Hanson. Solving Least Squares Problems. Prentice-Hall. 1974.
3. M. Vélez-Reyes, S. Rosario, A. Puetz and R. B. Lockwood. "Iterative Algorithms for Unmixing of Hyperspectral Imagery." In Proceedings of SPIE: Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery IX, Vol. 5093, April 2003.
4. D. D. Lee and H. S. Seung. "Learning the Parts of Objects by Non-negative Matrix Factorization." In Nature Vol. 401, pp. 788-791, 1999.
5. D. D. Lee and H. Sebastian Seung. "Algorithms for Non-negative Matrix Factorization." In Advances in Neural Information Processing, pp. 556-562, 2001.
6. D. D. Lee and H. S. Seung. "Unsupervised Learning by Convex and Conic Coding." In Proceedings of the Conference on Neural Information Processing Systems, Vol. 9, pp. 515-521, 1997.
7. D. Donoho and V. Stodden. "When does Non-Negative Matrix Factorization give a correct Decomposition into Parts?." In NIPS Workshop on ICA: Sparse Representations in Signal Processing, Whistler, Canada,2003.
8. P. Sajda, S. Du and L. Parra. "Nonnegative Matrix Factorization for Rapid Recovery of Constituent Spectra in Magnetic Resonance Chemical Shift Imaging of the Brain." In IEEE Transactions on Medical Imaging, Vol. 23, No. 12, December 2004.
9. Y. H. Hu, H. B. Lee and F. L. Scarpace. "Optimal Linear Spectral Unmixing." In IEEE Transactions on Geoscience, and Remote Sensing, Vol. 37, No. 12, January 1999.
10. M. Vélez-Reyes and S. Rosario. "Solving Abundance Estimation in Hyperspectral Unmixing as a Least Distance Problem." In Proceedings of the IEEE International Geosciences and Remote Sensing Symposium, Alaska, 2004.
11. K. Kontantinides and K. Yao. "Statistical Analysis of effective Singular Values in Matrix Rank Determination." In IEEE Transaction on Acoustics, Speech, and Signal Processing. Vol. 36, No. 5, May 1988.
12. A. Plaza and C. Chang. "An Improved N-FINDR Algorithm in Implementation. In Proceedings of SPIE: Algorithms and Technology for Multispectral, Hyperspectral, and Ultraspectral Imagery XI, Vol. 5806 , April 2005.
13. J. M. van den Hof and J. H. van Schuppen. "Positive Matrix Factorization via Extermal Polyhedral Cones." Linear Algebra and its Applications, Vol.293, pp. 171-186, 1999.
14. A. N. Langville, M. W. Berry, M. Browne, V. P. Pauca, and R. J. Plemmons, "A Survey of Algorithms and Applications for the Nonnegative Matrix Factorization." In Computational Statistics and Data Analysis. Elsevier. Submitted Jan. 2006.
15. A. N. Langville, C. D. Meyer, R. Albright, J. Cox, and D. Duling. "Initializations for the Nonnegative Matrix Factorization." In Proceedings of the Twelfth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, August 23-26, 2006.
16. S. Wild. Seeding non-negative Matrix Factorizations with Spherical K-means Clustering. Masters thesis, University of Colorado, 2003.
17. S. Wild, J. Curry, and A. Dougherty. "Motivating Non-negative Matrix Factorizations." In Eighth SIAM Conference on Applied Linear Algebra, Philadelphia, 2003.
18. M. Velez-Reyes, L. O. Jimenez, et. al. "Comparison of Matrix Factorization Algorithmes for Band Selection in Hyperspectral Imagery." In Proceedings of SPIE: Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery VI, Vol. 4049, April 2000.
19. S. Wild, J. Curry, and A. Dougherty. "Improving Non-negative Matrix Factorizations Through Structured Initialization." In Journal of Pattern Recognition, Vol. 37, No. 11, pp. 2217-2232, 2004.
20. A. Sen, and M. Srivastava. Regression Analysis: Theory, Methods, and Applications. Springer-Verlag. 1990.
21. C. Kwan, B. Ayhan, G. Chen, J. Wang, B. Ji, and C. Chang. "A Novel Approach for Spectral Unmixing, Classification, and Concentration Estimation of Chemical and Biological Agents." In IEEE Transactions on Geoscience and Remote Sensing, Vol. 44, No. 2, February 2006.
22. A. Umaña-Díaz. Determining the Dimensionality of Hyperspectral Imagery. Masters thesis, University of Puerto Rico, 2003.
23. M. Vélez-Reyes. Decomposition Algorithms for Parameter estimation. Doctoral Dissertation, Massachusets Institute of Technology, 1992.
24. Y.M. Masalmah, M. Vélez-Reyes, and S. Rosario-Torres, "An Algorithm for Unsupervised Unmixing of Hyperspectral Imagery using Positive Matrix Factorization." In Proceedings of SPIE: Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XI, Vol. 5806, April 2005.
25. Y.M. Masalmah and M. Vélez-Reyes "A Comparison of Algorithms to compute the Positive Matrix Factorization and Their Application to unsupervised unmixing." In Proceedings of SPIE: Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XII, Vol. 6233, April 2006.
26. Y.M. Masalmah and M. Vélez-Reyes, "The Impact of Initialization Procedures on Unsupervised Unmixing of Hyperspectral Imagery using the Constrained Positive Matrix Factorization ." In Proceedings of SPIE: Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XIII, Vol. 6565, March 2007.