Abstract
Recently, many methods for hyperspectral unmixing have been proposed. These methods are often based on nonnegative matrix factorization (NMF), which naturally inherits the non-negative advantage and is in line with the common sense of physics. Although there are many ways to perform NMF-based hyperspectral unmixing, these methods can only unmix one hyperspectral image at a time. In practice, we may often collect two or more similar hyperspectral images, and the end of the hyperspectral images of the signal could be only slightly different. Traditional NMF-based hyperspectral unmixing methods cannot take advantage of the fact that different hyper-spectral images may have similar or even the same end-element signals. Accordingly, in order to improve the performance of NMF-based hyperspectral unmixing, we present an algorithm in this paper that can process two hyperspectral images, simultaneously, and makes full use of the available information when most of the signals at the two end-points are similar. This improves the effect of end-element extraction in hyperspectral unmixing evidenced by experimental results on both synthetic and real-world data.
Similar content being viewed by others
References
Shang S, Chen L, Zheng K, Jensen CS, Wei Z, Kalnis P (2018) Parallel trajectory-to-location join. IEEE Transactions on Knowledge and Data Engineering
Du B, Zhang M, Zhang L, Hu R, Tao D (2019) An improved quantum-behaved particle swarm optimization for endmember extraction. IEEE Transactions on Geoscience and Remote Sensing
Qian Y, Jia S, Zhou J, Robles-Kelly A (2011) L1/2 sparsity constrained nonnegative matrix factorization for hyperspectral unmixing. In: International conference on digital image computing: techniques and applications, pp 447–453
Du B, Wang Y, Wu C, Zhang L (2018) Unsupervised scene change detection via latent Dirichlet allocation and multivariate alteration detection. IEEE J Selected Topics Appl Earth Observ Remote Sens 11(12):4676–4689
Lu X, Wu H, Yuan Y (2014) Double constrained nmf for hyperspectral unmixing. IEEE Trans Geosci Remote Sens 52(5):2746–2758
Jia S, Qian Y (2009) Constrained nonnegative matrix factorization for hyperspectral unmixing. IEEE Trans Geosci Remote Sens 47(1):161–173
Shi Q, Du B, Zhang L (2015) Spatial coherence-based batch-mode active learning for remote sensing image classification. IEEE Trans Image Process 24(7):2037–2050
Winter ME (1999) N-findr: an algorithm for fast autonomous spectral end-member determination in hyperspectral data. Proceedings of SPIE - The International Society for Optical Engineering 3753:266–275
Wang J, Chang CI (2006) Applications of independent component analysis in endmember extraction and abundance quantification for hyperspectral imagery. IEEE Trans Geosci Remote Sens 44(9):2601–2616
Nascimento JMP, Dias JMB (2005) Vertex component analysis: a fast algorithm to unmix hyperspectral data. IEEE Trans Geosci Remote Sens 43(4):898–910
Chen J, Jia X, Yang W, Matsushita B (2009) Generalization of subpixel analysis for hyperspectral data with flexibility in spectral similarity measures. IEEE Trans Geosci Remote Sens 47(7):2165–2171
Li J, Bioucas-Dias JM (2009) Bioucas-Dias: minimum volume simplex: a fast algorithm to unmix hyperspectral data. In: Geoscience and remote sensing symposium, 2008. IGARSS 2008. IEEE International, pp III – 250–III – 253
Bioucas-Dias JM (2009) A variable splitting augmented lagrangian approach to linear spectral unmixing. In: First Workshop on hyperspectral image and signal processing: evolution in remote sensing, 2009. WHISPERS ’09, pp 1–4
Lillesand TM, Kiefer RW (2000) Remote sensing and image interpretation. Wiley
Eggert J, Korner E (2004) Sparse coding and nmf. In: IEEE International joint conference on neural networks, 2004. Proceedings, vol 4, pp 2529–2533
Lu X, Wu H, Yuan Y, Yan P, Li X (2013) Manifold regularized sparse nmf for hyperspectral unmixing. IEEE Trans Geosci Remote Sens 51(5):2815–2826
Yue X, Xu J, Chen B, He Y (2019) A practical group signatures for providing privacy-preserving authentication with revocation, pp 226–245, 06
Shang S, Ding R, Zheng K, Jensen CS, Kalnis P, Zhou X (2014) Personalized trajectory matching in spatial networks. VLDB J—Int J Very Large Data Bases 23(3):449–468
Shang S, Chen L, Wei Z, Jensen CS, Zheng K, Kalnis P (2018) Parallel trajectory similarity joins in spatial networks. VLDB J—Int J Very Large Data Bases 27(3):395–420
Paatero P (1994) Positive matrix factorization: a nonnegative factor model with optimal utilization of error estimates of data values. Environmetrics 5(2):111–126
Lee DD, Seung HS (1999) Learning the parts of objects by non-negative matrix factorization. Nature 401:788–791
Hoyer PO (2004) Non-negative matrix factorization with sparseness constraints. J Mach Learn Res 5(1):1457–1469
Zhang L, Song L, Du B, Zhang Y (2019) Nonlocal low-rank tensor completion for visual data. IEEE Transactions on Cybernetics
Rajapakse M, Tan J, Rajapakse J (2004) Color channel encoding with nmf for face recognition. In: 2004 International conference on image processing, 2004. ICIP ’04., vol 3, pp 2007–2010
Iskandar A (2017) Topic extraction method using red-nmf algorithm for detecting outbreak of some disease on twitter. AIP Conf Proc 1825:03
Hamme HV (2012) An on-line nmf model for temporal pattern learning: theory with application to automatic speech recognition. In: Proceedings of the 10th international conference on latent variable analysis and signal separation, LVA/ICA’12. Springer, Berlin, pp 306–313
Sandler R, Lindenbaum M (2011) Nonnegative matrix factorization with earth mover’s distance metric for image analysis. IEEE Trans Pattern Anal Mach Intell 33 (8):1590–1602
Salehani YE, Gazor S (2017) Smooth and sparse regularization for nmf hyperspectral unmixing. IEEE J Selected Topics Appl Earth Observ Remote Sens PP (99):1–16
Qian Y, Jia S, Zhou J, Robles-Kelly A (2010) L1/2 sparsity constrained nonnegative matrix factorization for hyperspectral unmixing. In: 2010 International conference on digital image computing: techniques and applications, pp 447–453
Qian Y, Jia S, Zhou J, Robles-Kelly A (2011) Hyperspectral unmixing via l1/2 sparsity-constrained nonnegative matrix factorization. IEEE Transon Geosc Remote Sens 49(11):4282–4297
Miao L, Qi H (2007) Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization. IEEE Trans Geosc Remote Sens 45(3):765–777
Févotte C, Idier J (2010) Algorithms for nonnegative matrix factorization with the β-divergence. Neural Comput 23(9):2421–2456
Xu W, Liu X, Gong Y (2003) Document clustering based on non-negative matrix factorization. In: Proceedings of the 26th annual international ACM SIGIR conference on research and development in informaion retrieval, SIGIR ’03. ACM, New York, pp 267–273
Guan N, Tao D, Luo Z, Bo Y (2012) Nenmf: an optimal gradient method for nonnegative matrix factorization. IEEE Trans Signal Process 60(6):2882–2898
Pauca PV, Piper J, Plemmons RJ (2006) Nonnegative matrix factorization for spectral data analysis. Linear Algebra Appl 416(1):29–47
Pauca VP, Piper J, Plemmons M, Giffin R (2004) Object characterization from spectral data using nonnegative factorization and information theory. AMOS Technical Conference
Du B, Zhang M, Zhang L, Hu R, Dacheng T (2016) PLTD patch-based low-rank tensor decomposition for hyperspectral images. IEEE Trans Multimed 19 (1):67–79
Hoyer PO (2002) Non-negative sparse coding. IEEE cs.ne/0202009(02):557–565
Vavasis SA (2009) On the complexity of nonnegative matrix factorization. SIAM J Optim 20(3):1364–1377
Swayze GA, Clark RN, King TV, Gallagher A, Calvin WM (1993) The U.S. geological survey, digital spectral library: Version 1: 0.2 to 3.0 m. In: Bulletin of the American astronomical society, p 1033
Wang W, Qian Y (2015) Adaptive L1/2 sparsity-constrained nmf with half-thresholding algorithm for hyperspectral unmixing. IEEE J Selected Topics Appl Earth Observ Remote Sens 8(6):2618–2631
Author information
Authors and Affiliations
Corresponding authors
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Yang, J., Jia, M., Xu, C. et al. Joint hyperspectral unmixing for urban computing. Geoinformatica 24, 247–265 (2020). https://doi.org/10.1007/s10707-019-00375-w
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10707-019-00375-w