Advertisement

A Novel Geometric Mean Feature Space Discriminant Analysis Method for Hyperspectral Image Feature Extraction

  • Li Li
  • Hongwei GeEmail author
  • Jianqiang GaoEmail author
  • Yixin Zhang
  • Yubing Tong
  • Jun Sun
Article
  • 27 Downloads

Abstract

Hyperspectral image contains abundant spectral information with hundreds of spectral continuous bands that allow us to distinguish different classes with more details. However, the number of available training samples is limited and the high dimensionality of hyperspectral data increases the computational complexity and even also may degrade the classification accuracy. In addition, the bottom line is that only original spectral is difficult to well represent or reveal intrinsic geometry structure of the hyperspectral image. Thus, feature extraction is an important step before classification of high dimensional data. In this paper, we proposed a novel supervised feature extraction method that uses a new geometric mean vector to construct geometric between-class scatter matrix (\(S_b^G\)) and geometric within-class scatter matrix (\(S_w^G\)) instead of traditional mean vector of state-of-the-art methods. The geometric mean vector not only can reveal intrinsic geometry structure of the hyperspectral image, but also can improve the ability of learning nonlinear correlation features by maximum likelihood classification (MLC). The proposed method is called geometric mean feature space discriminant analysis (GmFSDA) that uses three measures to produce the extracted features. GmFSDA, at first, maximizes the geometric between-spectral scatter matrix to increase the difference between extracted features. In the second step of GmFSDA, maximizes the between-class scatter and minimizes the within-class scatter simultaneously. The experimental results on three real-world hyperspectral image datasets show the better performance of GmFSDA in comparison with other feature extraction methods in small sample size situation by using MLC.

Keywords

Hyperspectral image Feature extraction Geometric mean vector Feature space discriminant analysis Classification 

Mathematics Subject Classification

68T10 68U10 

Notes

Acknowledgements

This work is partially supported by the Graduate Innovation Foundation of Jiangsu Province under Grant No. KYLX16_0781, the 111 Project under Grant No. B12018, and PAPD of Jiangsu Higher Education Institutions, China, and the Doctoral Research Foundation of Jining Medical University under Grant No. 2018JYQD03, and a Project of Shandong Province Higher Educational Science and Technology Program under Grant No. J18KA217.

References

  1. 1.
    David L (2002) Hyperspectral image data analysis as a high dimensional signal processing problem. IEEE Signal Process Mag 19(1):17–28MathSciNetCrossRefGoogle Scholar
  2. 2.
    Hosseini SA, Ghassemian H (2016) Hyperspectral data feature extraction using rational function curve fitting. Int J Pattern Recognit Artif Intell 30(01):1650001.  https://doi.org/10.1142/S0218001416500014 MathSciNetCrossRefGoogle Scholar
  3. 3.
    Hosseini SA, Ghassemian H (2016) Rational function approximation for feature reduction in hyperspectral data. Remote Sens Lett 7(2):101–110CrossRefGoogle Scholar
  4. 4.
    Imani M, Ghassemian H (2017) High-dimensional image data feature extraction by double discriminant embedding. Pattern Anal Appl 20(2):473–484MathSciNetCrossRefGoogle Scholar
  5. 5.
    Imani M, Ghassemian H (2016) Binary coding based feature extraction in remote sensing high dimensional data. Inf Sci 342:191–208CrossRefGoogle Scholar
  6. 6.
    Jia X, Kuo BC, Crawford MM (2013) Feature mining for hyperspectral image classification. Proc IEEE 101(3):676–697CrossRefGoogle Scholar
  7. 7.
    Maji P, Garai P (2013) Fuzzy-rough simultaneous attribute selection and feature extraction algorithm. IEEE Trans Cybern 43(4):1166–1177CrossRefGoogle Scholar
  8. 8.
    Li S, Qiu J, Yang X et al (2014) A novel approach to hyperspectral band selection based on spectral shape similarity analysis and fast branch and bound search. Eng Appl Artif Intell 27:241–250CrossRefGoogle Scholar
  9. 9.
    Esfandian N, Razzazi F, Behrad A (2012) A clustering based feature selection method in spectro-temporal domain for speech recognition. Eng Appl Artif Intell 25(6):1194–1202CrossRefGoogle Scholar
  10. 10.
    Dernoncourt D, Hanczar B, Zucker JD (2014) Analysis of feature selection stability on high dimension and small sample data. Comput Stat Data Anal 71:681–693MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Zhang L, Zhong Y, Huang B et al (2007) Dimensionality reduction based on clonal selection for hyperspectral imagery. IEEE Trans Geosci Remote Sens 45(12):4172–4186CrossRefGoogle Scholar
  12. 12.
    Hotelling H (1933) Analysis of a complex of statistical variables into principal components. Educ Psychol 24(6):417–441CrossRefzbMATHGoogle Scholar
  13. 13.
    Liao W, Pizurica A, Scheunders P et al (2013) Semisupervised local discriminant analysis for feature extraction in hyperspectral images. IEEE Trans Geosci Remote Sens 51(1):184–198CrossRefGoogle Scholar
  14. 14.
    Plaza A, Martinez P, Plaza J et al (2005) Dimensionality reduction and classification of hyperspectral image data using sequences of extended morphological transformations. IEEE Transn Geosci Remote Sens 43(3):466–479CrossRefGoogle Scholar
  15. 15.
    Fauvel M, Chanussot J, Benediktsson JA (2009) Kernel principal component analysis for the classification of hyperspectral remote sensing data over urban areas. EURASIP J Adv Signal Process. Article ID 783194.  https://doi.org/10.1155/2009/783194
  16. 16.
    Villa A, Chanussot J, Benediktsson JA et al (2013) Unsupervised methods for the classification of hyperspectral images with low spatial resolution. Pattern Recognit 46(6):1556–1568CrossRefGoogle Scholar
  17. 17.
    Chang CI, Ren H (2000) An experiment-based quantitative and comparative analysis of target detection and image classification algorithms for hyperspectral imagery. IEEE Trans Geosci Remote Sens 38(2):1044–1063CrossRefGoogle Scholar
  18. 18.
    Kuo BC, Landgrebe DA (2004) Nonparametric weighted feature extraction for classification. IEEE Trans Geosci Remote Sens 42(5):1096–1105CrossRefGoogle Scholar
  19. 19.
    Scholkopf B, Smola A, Muller KR (1998) Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput 10:1299–1319CrossRefGoogle Scholar
  20. 20.
    Baudat G, Anouar F (2000) Generalized discriminant analysis using a kernel approach. Neural Comput 12(10):2385–2404CrossRefGoogle Scholar
  21. 21.
    Chen S, Zhang D (2011) Semisupervised dimensionality reduction with pairwise constraints for hyperspectral image classification. IEEE Geosci Remote Sens Lett 8(2):369–373CrossRefGoogle Scholar
  22. 22.
    He X, Niyogi P (2004) Locality preserving projections. In: Advances in neural information processing systems, pp 153–160Google Scholar
  23. 23.
    Zhang T, Yang J, Zhao D et al (2007) Linear local tangent space alignment and application to face recognition. Neurocomputing 70(7):1547–1553CrossRefGoogle Scholar
  24. 24.
    He X, Cai D, Han J (2008) Learning a maximum margin subspace for image retrieval. IEEE Trans Knowl Data Eng 20(2):189–201CrossRefGoogle Scholar
  25. 25.
    Yang M, Zhang L, Chi-Keung Shiu S, Zhang Z (2012) Monogenic binary coding: an efficient local feature extraction approach to face recognition. IEEE Trans Inf Forensics Secur 7:1738–1751CrossRefGoogle Scholar
  26. 26.
    Zhou Y, Peng J, Chen CLP (2015) Dimension reduction using spatial and spectral regularized local discriminant embedding for hyperspectral image classification. IEEE Trans Geosci Remote Sens 53:1082–1095CrossRefGoogle Scholar
  27. 27.
    Li L, Ge H, Gao J (2017) A spectral-spatial kernel-based method for hyperspectral imagery classification. Adv Sp Res 59(4):954–967CrossRefGoogle Scholar
  28. 28.
    Gao J, Xu L (2016) A novel spatial analysis method for remote sensing image classification. Neural Process Lett 43(3):805–821CrossRefGoogle Scholar
  29. 29.
    Gao J, Xu L, Shen J et al (2015) A novel information transferring approach for the classification of remote sensing images. EURASIP J Adv Signal Process 2015(1):38CrossRefGoogle Scholar
  30. 30.
    Gao J, Xu L, Huang F (2016) A spectral-textural kernel-based classification method of remotely sensed images. Neural Comput Appl 27(2):431–446CrossRefGoogle Scholar
  31. 31.
    Gao J, Xu L (2015) An efficient method to solve the classification problem for remote sensing image. AEU-Int J Electron Commun 69(1):198–205CrossRefGoogle Scholar
  32. 32.
    Gao J, Xu L, Shi A et al (2014) A kernel-based block matrix decomposition approach for the classification of remotely sensed images. Appl Math Comput 228:531–545MathSciNetzbMATHGoogle Scholar
  33. 33.
    Hosseini A, Ghassemian H (2012) Classification of hyperspectral and multispectral images by using fractal dimension of spectral response curve. In: 2012 20th Iranian conference on electrical engineering (ICEE). IEEE, pp 1452–1457Google Scholar
  34. 34.
    Hosseini SA, Ghassemian H (2013) A new hyperspectral image classification approach using fractal dimension of spectral response curve. In: 2013 21st Iranian conference on electrical engineering (ICEE). IEEE, pp 1–6Google Scholar
  35. 35.
    Li L, Ge H, Gao J (2018) Hyperspectral image feature extraction using maclaurin series function curve fitting. Neural Process Lett.  https://doi.org/10.1007/s11063-018-9825-5 Google Scholar
  36. 36.
    Imani M, Ghassemian H (2015) Feature space discriminant analysis for hyperspectral data feature reduction. ISPRS J Photogramm Remote Sens 102:1–13CrossRefGoogle Scholar
  37. 37.
    Elton EJ, Gruber MJ, Brown SJ et al (2009) Modern portfolio theory and investment analysis. Wiley, HobokenGoogle Scholar
  38. 38.
    Rietz HL (1916) The mathematical theory of probabilities. Science 43(1121):896–897CrossRefGoogle Scholar
  39. 39.
    Chen LF, Liao HYM, Ko MT et al (2000) A new LDA-based face recognition system which can solve the small sample size problem. Pattern Recognit 33(10):1713–1726CrossRefGoogle Scholar
  40. 40.
    Purdue Research Foundation, Hyperspectral images by multiSpec (2015). https://engineering.purdue.edu/~biehl/MultiSpec/
  41. 41.
    Universidad-del-Pais-Vasco, Hyperspectral remote sensing scenes (2014). http://www.ehu.eus/ccwintco/index.php?title=Hyperspectral_Remote_Sensing_Scenes
  42. 42.
    Zhang L, Zhang L, Du B et al (2019) Hyperspectral image unsupervised classification by robust manifold matrix factorization. Inf Sci 485:154–169MathSciNetCrossRefGoogle Scholar
  43. 43.
    Zhang L, Zhang L, Tao D et al (2011) On combining multiple features for hyperspectral remote sensing image classification. IEEE Trans Geosci Remote Sens 50(3):879–893CrossRefGoogle Scholar
  44. 44.
    Zhang L, Zhang L, Tao D et al (2013) A modified stochastic neighbor embedding for multi-feature dimension reduction of remote sensing images. ISPRS J Photogramm Remote Sens 83:30–39CrossRefGoogle Scholar
  45. 45.
    Zhang Q, Zhang L, Zhang L et al (2015) Ensemble manifold regularized sparse low-rank approximation for multiview feature embedding. Pattern Recognit 48(10):3102–3112CrossRefGoogle Scholar
  46. 46.
    Zhang L, Zhang Q, Du B et al (2016) Simultaneous spectral-spatial feature selection and extraction for hyperspectral images. IEEE Trans Cybern 48(1):16–28CrossRefGoogle Scholar
  47. 47.
    Zhu X, Zhang L, Zhang L et al (2016) Multidomain subspace classification for hyperspectral images. IEEE Trans Geosci Remote Sens 54(10):6138–6150CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Jiangsu Provincial Engineering Laboratory of Pattern Recognition and Computational IntelligenceJiangnan UniversityWuxiChina
  2. 2.School of Internet of ThingsJiangnan UniversityWuxiChina
  3. 3.School of Medical Information EngineeringJining Medical UniversityRizhaoChina
  4. 4.School of ScienceJiangnan UniversityWuxiChina
  5. 5.Medical Image Processing Group, Department of RadiologyUniversity of PennsylvaniaPhiladelphiaUSA

Personalised recommendations