Skip to main content
SpringerLink
Log in

Band selection using sparse nonnegative matrix factorization with the thresholded Earth’s mover distance for hyperspectral imagery classification

  • Methodology Article
  • Published:
Earth Science Informatics Aims and scope Submit manuscript

Abstract

A sparse nonnegative matrix factorization method with the thresholded ground distance (SNMF-TEMD) is proposed to solve the band selection problem in hyperspectral imagery (HSI) classification. The SNMF-TEMD assumes that band vectors are sampled from a union of low-dimensional subspaces and approximates a HSI data matrix with the product of a basis matrix constructed from subspaces and a sparse coefficient matrix. The SNMF-TEMD utilizes the TEMD metric to better measures approximation errors during the optimization of HSI data factorization. The TEMD metric makes up the theoretical drawbacks in the Euclidean distance (ED) and Kullback–Leibler divergence (KLD) metrics when measuring the approximation errors in HSI datasets. The SNMF-TEMD is solved by the combination of min-cost-flow algorithm and multiplicative update rules. The band cluster assignments are found according to positions of largest entries in columns of the coefficient matrix and the desired band subset constitutes with the bands closest to their cluster centers. Three groups of experiments on two HSI datasets are performed to explore the performance of SNMF-TEMD. Four popular band selection methods are used to make comparisons: affinity propagation (AP), maximum-variance principal component analysis (MVPCA), SNMF with ED metric (SNMF-ED) and SNMF with KLD metric (SNMF-KLD). Experimental results show that SNMF-TEMD outperforms all four methods in classification accuracy and its computational speed is slower than SNMF-ED and SNMF-KLD. SNMF-TEMD is a better choice for band selection among all five methods because of its overwhelming advantage in classification and the popular speed remedy scheme from parallel computing and high-performance computers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows: theory, algorithms, and applications. Englwood Cliffs, New Jersey

    Google Scholar 

  • Arzuaga-Cruz E, Jimenez-Rodriguez LO, Velez-Reyes M (2003) Unsupervised feature extraction and band subset selection techniques based on relative entropy criteria for hyperspectral data analysis. AeroSense 2003:462–473

    Google Scholar 

  • Ball JE, West T, Prasad S, Bruce LM (2007) Level set hyperspectral image segmentation using spectral information divergence-based best band selection. Proceedings of 2007 I.E. International Geoscience and Remote Sensing Symposium (IGARSS 2007) 4053–4056

  • Cai D, He X, Han J, Huang TS (2011) Graph regularized nonnegative matrix factorization for data representation. IEEE Transactions on Pattern Analysis and Machine Intelligence 33(8):1548–1560

    Article  Google Scholar 

  • Candes EJ, Romberg JK, Tao T (2006) Stable signal recovery from incomplete and inaccurate measurements. Commun Pure Appl Math 59(8):1207–1223

    Article  Google Scholar 

  • Chang C-I, Du Q, Sun T-L, Althouse ML (1999) A joint band prioritization and band-decorrelation approach to band selection for hyperspectral image classification. IEEE Trans Geosci Remote Sens 37(6):2631–2641

    Article  Google Scholar 

  • Chang C-I, Wang S (2006) Constrained band selection for hyperspectral imagery. IEEE Trans Geosci Remote Sens 44(6):1575–1585

    Article  Google Scholar 

  • Cover T, Hart P (1967) Nearest neighbor pattern classification. IEEE Trans Inf Theory 13(1):21–27

    Article  Google Scholar 

  • Donoho D, Stodden V (2004) When does non-negative matrix factorization give a correct decomposition into parts? Advances in Neural Information Processing Systems 2004:1141–1148

    Google Scholar 

  • Du B, Zhang L (2014a) Target detection based on a dynamic subspace Pattern Recognition 47:344–358

  • Du B, Zhang L (2014b) A Discriminative Metric Learning Based Anomaly Detection Method IEEE Transactions on Geoscience and Remote Sensing 52(11):6844–6857

    Google Scholar 

  • Du H, Qi H, Wang X, Ramanath R, Snyder WE (2003) Band selection using independent component analysis for hyperspectral image processing. Proceedings of 32nd IEEE Applied Imagery Pattern Recognition Workshop 93–98

  • Du Q (2003) Band selection and its impact on target detection and classification in hyperspectral image analysis. Proceedings of 2003 I.E. Workshop on Advances in Techniques for Analysis of Remotely Sensed Data 374–377

  • Du Q, Bioucas-Dias JM, Plaza A (2012) Hyperspectral band selection using a collaborative sparse model. Proceedings of 2012 I.E. International Geoscience and Remote Sensing Symposium (IGARSS) 3054–3057

  • Gao Y, Church G (2005) Improving molecular cancer class discovery through sparse non-negative matrix factorization. Bioinformatics 21(21):3970–3975

    Article  Google Scholar 

  • Goldberg AV (1997) An efficient implementation of a scaling minimum-cost flow algorithm. Journal of Algorithms 22(1):1–29

    Article  Google Scholar 

  • Guan N, Tao D, Luo Z, Yuan B (2011) Manifold regularized discriminative nonnegative matrix factorization with fast gradient descent. IEEE Trans Image Process 20(7):2030–2048

    Article  Google Scholar 

  • Guan N, Tao D, Luo Z, Yuan B (2012) NeNMF: an optimal gradient method for nonnegative matrix factorization. IEEE Trans Signal Process 60(6):2882–2898

    Article  Google Scholar 

  • Guo B, Gunn SR, Damper R, Nelson J (2006) Band selection for hyperspectral image classification using mutual information. IEEE Geosci Remote Sens Lett 3(4):522–526

    Article  Google Scholar 

  • Hazan T, Shashua A (2007) Analysis of L2-loss for probabilistically valid factorizations under general additive noise. Technical Report 2007–13, The Hebrew University

  • Hoyer PO Non-negative sparse coding (2002). Proceedings of the 12th IEEE Workshop on Neural Networks for Signal Processing 557–565

  • Hoyer PO (2004) Non-negative matrix factorization with sparseness constraints The. J Mach Learn Res 5:1457–1469

    Google Scholar 

  • Jia S, Qian Y (2009) Constrained nonnegative matrix factorization for hyperspectral unmixing. IEEE Trans Geosci Remote Sens 47(1):161–173

    Article  Google Scholar 

  • Karavasilis V, Nikou C, Likas A (2011) Visual tracking using the. Earth Mover's Distance between Gaussian mixtures and Kalman filtering Image and Vision Computing 29(5):295–305

    Google Scholar 

  • Keith DJ, Schaeffer BA, Lunetta RS, Gould RW Jr, Rocha K, Cobb DJ (2014) Remote sensing of selected water-quality indicators with the hyperspectral imager for the coastal ocean (HICO) sensor. Int J Remote Sens 35(9):2927–2962

    Article  Google Scholar 

  • Keshava N (2004) Distance metrics and band selection in hyperspectral processing with applications to material identification and spectral libraries. IEEE Trans Geosci Remote Sens 42(7):1552–1565

    Article  Google Scholar 

  • Kim H, Park H (2007) Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis. Bioinformatics 23(12):1495–1502

    Article  Google Scholar 

  • Kundu MK, Chowdhury M, Banerjee M (2012) Interactive image retrieval using M-band wavelet, earth mover’s distance and fuzzy relevance feedback. International Journal of Machine Learning and Cybernetics 3(4):285–296

    Article  Google Scholar 

  • J-m L, Y-t Q (2011) Clustering-based hyperspectral band selection using sparse nonnegative matrix factorization. Journal of Zhejiang University SCIENCE C 12(7):542–549

    Article  Google Scholar 

  • Li L, Zhang Y (2009) SENSC. A stable efficient algorithm for nonnegative sparse coding Acta Automatica Sinica 35(10):1257–1271

    Google Scholar 

  • Matlab 2013b (2013). Natick, MA: Mathworks. http://www.mathworks.com

  • Melgani F, Bruzzone L (2004) Classification of hyperspectral remote sensing images with support vector machines IEEE Transactions on Geoscience and Remote Sensing 42:1778–1790

    Google Scholar 

  • Morup M, Madsen KH, Hansen LK Approximate L0 constrained non-negative matrix and tensor factorization. Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS 2008) 1328–1331

  • Murphy RJ, Monteiro ST (2013) Mapping the distribution of ferric iron minerals on a vertical mine face using derivative analysis of hyperspectral imagery (430–970 nm). ISPRS J Photogramm Remote Sens 75:29–39

    Article  Google Scholar 

  • Peharz R, Pernkopf F (2012) Sparse nonnegative matrix factorization with L0-constraints. Neurocomputing 80:38–46

    Article  Google Scholar 

  • Pele O, Werman M Fast and robust earth mover's distances (2009). Proceddings of 2009 I.E. 12th international conference on Computer vision 460–467

  • Qian Y, Yao F, Jia S (2009) Band selection for hyperspectral imagery using affinity propagation. IET Comput Vis 3(4):213–222

    Article  Google Scholar 

  • Ramirez C, Kreinovich V, Argaez M (2013) Why L1 Is a Good Approximation to L0. A Geometric Explanation Journal of Uncertain Systems 7(3):203–207

    Google Scholar 

  • Ren Z, Yuan J, Zhang Z (2011) Robust hand gesture recognition based on finger-earth mover's distance with a commodity depth camera. Proceedings of the 19th ACM international conference on Multimedia 1093–1096

  • Rubner Y, Tomasi C (2000) Perceptual metrics for image database navigation vol 1. Springer

  • Sandler R, Lindenbaum M (2011) Nonnegative matrix factorization with Earth mover's distance metric for image analysis IEEE Transactions on Pattern. Analysis and Machine Intelligence 33(8):1590–1602

    Article  Google Scholar 

  • Shi B, Chen N, Sun W (2014) Sparse Nonnegative Matrix Factorization for Hyperspectral Optimal Band Selection Acta Geodaetica et Cartographica Sinica 42(3):351–358 [in Chinese]

    Google Scholar 

  • Steinwart I, Christmann A (2008) Support vector machines. Springer, Verlag

    Google Scholar 

  • Sun W, Halevy A, Benedetto J, Czaja W, Liu C, Wu H, Shi B, Li W (2014) UL-Isomap based nonlinear dimensionality reduction for hyperspectral imagery classification ISPRS. Journal of Photogrammetry and Remote Sensing 89:25–36

    Article  Google Scholar 

  • Tong X, Xie H, Weng Q (2013) Urban land cover classification with airborne hyperspectral data: what features to Use? IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 99:1–12

    Google Scholar 

  • Wang T, Du B, Zhang L (2013) A kernel-based target-constrained interference-minimized filter for hyperspectral sub-pixel target detection. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 6:626–637

    Article  Google Scholar 

  • Wang Y-X, Zhang Y-J (2013) Nonnegative matrix factorization. A comprehensive review IEEE Transactions on Knowledge and Data Engineering 25(6):1336–1353

    Article  Google Scholar 

  • Wen J, Tian Z, Liu X, Lin W (2013) Neighborhood preserving orthogonal. PNMF feature extraction for hyperspectral image classification IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 6(2):759–768

    Article  Google Scholar 

  • Wen J, Zhao Y, Zhang X, Yan W, Lin W (2014) Local discriminant non-negative matrix factorization feature extraction for hyperspectral image classification. Int J Remote Sens 35(13):5073–5093

    Article  Google Scholar 

  • Xia W, Wang B, Zhang L (2013) Band selection for hyperspectral imagery: a new approach based on complex networks. IEEE Geosci Remote Sens Lett 10(5):1229–1233

    Article  Google Scholar 

  • Xiao Z, Bourennane S (2014) Constrained nonnegative matrix factorization and hyperspectral image dimensionality reduction. Remote Sensing Letters 5(1):46–54

    Article  Google Scholar 

  • Yang H, Du Q, Su H, Sheng Y (2011a) An efficient method for supervised hyperspectral band selection. IEEE Geosci Remote Sens Lett 8(1):138–142

    Article  Google Scholar 

  • Yang Z, Zhou G, Xie S, Ding S, Yang J-M, Zhang J (2011b) Blind spectral unmixing based on sparse nonnegative matrix factorization. IEEE Trans Image Process 20(4):1112–1125

    Article  Google Scholar 

  • Zhu F, Wang Y, Xiang S, Fan B, Pan C (2014) Structured Sparse Method for Hyperspectral Unmixing ISPRS Journal of Photogrammetry and Remote Sensing 88:101–118

    Article  Google Scholar 

Download references

Acknowledgment

This work was funded by National Nature Science Foundation of China (41401389, 41171073, 41471004), by Research Project of Zhejiang Educational Committee (Y201430436), by Ningbo Natural Science Foundation (2014A610173), by Natural Science Foundation of Zhejiang Province(Y5110321), by the Discipline Construction Project of Ningbo University (ZX2014000400) and by the K. C. Wong Magna Fund in Ningbo University. The authors would like to thank the editor and referees for their suggestions which improved the manuscript.

Author information

Authors and Affiliations

  1. College of Architectural Engineering, Civil Engineering and Environment, Ningbo University, 818 Fenghua Rd, 50# Postbox, Ningbo, Zhejiang, China, 315211

    Weiwei Sun & Jialin Li

  2. Institute of Urban Development, Shanghai Normal University, 100 Guilin Rd, Shanghai, China, 200234

    Weiyue Li

  3. The Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin, Austin, USA, 78712

    Yenming Mark Lai

Authors
  1. Weiwei Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weiyue Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jialin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yenming Mark Lai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Weiwei Sun.

Additional information

Communicated by: H. A. Babaie

Electronic supplementary material

Below is the link to the electronic supplementary material.

ESM 1

(DOC 913 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, W., Li, W., Li, J. et al. Band selection using sparse nonnegative matrix factorization with the thresholded Earth’s mover distance for hyperspectral imagery classification. Earth Sci Inform 8, 907–918 (2015). https://doi.org/10.1007/s12145-014-0201-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12145-014-0201-3

Keywords

Search

Navigation