Dimensionality reduction, classification, and spectral mixture analysis using nonnegative underapproximation

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 7695, Issue , 2010, Pages

  Gillis, Nicolas ^a   Plemmons, Robert J ^b  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b WAKE FOREST UNIVERSITY   (United States)

Author keywords

Classification; Dimensionality reduction; Hyperspectral images; Nonnegative Matrix Factorization; Spectral mixture analysis; Underapproximation

Indexed keywords

DIMENSIONALITY REDUCTION; HYPER-SPECTRAL IMAGES; NONNEGATIVE MATRIX FACTORIZATION; SPECTRAL MIXTURE ANALYSIS; UNDER-APPROXIMATION;

FACTORIZATION; FEATURE EXTRACTION; IMAGE RECONSTRUCTION; LIGHT MEASUREMENT; MIXTURES; REMOTE SENSING;

MATRIX ALGEBRA;

EID: 77953799944     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.849345     Document Type: Conference Paper

References (24)

1. Lee, D. and Seung, H., "Learning the parts of objects by nonnegative matrix factorization", Nature 401, 788-791 (1999).
2. Berry, M., Browne, M., Langville, A., Pauca, P., and Plemmons, R., "Algorithms and applications for approximate nonnegative matrix factorization", Computational Statistics and Data Analysis 52, 155-173 (2007).
3. Boardman, J., "Geometric mixture analysis of imaging spectrometry data", in [Proc. IGARSS 4, Pasadena, Calif., pp. 2369-2371], (1994).
4. Craig, M., "Minimum-volume tranforms for remotely sensed data", IEEE Transactions on Geoscience and Remote Sensing 32 (3), 542-552 (1994).
5. Pauca, P., Piper, J., and Plemmons, R., "Nonnegative matrix factorization for spectral data analysis", Linear Algebra and its Applications 406 (1), 29-47 (2006). (Pubitemid 43737212)
6. Zhang, Q., Wang, H., Plemmons, R., and Pauca, P., "Tensor methods for hyperspectral data analysis: a space object material identification study", J. Optical Soc. Amer. A 25 (12), 3001-3012 (2008).
7. Vavasis, S. A., "On the complexity of nonnegative matrix factorization", SIAM Journal on Optimization 20(3), 1364-1377 (2009).
8. Cichocki, A., Amari, S., Zdunek, R., and Phan, A., [Non-negative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation], Wiley-Blackwell (2009).
9. Laurberg, H., Christensen, M., Plumbley, M., Hansen, L., and Jensen, S., "Theorems on positive data: On the uniqueness of NMF", Computational Intelligence and Neuroscience 2008. Article ID 764206.
10. Hoyer, P., "Nonnegative matrix factorization with sparseness constraints", J. Machine Learning Research 5, 1457-1469 (2004).
11. Ding, C., Li, T., Peng, W., and Park, H., "Orthogonal nonnegative matrix tri-factorizations for clustering", in [Proc. SIGKDD, Int. Conf. on Knowledge Discovery and Data Mining], 126-135 (2006).
12. Li, H., Adal, C., Wang, W., Emge, D., and Cichocki, A., "Non-negative matrix factorization with orthogonality constraints and its application to raman spectroscopy", The Journal of VLSI Signal Processing 48, 83-97 (2007).
13. Miao, L. and Qi, H., "Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization", IEEE Transactions on Geoscience and Remote Sensing 45 (3), 765-777 (2007).
14. Masalmah, Y. and Veléz-Reyes, M., "A full algorithm to compute the constrained positive matrix factorization and its application in unsupervised unmixing of hyperspectral imagery", in [Proc. SPIE, Vol. 6966; doi:10.1117/12.779444], (2008).
15. Ifarraguerri, A. and Chang, C.-I., "Multispectral and hyperspectral image analysis with convex cones", IEEE Transactions on Geoscience and Remote Sensing 37(2), 756-770 (1999).
16. Golub, G. and Van Loan, C., [Matrix Computation, 3rd Edition], The Johns Hopkins University Press Baltimore (1996).
17. Gillis, N., Approximation et sous-approximation de matrices par factorisation positive: algorithmes, complexité et applications, Master's thesis, Université catholique de Louvain (2007). In French.
18. Gillis, N. and Glineur, F., "Using underapproximations for sparse nonnegative matrix factorization", Pattern Recognition 43(4), 1676-1687 (2010).
19. Gillis, N. and Glineur, F., "Nonnegative factorization and the maximum edge biclique problem", CORE Discussion paper 2008/64 (2008).
20. 1 approximation", BIT Numerical Mathematics 30 (2), 301-3106 (1990).
21. Chen, D. and Plemmons, R., "Nonnegativity Constraints in Numerical Analysis", in [A. Bultheel and R. Cools (Eds.), Symposium on the Birth of Numerical Analysis, World Scientific Press.], (2009).
22. Guo, Z., Todd Wittman, T., and Osher, S., "L1 unmixing and its application to hyperspectral image enhancement", in [Proc. SPIE Conference on Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XV], (2009).
23. Winter, M., "N-findr: an algorithm for fast autonomous spectral end-member determination in hyperspectral data", in [Proc. SPIE Conference on Imaging Spectrometry V], (1999).
24. Li, F., Ng, M., and Plemmons, R., "Coupled segmentation and denoising/deblurring models for hyperspectral material identification", Available at http://www.wfu.edu/~plemmons (2009).