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Non-negative matrix factorization based unmixing for principal component transformed hyperspectral data

Author(s): Xiu-rui Geng, Lu-yan Ji, Kang Sun
Affiliation(s): Key Laboratory of Technology in Geo-spatial Information Processing and Application System, Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China; more
Corresponding email(s): gengxr@sina.com, jily@mail.ustc.edu.cn, sunkang-1234@163.com
Key Words: Non-negative matrix factorization (NMF), Principal component analysis (PCA), Endmember, Hyperspectral

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Xiu-rui Geng, Lu-yan Ji, Kang Sun. Non-negative matrix factorization based unmixing for principal component transformed hyperspectral data[J]. Frontiers of Information Technology & Electronic Engineering,in press.https://doi.org/10.1631/FITEE.1600028

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author="Xiu-rui Geng, Lu-yan Ji, Kang Sun",
journal="Frontiers of Information Technology & Electronic Engineering",
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%T Non-negative matrix factorization based unmixing for principal component transformed hyperspectral data
%A Xiu-rui Geng
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%A Kang Sun
%J Frontiers of Information Technology & Electronic Engineering
%P 403-412
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T1 - Non-negative matrix factorization based unmixing for principal component transformed hyperspectral data
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A1 - Kang Sun
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EP - 412
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Y1 - in press
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doi="https://doi.org/10.1631/FITEE.1600028"

Abstract
Chinese Summary
Academic Network
Reviewer Comment

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.

Abstract: This paper proposed to combine PCA and OP process to realize dimensionality reduction for the multiplicative updating rule of NMF. Benefiting from PCA, the new method can obtain better unmixing performance comparing to NMF regarding to both computational complexity and accuracy. The idea is new and the paper is well organized.

高光谱图像主成分非负矩阵分解方法

目的：在高光谱混合像元分析技术领域中，非负矩阵分解的应用十分广泛。然而，由于高光谱数据量较大，导致使用非负矩阵分解的计算复杂度很高。另一方面，非负矩阵分解对高光谱数据中的噪声十分敏感。虽然主成分分析技术可以很好地解决这两个问题，但是由于经过主成分分析变换后的数据存在负值，使得基于乘式迭代的非负矩阵分解技术不能直接应用于主成分变换后的数据。因此，本文着力于提出一种可以应用于主成分变换后数据的非负矩阵分解方法。
创新点：本文研究了主成分分析的两个步骤（平移和投影）对非负矩阵分解的影响。然后提出了利用强迫正交的手段将主成分变换后的数据重新旋转到第一象限，使之能够适用于非负矩阵分解的乘式迭代公式。
方法：研究了主成分分析对非负矩阵分解的影响，并提出了消除主成分变换数据负值的方法。
结论：本文提出了一种在主成分特征空间中使用非负矩阵分解的高光谱图像解混方法。该方法使用强迫正交有效解决了主成分变换后的负值问题。模拟和真实数据均表明，相比于原始的非负矩阵分解，本文所提方法速度更快，提取的端元误差更小。

关键词组：非负矩阵分解；主成分分析；端元；高光谱

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Reference

[1]Ambikapathi, A., Chan, T.H., Ma, W.K., et al., 2011. Chance-constrained robust minimum-volume enclosing simplex algorithm for hyperspectral unmixing. IEEE Trans. Geosci. Remote Sens., 49(11):4194-4209.

[2]Berman, M., Kiiveri, H., Lagerstrom, R., et al., 2004. ICE: a statistical approach to identifying endmembers in hyperspectral images. IEEE Trans. Geosci. Remote Sens., 42(10):2085-2095.

[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.

[4]Bioucas-Dias, J.M., Plaza, A., Dobigeon, N., et al., 2012. Hyperspectral unmixing overview: geometrical, statistical, and sparse regression-based approaches. IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., 5(2):354-379.

[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., et al., 2009. A convex analysis-based minimum-volume enclosing simplex algorithm for hyperspectral unmixing. IEEE Trans. Signal Process., 57(11):4418-4432.

[7]Chang, C.I., Wu, C.C., Liu, M., et al., 2006. A new growing method for simplex-based endmember extraction algorithm. IEEE Trans. Geosci. Remote Sens., 44(10):2804-2819.

[8]Craig, M.D., 1994. Minimum-volume transforms for remotely sensed data. IEEE Trans. Geosci. Remote Sens., 32(3):542-552.

[9]Geng, X.R., Ji, L.Y., Zhao, Y.C., et al., 2013a. A new endmember generation algorithm based on a geometric optimization model for hyperspectral images. IEEE Geosci. Remote Sens. Lett., 10(4):811-815.

[10]Geng, X.R., Xiao, Z.Q., Ji, L.Y., et al., 2013b. A Gaussian elimination based fast endmember extraction algorithm for hyperspectral imagery. ISPRS J. Photogr. Remote Sens., 79:211-218.

[11]Geng, X.R., Sun, K., Ji, L.Y., et al., 2015. Optimizing the endmembers using volume invariant constrained model. IEEE Trans. Image Process., 24(11):3441-3449.

[12]Green, B.F., 1952. The orthogonal approximation of an oblique structure in factor analysis. Psychometrika, 17(4):429-440.

[13]Green, R.O., Eastwood, M.L., Sarture, C.M., et al., 1998. Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS). Remote Sens. Environ., 65(3):227-248.

[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.

[15]Hendrix, E.M.T., Garcia, I., Plaza, J., et al., 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.

[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.

[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.

[18]Ji, L.Y., Geng, X.R., Yu, K., et al., 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.

[19]Ji, L.Y., Geng, X.R., Sun, K., et al., 2015. Modified N-FINDR endmember extraction algorithm for remote-sensing imagery. Int. J. Remote Sens., 36(8):2148-2162.

[20]Jia, S., Qian, Y.T., 2009. Constrained nonnegative matrix factorization for hyperspectral unmixing. IEEE Trans. Geosci. Remote Sens., 47(1):161-173.

[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.

[23]Lee, D.D., Seung, H.S., 1999. Learning the parts of objects by non-negative matrix factorization. Nature, 401(6755):788-791.

[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.

[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.

[26]Liu, X.S., Xia, W., Wang, B., et al., 2011. An approach based on constrained nonnegative matrix factorization to unmix hyperspectral data. IEEE Trans. Geosci. Remote Sens., 49(2):757-772.

[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.

[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.

[29]Neville, R.A., Staenz, K., Szeredi, T., et al., 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.

[31]Plaza, A., Martinez, P., Perez, R., et al., 2004. A quantitative and comparative analysis of endmember extraction algorithms from hyperspectral data. IEEE Trans. Geosci. Remote Sens., 42(3):650-663.

[32]Schönemann, P.H., 1966. A generalized solution of the orthogonal procrustes problem. Psychometrika, 31(1):1-10.

[33]Sun, K., Geng, X.R., Wang, P.S., et al., 2014. A fast endmember extraction algorithm based on Gram determinant. IEEE Geosci. Remote Sens. Lett., 11(6):1124-1128.

[34]Swayze, G., Clark, R.N., Kruse, F., et al., 1992. Ground-truthing 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., et al., 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.

[36]Tao, X.T., Wang, B., Zhang, L.M., et al., 2007b. A new scheme for decomposition of mixed pixels based on nonnegative matrix factorization. IEEE Int. Geoscience and Remote Sensing Symp., p.1759-1762.

[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.

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

[40]Zymnis, A., Kim, S.J., Skaf, J., et al., 2007. Hyperspectral image unmixing via alternating projected subgradients. 41st Asilomar Conf. on Signals, Systems and Computers, p.1164-1168.

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高光谱图像主成分非负矩阵分解方法

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