Non-negativematrix factorization based unmixing for principal component transformed hyperspectral data

Abstract

Non-negative matrix factorization (NMF) has been widely used in mixture analysis for hyperspectral remote sensing. When used for spectral unmixing analysis, however, it has two main shortcomings: (1) since the dimensionality of hyperspectral data is usually very large, NMF tends to suffer from large computational complexity for the popular multiplicative iteration rule; (2) NMF is sensitive to noise (outliers), and thus the corrupted data will make the results of NMF meaningless. Although principal component analysis (PCA) can be used to mitigate these two problems, the transformed data will contain negative numbers, hindering the direct use of the multiplicative iteration rule of NMF. In this paper, we analyze the impact of PCA on NMF, and find that multiplicative NMF can also be applicable to data after principal component transformation. Based on this conclusion, we present a method to perform NMF in the principal component space, named ‘principal component NMF’ (PCNMF). Experimental results show that PCNMF is both accurate and time-saving.

Keywords

Non-negative matrix factorization (NMF) / Principal component analysis (PCA) / Endmember / Hyperspectral

References

[1] Ambikapathi, A., Chan, T.H., Ma, W.K., , 2011. Chance-constrained robust minimum-volume enclosing simplex algorithm for hyperspectral unmixing. IEEE Trans. Geosci. Remote Sens., 49(11):4194–4209. http://dx.doi.org/10.1109/TGRS.2011.2151197

[2] Berman, M., Kiiveri, H., Lagerstrom, R., , 2004. ICE: a statistical approach to identifying endmembers in hyperspectral images. IEEE Trans. Geosci. Remote Sens., 42(10):2085–2095. http://dx.doi.org/10.1109/TGRS.2004.835299

[3] Bioucas-Dias, J.M., 2009. A variable splitting augmented Lagrangian approach to linear spectral unmixing. 1st Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, p.1–4. http://dx.doi.org/10.1109/WHISPERS.2009.5289072

[4] Bioucas-Dias, J.M., Plaza, A., Dobigeon, N., , 2012. Hyperspectral unmixing overview: geometrical, statistical, and sparse regression-based approaches. IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., 5(2):354–379. http://dx.doi.org/10.1109/JSTARS.2012.2194696

[5] Boardman, J.W., 1992. Automated spectral unmixing of AVIRIS data using convex geometry concepts. Summaries of the 4th Annual JPL Airborne Geoscience Workshop, p.11–14.

[6] Chan, T.H., Chi, C.Y., Huang, Y.M., , 2009. A convex analysis-based minimum-volume enclosing simplex algorithm for hyperspectral unmixing. IEEE Trans. Signal Process., 57(11):4418–4432. http://dx.doi.org/10.1109/TSP.2009.2025802

[7] Chang, C.I., Wu, C.C., Liu, M., , 2006. A new growing method for simplex-based endmember extraction algorithm. IEEE Trans. Geosci. Remote Sens., 44(10):2804–2819. http://dx.doi.org/10.1109/TGRS.2006.881803

[8] Craig, M.D., 1994. Minimum-volume transforms for remotely sensed data. IEEE Trans. Geosci. Remote Sens., 32(3):542–552. http://dx.doi.org/10.1109/36.297973

[9] Geng, X.R., Ji, L.Y., Zhao, Y.C., , 2013a. A new endmember generation algorithm based on a geometric optimization model for hyperspectral images. IEEE Geosci. Remote Sens. Lett., 10(4):811–815. http://dx.doi.org/10.1109/LGRS.2012.2224635

[10] Geng, X.R., Xiao, Z.Q., Ji, L.Y., , 2013b. A Gaussian elimination based fast endmember extraction algorithm for hyperspectral imagery. ISPRS J. Photogr. Remote Sens., 79:211–218. http://dx.doi.org/10.1016/j.isprsjprs.2013.02.020

[11] Geng, X.R., Sun, K., Ji, L.Y., , 2015. Optimizing the endmembers using volume invariant constrained model. IEEE Trans. Image Process., 24(11):3441-3449. http://dx.doi.org/10.1109/TIP.2015.2446196

[12] Green, B.F., 1952. The orthogonal approximation of an oblique structure in factor analysis. Psychometrika, 17(4):429–440. http://dx.doi.org/10.1007/BF02288918

[13] Green, R.O., Eastwood, M.L., Sarture, C.M., , 1998. Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS). Remote Sens. Environ., 65(3):227–248. http://dx.doi.org/10.1016/S0034-4257(98)00064-9

[14] Heinz, D.C., Chang, C.I., 2001. Fully constrained least squares linear spectral mixture analysis method for material quantification in hyperspectral imagery. IEEE Trans. Geosci. Remote Sens., 39(3):529–545. http://dx.doi.org/10.1109/36.911111

[15] Hendrix, E.M.T., Garcia, I., Plaza, J., , 2012. A new minimum-volume enclosing algorithm for endmember identification and abundance estimation in hyperspectral data. IEEE Trans. Geosci. Remote Sens., 50(7):2744–2757. http://dx.doi.org/10.1109/TGRS.2011.2174443

[16] Heylen, R., Burazerovic, D., Scheunders, P., 2011. Fully constrained least squares spectral unmixing by simplex projection. IEEE Trans. Geosci. Remote Sens., 49(11):4112–4122. http://dx.doi.org/10.1109/TGRS.2011.2155070

[17] Huck, A., Guillaume, M., Blanc-Talon, J., 2010. Minimum dispersion constrained nonnegative matrix factorization to unmix hyperspectral data. IEEE Trans. Geosci. Remote Sens., 48(6):2590–2602. http://dx.doi.org/10.1109/TGRS.2009.2038483

[18] Ji, L.Y., Geng, X.R., Yu, K., , 2013. A new non-negative matrix factorization method based on barycentric coordinates for endmember extraction in hyperspectral remote sensing. Int. J. Remote Sens., 34(19):6577–6586. http://dx.doi.org/10.1080/01431161.2013.804223

[19] Ji, L.Y., Geng, X.R., Sun, K., , 2015. Modified NFINDR endmember extraction algorithm for remotesensing imagery. Int. J. Remote Sens., 36(8):2148–2162. http://dx.doi.org/10.1080/01431161.2015.1034895

[20] Jia, S., Qian, Y.T., 2009. Constrained nonnegative matrix factorization for hyperspectral unmixing. . IEEE Trans Geosci. Remote Sens., 47(1):161–173. http://dx.doi.org/10.1109/TGRS.2008.2002882

[21] Jolliffe, I.T., 2002. Principal Component Analysis. Springer.

[22] Keshava, N., Mustard, J.F., 2002. Spectral unmixing. IEEE Signal Process. Mag., 19(1):44–57. http://dx.doi.org/10.1109/79.974727

[23] Lee, D.D., Seung, H.S., 1999. Learning the parts of objects by non-negative matrix factorization. Nature, 401(6755):788–791. http://dx.doi.org/10.1038/44565

[24] Li, J., Bioucas-Dias, J.M., 2008. Minimum volume simplex analysis: a fast algorithm to unmix hyperspectral data. IEEE Int. Geoscience and Remote Sensing Symp., p.250–253. http://dx.doi.org/10.1109/IGARSS.2008.4779330

[25] Liu, J.M., Zhang, J.S., 2012. A new maximum simplex volume method based on householder transformation for endmember extraction. IEEE Trans. Geosci. Remote Sens., 50(1):104–118. http://dx.doi.org/10.1109/TGRS.2011.2158829

[26] Liu, X.S., Xia, W., Wang, B., , 2011. An approach based on constrained nonnegative matrix factorization to unmix hyperspectral data. IEEE Trans. Geosci. Remote Sens., 49(2):757–772. http://dx.doi.org/10.1109/TGRS.2010.2068053

[27] Miao, L.D., Qi, H.R., 2007. Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization. IEEE Trans. Geosci. Remote Sens., 45(3):765–777. http://dx.doi.org/10.1109/TGRS.2006.888466

[28] Nascimento, J.M.P., Bioucas-Dias, J.M., 2005. Vertex component analysis: a fast algorithm to unmix hyperspectral data. IEEE Trans. Geosci. Remote Sens., 43(4):898–910. http://dx.doi.org/10.1109/TGRS.2005.844293

[29] Neville, R.A., Staenz, K., Szeredi, T., , 1999. Automatic endmember extraction from hyperspectral data for mineral exploration. Canadian Symp. on Remote Sensing, p.21–24.

[30] Parente, M., Plaza, A., 2010. Survey of geometric and statistical unmixing algorithms for hyperspectral images. 2nd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, p.1–4. http://dx.doi.org/10.1109/WHISPERS.2010.5594929

[31] Plaza, A., Martinez, P., Perez, R., , 2004. A quantitative and comparative analysis of endmember extraction algorithms from hyperspectral data. IEEE Trans. Geosci. Remote Sens., 42(3):650–663. http://dx.doi.org/10.1109/TGRS.2003.820314

[32] Schönemann, P.H., 1966. A generalized solution of the orthogonal procrustes problem. Psychometrika, 31(1):1–10. http://dx.doi.org/10.1007/BF02289451

[33] Sun, K., Geng, X.R., Wang, P.S., , 2014. A fast endmember extraction algorithm based on Gram determinant. IEEE Geosci. Remote Sens. Lett., 11(6):1124–1128. http://dx.doi.org/10.1109/LGRS.2013.2288093

[34] Swayze, G., Clark, R.N., Kruse, F., , 1992. Groundtruthing AVIRIS mineral mapping at Cuprite, Nevada. Summaries of the 3rd Annual JPL Airborne Geoscience Workshop, p.47–49.

[35] Tao, X.T., Wang, B., Zhang, L.M., , 2007a. A new endmember extraction algorithm based on orthogonal bases of subspace formed by endmembers. IEEE Int. Geoscience and Remote Sensing Symp., p.2006–2009. http://dx.doi.org/10.1109/IGARSS.2007.4423223

[36] Tao, X.T., Wang, B., Zhang, L.M., , 2007b. A new scheme for decomposition of mixed pixels based on nonnegative matrix factorization. IEEE Int. Geoscience and Remote Sensing Symp., p.1759–1762. http://dx.doi.org/10.1109/IGARSS.2007.4423160

[37] Winter, M.E., 1999. N-FINDR: an algorithm for fast autonomous spectral end-member determination in hyperspectral data. SPIE, 3753:266–275.

[38] Zhang, J.K., Rivard, B., Rogge, D.M., 2008. The successive projection algorithm (SPA), an algorithm with a spatial constraint for the automatic search of endmembers in hyperspectral data. Sensors, 8(2):1321–1342. http://dx.doi.org/10.3390/s8021321

[39] Zhu, F.Y., Wang, Y., Xiang, S.M., , 2014. Structured sparse method for hyperspectral unmixing. ISPRS J. Photogr. Remote Sens., 88:101–118.

[40] Zymnis, A., Kim, S.J., Skaf, J., , 2007. Hyperspectral image unmixing via alternating projected subgradients. 41st Asilomar Conf. on Signals, Systems and Computers, p.1164–1168. http://dx.doi.org/10.1109/ACSSC.2007.4487406

RIGHTS & PERMISSIONS

2016 Zhejiang University and Springer-Verlag Berlin Heidelberg