Abstract

A semisupervised deformed kernel function, using low-rank representation with consideration of local geometrical structure of data, is presented for the classification of hyperspectral images. The proposed method incorporates the wealth of unlabeled information to deal with the limited labeled samples situation as a common case in HSIs applications. The proposed kernel needs to be computed before training the classifier, e.g., a support vector machine, and it relies on combining the standard radial basis function kernel based on labeled information and the low-rank representation kernel obtained using all available (labeled and unlabeled) information. The low-rank representation kernel can overcome the difficulties of clustering methods that are used to construct the kernels such as bagged kernel and multi-scale bagged kernel. The experimental results of two well-known HSIs data sets demonstrate the effectiveness of the proposed method in comparison with cluster kernels obtained using traditional clustering methods and graph learning methods.

© 2020 Optical Society of America

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References

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    [Crossref]

2019 (2)

D. H. Foster and K. Amano, “Hyperspectral imaging in color vision research: tutorial,” J. Opt. Soc. Am. A 36, 606–627 (2019).
[Crossref]

X. Jin, Y. Gu, and T. Liu, “Intrinsic image recovery from remote sensing hyperspectral images,” IEEE Trans. Geosci. Remote Sens. 57, 224–238 (2019).
[Crossref]

2018 (1)

S. A. Ahmadi, N. Mehrshad, and S. M. Razavi, “Semisupervised dimensionality reduction for hyperspectral images based on the combination of semisupervised learning and metric learning,” Imag. Sci. J. 66, 320–327 (2018).
[Crossref]

2017 (4)

L. Pan, H. Li, H. Meng, W. Li, Q. Du, and W. J. Emery, “Hyperspectral image classification via low-rank and sparse representation with spectral consistency constraint,” IEEE Geosci. Remote Sens. Lett. 14, 2117–2121 (2017).
[Crossref]

L. Fei, Y. Xu, X. Fang, and J. Yang, “Low rank representation with adaptive distance penalty for semi-supervised subspace classification,” Pattern Recogn. 67, 252–262 (2017).
[Crossref]

P. Li, J. Yu, M. Wang, L. Zhang, D. Cai, and X. Li, “Constrained low-rank learning using least squares-based regularization,” IEEE Trans. Cybern. 47, 4250–4262 (2017).
[Crossref]

X. Wang and F. Liu, “Weighted low-rank representation-based dimension reduction for hyperspectral image classification,” IEEE Geosci. Remote Sens. Lett. 14, 1938–1942 (2017).
[Crossref]

2016 (3)

Y. Chen, H. Jiang, C. Li, X. Jia, and P. Ghamisi, “Deep feature extraction and classification of hyperspectral images based on convolutional neural networks,” IEEE Trans. Geosci. Remote Sens. 54, 6232–6251 (2016).
[Crossref]

R. Luo, W. Liao, X. Huang, Y. Pi, and W. Philips, “Feature extraction of hyperspectral images with semisupervised graph learning,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 9, 4389–4399 (2016).
[Crossref]

W. Du, M. Lv, Q. Hou, and L. Jing, “Semisupervised dimension reduction based on pairwise constraint propagation for hyperspectral images,” IEEE Geosci. Remote Sens. Lett. 13, 1880–1884 (2016).
[Crossref]

2015 (6)

M. Borhani and H. Ghassemian, “Kernel multivariate spectral–spatial analysis of hyperspectral data,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 8, 2418–2426 (2015).
[Crossref]

L. Fang, S. Li, X. Kang, and J. A. Benediktsson, “Spectral–spatial classification of hyperspectral images with a superpixel-based discriminative sparse model,” IEEE Trans. Geosci. Remote Sens. 53, 4186–4201 (2015).
[Crossref]

Z. Xue, P. Du, J. Li, and H. Su, “Simultaneous sparse graph embedding for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 53, 6114–6133 (2015).
[Crossref]

A. Soltani-Farani, H. R. Rabiee, and S. A. Hosseini, “Spatial-aware dictionary learning for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 53, 527–541 (2015).
[Crossref]

L. Huo, P. Tang, Z. Zhang, and D. Tuia, “Semisupervised classification of remote sensing images with hierarchical spatial similarity,” IEEE Geosci. Remote Sens. Lett. 12, 150–154 (2015).
[Crossref]

Y. Motai, “Kernel association for classification and prediction: a survey,” IEEE Trans. Neural Netw. Learn. Syst. 26, 208–223 (2015).
[Crossref]

2014 (4)

J. Chen and J. Yang, “Robust subspace segmentation via low-rank representation,” IEEE Trans. Cybern. 44, 1432–1445 (2014).
[Crossref]

J. Xia, J. Chanussot, P. Du, and X. He, “(Semi-) supervised probabilistic principal component analysis for hyperspectral remote sensing image classification,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 7, 2224–2236 (2014).
[Crossref]

E. Izquierdo-Verdiguier, L. Gómez-Chova, L. Bruzzone, and G. Camps-Valls, “Semisupervised kernel feature extraction for remote sensing image analysis,” IEEE Trans. Geosci. Remote Sens. 52, 5567–5578 (2014).
[Crossref]

P. Quesada-Barriuso, F. Argüello, and D. B. Heras, “Spectral–spatial classification of hyperspectral images using wavelets and extended morphological profiles,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 7, 1177–1185 (2014).
[Crossref]

2013 (5)

J. Li, P. R. Marpu, A. Plaza, J. M. Bioucas-Dias, and J. A. Benediktsson, “Generalized composite kernel framework for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 51, 4816–4829 (2013).
[Crossref]

J. Arenas-Garcia, K. B. Petersen, G. Camps-Valls, and L. K. Hansen, “Kernel multivariate analysis framework for supervised subspace learning: a tutorial on linear and kernel multivariate methods,” IEEE Signal Process. Mag. 30(4), 16–29 (2013).
[Crossref]

Y. Gu and K. Feng, “Optimized Laplacian SVM with distance metric learning for hyperspectral image classification,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 6, 1109–1117 (2013).
[Crossref]

X. Jia, B. Kuo, and M. M. Crawford, “Feature mining for hyperspectral image classification,” Proc. IEEE 101, 676–697 (2013).
[Crossref]

X. Lu, Y. Wang, and Y. Yuan, “Graph-regularized low-rank representation for destriping of hyperspectral images,” IEEE Trans. Geosci. Remote Sens. 51, 4009–4018 (2013).
[Crossref]

2012 (1)

W. Liao, R. Bellens, A. Pizurica, W. Philips, and Y. Pi, “Classification of hyperspectral data over urban areas using directional morphological profiles and semi-supervised feature extraction,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 5, 1177–1190 (2012).
[Crossref]

2010 (1)

E. J. Candes and Y. Plan, “Matrix completion with noise,” Proc. IEEE 98, 925–936 (2010).
[Crossref]

2009 (3)

E. J. Candès and B. Recht, “Exact matrix completion via convex optimization,” Found. Comput. Math. 9, 717–772 (2009).
[Crossref]

D. Tuia and G. Camps-Valls, “Semisupervised remote sensing image classification with cluster kernels,” IEEE Geosci. Remote Sens. Lett. 6, 224–228 (2009).
[Crossref]

B. Mojaradi, H. Abrishami-Moghaddam, M. J. V. Zoej, and R. P. W. Duin, “Dimensionality reduction of hyperspectral data via spectral feature extraction,” IEEE Trans. Geosci. Remote Sens. 47, 2091–2105 (2009).
[Crossref]

2007 (1)

S. Yang, S. Yan, C. Zhang, and X. Tang, “Bilinear analysis for kernel selection and nonlinear feature extraction,” IEEE Trans. Neural Netw. 18, 1442–1452 (2007).
[Crossref]

2006 (2)

M. Belkin, P. Niyogi, and V. Sindhwani, “Manifold regularization: a geometric framework for learning from labeled and unlabeled examples,” J. Mach. Learn. Res. 7, 2399–2434 (2006).

L. Bruzzone, M. Chi, and M. Marconcini, “A novel transductive SVM for semisupervised classification of remote-sensing images,” IEEE Trans. Geosci. Remote Sens. 44, 3363–3373 (2006).
[Crossref]

2005 (1)

G. Camps-Valls and L. Bruzzone, “Kernel-based methods for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 43, 1351–1362 (2005).
[Crossref]

2004 (1)

F. Melgani and L. Bruzzone, “Classification of hyperspectral remote sensing images with support vector machines,” IEEE Trans. Geosci. Remote Sens. 42, 1778–1790 (2004).
[Crossref]

Abrishami-Moghaddam, H.

B. Mojaradi, H. Abrishami-Moghaddam, M. J. V. Zoej, and R. P. W. Duin, “Dimensionality reduction of hyperspectral data via spectral feature extraction,” IEEE Trans. Geosci. Remote Sens. 47, 2091–2105 (2009).
[Crossref]

Ahmadi, S. A.

S. A. Ahmadi, N. Mehrshad, and S. M. Razavi, “Semisupervised dimensionality reduction for hyperspectral images based on the combination of semisupervised learning and metric learning,” Imag. Sci. J. 66, 320–327 (2018).
[Crossref]

Amano, K.

Arenas-Garcia, J.

J. Arenas-Garcia, K. B. Petersen, G. Camps-Valls, and L. K. Hansen, “Kernel multivariate analysis framework for supervised subspace learning: a tutorial on linear and kernel multivariate methods,” IEEE Signal Process. Mag. 30(4), 16–29 (2013).
[Crossref]

Argüello, F.

P. Quesada-Barriuso, F. Argüello, and D. B. Heras, “Spectral–spatial classification of hyperspectral images using wavelets and extended morphological profiles,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 7, 1177–1185 (2014).
[Crossref]

Belkin, M.

M. Belkin, P. Niyogi, and V. Sindhwani, “Manifold regularization: a geometric framework for learning from labeled and unlabeled examples,” J. Mach. Learn. Res. 7, 2399–2434 (2006).

Bellens, R.

W. Liao, R. Bellens, A. Pizurica, W. Philips, and Y. Pi, “Classification of hyperspectral data over urban areas using directional morphological profiles and semi-supervised feature extraction,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 5, 1177–1190 (2012).
[Crossref]

Benediktsson, J. A.

L. Fang, S. Li, X. Kang, and J. A. Benediktsson, “Spectral–spatial classification of hyperspectral images with a superpixel-based discriminative sparse model,” IEEE Trans. Geosci. Remote Sens. 53, 4186–4201 (2015).
[Crossref]

J. Li, P. R. Marpu, A. Plaza, J. M. Bioucas-Dias, and J. A. Benediktsson, “Generalized composite kernel framework for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 51, 4816–4829 (2013).
[Crossref]

Bioucas-Dias, J. M.

J. Li, P. R. Marpu, A. Plaza, J. M. Bioucas-Dias, and J. A. Benediktsson, “Generalized composite kernel framework for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 51, 4816–4829 (2013).
[Crossref]

Borhani, M.

M. Borhani and H. Ghassemian, “Kernel multivariate spectral–spatial analysis of hyperspectral data,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 8, 2418–2426 (2015).
[Crossref]

Bruzzone, L.

E. Izquierdo-Verdiguier, L. Gómez-Chova, L. Bruzzone, and G. Camps-Valls, “Semisupervised kernel feature extraction for remote sensing image analysis,” IEEE Trans. Geosci. Remote Sens. 52, 5567–5578 (2014).
[Crossref]

L. Bruzzone, M. Chi, and M. Marconcini, “A novel transductive SVM for semisupervised classification of remote-sensing images,” IEEE Trans. Geosci. Remote Sens. 44, 3363–3373 (2006).
[Crossref]

G. Camps-Valls and L. Bruzzone, “Kernel-based methods for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 43, 1351–1362 (2005).
[Crossref]

F. Melgani and L. Bruzzone, “Classification of hyperspectral remote sensing images with support vector machines,” IEEE Trans. Geosci. Remote Sens. 42, 1778–1790 (2004).
[Crossref]

Cai, D.

P. Li, J. Yu, M. Wang, L. Zhang, D. Cai, and X. Li, “Constrained low-rank learning using least squares-based regularization,” IEEE Trans. Cybern. 47, 4250–4262 (2017).
[Crossref]

Camps-Valls, G.

E. Izquierdo-Verdiguier, L. Gómez-Chova, L. Bruzzone, and G. Camps-Valls, “Semisupervised kernel feature extraction for remote sensing image analysis,” IEEE Trans. Geosci. Remote Sens. 52, 5567–5578 (2014).
[Crossref]

J. Arenas-Garcia, K. B. Petersen, G. Camps-Valls, and L. K. Hansen, “Kernel multivariate analysis framework for supervised subspace learning: a tutorial on linear and kernel multivariate methods,” IEEE Signal Process. Mag. 30(4), 16–29 (2013).
[Crossref]

D. Tuia and G. Camps-Valls, “Semisupervised remote sensing image classification with cluster kernels,” IEEE Geosci. Remote Sens. Lett. 6, 224–228 (2009).
[Crossref]

G. Camps-Valls and L. Bruzzone, “Kernel-based methods for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 43, 1351–1362 (2005).
[Crossref]

Candes, E. J.

E. J. Candes and Y. Plan, “Matrix completion with noise,” Proc. IEEE 98, 925–936 (2010).
[Crossref]

Candès, E. J.

E. J. Candès and B. Recht, “Exact matrix completion via convex optimization,” Found. Comput. Math. 9, 717–772 (2009).
[Crossref]

Chanussot, J.

J. Xia, J. Chanussot, P. Du, and X. He, “(Semi-) supervised probabilistic principal component analysis for hyperspectral remote sensing image classification,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 7, 2224–2236 (2014).
[Crossref]

Chen, J.

J. Chen and J. Yang, “Robust subspace segmentation via low-rank representation,” IEEE Trans. Cybern. 44, 1432–1445 (2014).
[Crossref]

Chen, Y.

Y. Chen, H. Jiang, C. Li, X. Jia, and P. Ghamisi, “Deep feature extraction and classification of hyperspectral images based on convolutional neural networks,” IEEE Trans. Geosci. Remote Sens. 54, 6232–6251 (2016).
[Crossref]

Chi, M.

L. Bruzzone, M. Chi, and M. Marconcini, “A novel transductive SVM for semisupervised classification of remote-sensing images,” IEEE Trans. Geosci. Remote Sens. 44, 3363–3373 (2006).
[Crossref]

Crawford, M. M.

X. Jia, B. Kuo, and M. M. Crawford, “Feature mining for hyperspectral image classification,” Proc. IEEE 101, 676–697 (2013).
[Crossref]

Du, P.

Z. Xue, P. Du, J. Li, and H. Su, “Simultaneous sparse graph embedding for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 53, 6114–6133 (2015).
[Crossref]

J. Xia, J. Chanussot, P. Du, and X. He, “(Semi-) supervised probabilistic principal component analysis for hyperspectral remote sensing image classification,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 7, 2224–2236 (2014).
[Crossref]

Du, Q.

L. Pan, H. Li, H. Meng, W. Li, Q. Du, and W. J. Emery, “Hyperspectral image classification via low-rank and sparse representation with spectral consistency constraint,” IEEE Geosci. Remote Sens. Lett. 14, 2117–2121 (2017).
[Crossref]

Du, W.

W. Du, M. Lv, Q. Hou, and L. Jing, “Semisupervised dimension reduction based on pairwise constraint propagation for hyperspectral images,” IEEE Geosci. Remote Sens. Lett. 13, 1880–1884 (2016).
[Crossref]

Duin, R. P. W.

B. Mojaradi, H. Abrishami-Moghaddam, M. J. V. Zoej, and R. P. W. Duin, “Dimensionality reduction of hyperspectral data via spectral feature extraction,” IEEE Trans. Geosci. Remote Sens. 47, 2091–2105 (2009).
[Crossref]

Emery, W. J.

L. Pan, H. Li, H. Meng, W. Li, Q. Du, and W. J. Emery, “Hyperspectral image classification via low-rank and sparse representation with spectral consistency constraint,” IEEE Geosci. Remote Sens. Lett. 14, 2117–2121 (2017).
[Crossref]

Fang, L.

L. Fang, S. Li, X. Kang, and J. A. Benediktsson, “Spectral–spatial classification of hyperspectral images with a superpixel-based discriminative sparse model,” IEEE Trans. Geosci. Remote Sens. 53, 4186–4201 (2015).
[Crossref]

Fang, X.

L. Fei, Y. Xu, X. Fang, and J. Yang, “Low rank representation with adaptive distance penalty for semi-supervised subspace classification,” Pattern Recogn. 67, 252–262 (2017).
[Crossref]

Fei, L.

L. Fei, Y. Xu, X. Fang, and J. Yang, “Low rank representation with adaptive distance penalty for semi-supervised subspace classification,” Pattern Recogn. 67, 252–262 (2017).
[Crossref]

Feng, K.

Y. Gu and K. Feng, “Optimized Laplacian SVM with distance metric learning for hyperspectral image classification,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 6, 1109–1117 (2013).
[Crossref]

Foster, D. H.

Ghamisi, P.

Y. Chen, H. Jiang, C. Li, X. Jia, and P. Ghamisi, “Deep feature extraction and classification of hyperspectral images based on convolutional neural networks,” IEEE Trans. Geosci. Remote Sens. 54, 6232–6251 (2016).
[Crossref]

Ghassemian, H.

M. Borhani and H. Ghassemian, “Kernel multivariate spectral–spatial analysis of hyperspectral data,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 8, 2418–2426 (2015).
[Crossref]

Gómez-Chova, L.

E. Izquierdo-Verdiguier, L. Gómez-Chova, L. Bruzzone, and G. Camps-Valls, “Semisupervised kernel feature extraction for remote sensing image analysis,” IEEE Trans. Geosci. Remote Sens. 52, 5567–5578 (2014).
[Crossref]

Gu, Y.

X. Jin, Y. Gu, and T. Liu, “Intrinsic image recovery from remote sensing hyperspectral images,” IEEE Trans. Geosci. Remote Sens. 57, 224–238 (2019).
[Crossref]

Y. Gu and K. Feng, “Optimized Laplacian SVM with distance metric learning for hyperspectral image classification,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 6, 1109–1117 (2013).
[Crossref]

Hansen, L. K.

J. Arenas-Garcia, K. B. Petersen, G. Camps-Valls, and L. K. Hansen, “Kernel multivariate analysis framework for supervised subspace learning: a tutorial on linear and kernel multivariate methods,” IEEE Signal Process. Mag. 30(4), 16–29 (2013).
[Crossref]

He, X.

J. Xia, J. Chanussot, P. Du, and X. He, “(Semi-) supervised probabilistic principal component analysis for hyperspectral remote sensing image classification,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 7, 2224–2236 (2014).
[Crossref]

Heras, D. B.

P. Quesada-Barriuso, F. Argüello, and D. B. Heras, “Spectral–spatial classification of hyperspectral images using wavelets and extended morphological profiles,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 7, 1177–1185 (2014).
[Crossref]

Hosseini, S. A.

A. Soltani-Farani, H. R. Rabiee, and S. A. Hosseini, “Spatial-aware dictionary learning for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 53, 527–541 (2015).
[Crossref]

Hou, Q.

W. Du, M. Lv, Q. Hou, and L. Jing, “Semisupervised dimension reduction based on pairwise constraint propagation for hyperspectral images,” IEEE Geosci. Remote Sens. Lett. 13, 1880–1884 (2016).
[Crossref]

Huang, X.

R. Luo, W. Liao, X. Huang, Y. Pi, and W. Philips, “Feature extraction of hyperspectral images with semisupervised graph learning,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 9, 4389–4399 (2016).
[Crossref]

Huo, L.

L. Huo, P. Tang, Z. Zhang, and D. Tuia, “Semisupervised classification of remote sensing images with hierarchical spatial similarity,” IEEE Geosci. Remote Sens. Lett. 12, 150–154 (2015).
[Crossref]

Izquierdo-Verdiguier, E.

E. Izquierdo-Verdiguier, L. Gómez-Chova, L. Bruzzone, and G. Camps-Valls, “Semisupervised kernel feature extraction for remote sensing image analysis,” IEEE Trans. Geosci. Remote Sens. 52, 5567–5578 (2014).
[Crossref]

Jia, X.

Y. Chen, H. Jiang, C. Li, X. Jia, and P. Ghamisi, “Deep feature extraction and classification of hyperspectral images based on convolutional neural networks,” IEEE Trans. Geosci. Remote Sens. 54, 6232–6251 (2016).
[Crossref]

X. Jia, B. Kuo, and M. M. Crawford, “Feature mining for hyperspectral image classification,” Proc. IEEE 101, 676–697 (2013).
[Crossref]

Jiang, H.

Y. Chen, H. Jiang, C. Li, X. Jia, and P. Ghamisi, “Deep feature extraction and classification of hyperspectral images based on convolutional neural networks,” IEEE Trans. Geosci. Remote Sens. 54, 6232–6251 (2016).
[Crossref]

Jin, X.

X. Jin, Y. Gu, and T. Liu, “Intrinsic image recovery from remote sensing hyperspectral images,” IEEE Trans. Geosci. Remote Sens. 57, 224–238 (2019).
[Crossref]

Jing, L.

W. Du, M. Lv, Q. Hou, and L. Jing, “Semisupervised dimension reduction based on pairwise constraint propagation for hyperspectral images,” IEEE Geosci. Remote Sens. Lett. 13, 1880–1884 (2016).
[Crossref]

Kang, X.

L. Fang, S. Li, X. Kang, and J. A. Benediktsson, “Spectral–spatial classification of hyperspectral images with a superpixel-based discriminative sparse model,” IEEE Trans. Geosci. Remote Sens. 53, 4186–4201 (2015).
[Crossref]

Kuo, B.

X. Jia, B. Kuo, and M. M. Crawford, “Feature mining for hyperspectral image classification,” Proc. IEEE 101, 676–697 (2013).
[Crossref]

Li, C.

Y. Chen, H. Jiang, C. Li, X. Jia, and P. Ghamisi, “Deep feature extraction and classification of hyperspectral images based on convolutional neural networks,” IEEE Trans. Geosci. Remote Sens. 54, 6232–6251 (2016).
[Crossref]

Li, H.

L. Pan, H. Li, H. Meng, W. Li, Q. Du, and W. J. Emery, “Hyperspectral image classification via low-rank and sparse representation with spectral consistency constraint,” IEEE Geosci. Remote Sens. Lett. 14, 2117–2121 (2017).
[Crossref]

Li, J.

Z. Xue, P. Du, J. Li, and H. Su, “Simultaneous sparse graph embedding for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 53, 6114–6133 (2015).
[Crossref]

J. Li, P. R. Marpu, A. Plaza, J. M. Bioucas-Dias, and J. A. Benediktsson, “Generalized composite kernel framework for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 51, 4816–4829 (2013).
[Crossref]

Li, P.

P. Li, J. Yu, M. Wang, L. Zhang, D. Cai, and X. Li, “Constrained low-rank learning using least squares-based regularization,” IEEE Trans. Cybern. 47, 4250–4262 (2017).
[Crossref]

Li, S.

L. Fang, S. Li, X. Kang, and J. A. Benediktsson, “Spectral–spatial classification of hyperspectral images with a superpixel-based discriminative sparse model,” IEEE Trans. Geosci. Remote Sens. 53, 4186–4201 (2015).
[Crossref]

Li, W.

L. Pan, H. Li, H. Meng, W. Li, Q. Du, and W. J. Emery, “Hyperspectral image classification via low-rank and sparse representation with spectral consistency constraint,” IEEE Geosci. Remote Sens. Lett. 14, 2117–2121 (2017).
[Crossref]

Li, X.

P. Li, J. Yu, M. Wang, L. Zhang, D. Cai, and X. Li, “Constrained low-rank learning using least squares-based regularization,” IEEE Trans. Cybern. 47, 4250–4262 (2017).
[Crossref]

Liao, W.

R. Luo, W. Liao, X. Huang, Y. Pi, and W. Philips, “Feature extraction of hyperspectral images with semisupervised graph learning,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 9, 4389–4399 (2016).
[Crossref]

W. Liao, R. Bellens, A. Pizurica, W. Philips, and Y. Pi, “Classification of hyperspectral data over urban areas using directional morphological profiles and semi-supervised feature extraction,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 5, 1177–1190 (2012).
[Crossref]

Lin, Z.

Z. Lin, R. Liu, and Z. Su, “Linearized alternating direction method with adaptive penalty for low-rank representation,” in 24th International Conference on Neural Information Processing Systems, Granada, Spain (Curran Associates Inc., 2011), pp. 612–620.

Liu, F.

X. Wang and F. Liu, “Weighted low-rank representation-based dimension reduction for hyperspectral image classification,” IEEE Geosci. Remote Sens. Lett. 14, 1938–1942 (2017).
[Crossref]

Liu, R.

Z. Lin, R. Liu, and Z. Su, “Linearized alternating direction method with adaptive penalty for low-rank representation,” in 24th International Conference on Neural Information Processing Systems, Granada, Spain (Curran Associates Inc., 2011), pp. 612–620.

Liu, T.

X. Jin, Y. Gu, and T. Liu, “Intrinsic image recovery from remote sensing hyperspectral images,” IEEE Trans. Geosci. Remote Sens. 57, 224–238 (2019).
[Crossref]

Lu, X.

X. Lu, Y. Wang, and Y. Yuan, “Graph-regularized low-rank representation for destriping of hyperspectral images,” IEEE Trans. Geosci. Remote Sens. 51, 4009–4018 (2013).
[Crossref]

Luo, R.

R. Luo, W. Liao, X. Huang, Y. Pi, and W. Philips, “Feature extraction of hyperspectral images with semisupervised graph learning,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 9, 4389–4399 (2016).
[Crossref]

Lv, M.

W. Du, M. Lv, Q. Hou, and L. Jing, “Semisupervised dimension reduction based on pairwise constraint propagation for hyperspectral images,” IEEE Geosci. Remote Sens. Lett. 13, 1880–1884 (2016).
[Crossref]

Marconcini, M.

L. Bruzzone, M. Chi, and M. Marconcini, “A novel transductive SVM for semisupervised classification of remote-sensing images,” IEEE Trans. Geosci. Remote Sens. 44, 3363–3373 (2006).
[Crossref]

Marpu, P. R.

J. Li, P. R. Marpu, A. Plaza, J. M. Bioucas-Dias, and J. A. Benediktsson, “Generalized composite kernel framework for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 51, 4816–4829 (2013).
[Crossref]

Mehrshad, N.

S. A. Ahmadi, N. Mehrshad, and S. M. Razavi, “Semisupervised dimensionality reduction for hyperspectral images based on the combination of semisupervised learning and metric learning,” Imag. Sci. J. 66, 320–327 (2018).
[Crossref]

Melgani, F.

F. Melgani and L. Bruzzone, “Classification of hyperspectral remote sensing images with support vector machines,” IEEE Trans. Geosci. Remote Sens. 42, 1778–1790 (2004).
[Crossref]

Meng, H.

L. Pan, H. Li, H. Meng, W. Li, Q. Du, and W. J. Emery, “Hyperspectral image classification via low-rank and sparse representation with spectral consistency constraint,” IEEE Geosci. Remote Sens. Lett. 14, 2117–2121 (2017).
[Crossref]

Mojaradi, B.

B. Mojaradi, H. Abrishami-Moghaddam, M. J. V. Zoej, and R. P. W. Duin, “Dimensionality reduction of hyperspectral data via spectral feature extraction,” IEEE Trans. Geosci. Remote Sens. 47, 2091–2105 (2009).
[Crossref]

Motai, Y.

Y. Motai, “Kernel association for classification and prediction: a survey,” IEEE Trans. Neural Netw. Learn. Syst. 26, 208–223 (2015).
[Crossref]

Niyogi, P.

M. Belkin, P. Niyogi, and V. Sindhwani, “Manifold regularization: a geometric framework for learning from labeled and unlabeled examples,” J. Mach. Learn. Res. 7, 2399–2434 (2006).

Pan, L.

L. Pan, H. Li, H. Meng, W. Li, Q. Du, and W. J. Emery, “Hyperspectral image classification via low-rank and sparse representation with spectral consistency constraint,” IEEE Geosci. Remote Sens. Lett. 14, 2117–2121 (2017).
[Crossref]

Petersen, K. B.

J. Arenas-Garcia, K. B. Petersen, G. Camps-Valls, and L. K. Hansen, “Kernel multivariate analysis framework for supervised subspace learning: a tutorial on linear and kernel multivariate methods,” IEEE Signal Process. Mag. 30(4), 16–29 (2013).
[Crossref]

Philips, W.

R. Luo, W. Liao, X. Huang, Y. Pi, and W. Philips, “Feature extraction of hyperspectral images with semisupervised graph learning,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 9, 4389–4399 (2016).
[Crossref]

W. Liao, R. Bellens, A. Pizurica, W. Philips, and Y. Pi, “Classification of hyperspectral data over urban areas using directional morphological profiles and semi-supervised feature extraction,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 5, 1177–1190 (2012).
[Crossref]

Pi, Y.

R. Luo, W. Liao, X. Huang, Y. Pi, and W. Philips, “Feature extraction of hyperspectral images with semisupervised graph learning,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 9, 4389–4399 (2016).
[Crossref]

W. Liao, R. Bellens, A. Pizurica, W. Philips, and Y. Pi, “Classification of hyperspectral data over urban areas using directional morphological profiles and semi-supervised feature extraction,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 5, 1177–1190 (2012).
[Crossref]

Pizurica, A.

W. Liao, R. Bellens, A. Pizurica, W. Philips, and Y. Pi, “Classification of hyperspectral data over urban areas using directional morphological profiles and semi-supervised feature extraction,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 5, 1177–1190 (2012).
[Crossref]

Plan, Y.

E. J. Candes and Y. Plan, “Matrix completion with noise,” Proc. IEEE 98, 925–936 (2010).
[Crossref]

Plaza, A.

J. Li, P. R. Marpu, A. Plaza, J. M. Bioucas-Dias, and J. A. Benediktsson, “Generalized composite kernel framework for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 51, 4816–4829 (2013).
[Crossref]

Quesada-Barriuso, P.

P. Quesada-Barriuso, F. Argüello, and D. B. Heras, “Spectral–spatial classification of hyperspectral images using wavelets and extended morphological profiles,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 7, 1177–1185 (2014).
[Crossref]

Rabiee, H. R.

A. Soltani-Farani, H. R. Rabiee, and S. A. Hosseini, “Spatial-aware dictionary learning for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 53, 527–541 (2015).
[Crossref]

Razavi, S. M.

S. A. Ahmadi, N. Mehrshad, and S. M. Razavi, “Semisupervised dimensionality reduction for hyperspectral images based on the combination of semisupervised learning and metric learning,” Imag. Sci. J. 66, 320–327 (2018).
[Crossref]

Recht, B.

E. J. Candès and B. Recht, “Exact matrix completion via convex optimization,” Found. Comput. Math. 9, 717–772 (2009).
[Crossref]

Sindhwani, V.

M. Belkin, P. Niyogi, and V. Sindhwani, “Manifold regularization: a geometric framework for learning from labeled and unlabeled examples,” J. Mach. Learn. Res. 7, 2399–2434 (2006).

Soltani-Farani, A.

A. Soltani-Farani, H. R. Rabiee, and S. A. Hosseini, “Spatial-aware dictionary learning for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 53, 527–541 (2015).
[Crossref]

Su, H.

Z. Xue, P. Du, J. Li, and H. Su, “Simultaneous sparse graph embedding for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 53, 6114–6133 (2015).
[Crossref]

Su, Z.

Z. Lin, R. Liu, and Z. Su, “Linearized alternating direction method with adaptive penalty for low-rank representation,” in 24th International Conference on Neural Information Processing Systems, Granada, Spain (Curran Associates Inc., 2011), pp. 612–620.

Tang, P.

L. Huo, P. Tang, Z. Zhang, and D. Tuia, “Semisupervised classification of remote sensing images with hierarchical spatial similarity,” IEEE Geosci. Remote Sens. Lett. 12, 150–154 (2015).
[Crossref]

Tang, X.

S. Yang, S. Yan, C. Zhang, and X. Tang, “Bilinear analysis for kernel selection and nonlinear feature extraction,” IEEE Trans. Neural Netw. 18, 1442–1452 (2007).
[Crossref]

Tuia, D.

L. Huo, P. Tang, Z. Zhang, and D. Tuia, “Semisupervised classification of remote sensing images with hierarchical spatial similarity,” IEEE Geosci. Remote Sens. Lett. 12, 150–154 (2015).
[Crossref]

D. Tuia and G. Camps-Valls, “Semisupervised remote sensing image classification with cluster kernels,” IEEE Geosci. Remote Sens. Lett. 6, 224–228 (2009).
[Crossref]

Wang, M.

P. Li, J. Yu, M. Wang, L. Zhang, D. Cai, and X. Li, “Constrained low-rank learning using least squares-based regularization,” IEEE Trans. Cybern. 47, 4250–4262 (2017).
[Crossref]

Wang, X.

X. Wang and F. Liu, “Weighted low-rank representation-based dimension reduction for hyperspectral image classification,” IEEE Geosci. Remote Sens. Lett. 14, 1938–1942 (2017).
[Crossref]

Wang, Y.

X. Lu, Y. Wang, and Y. Yuan, “Graph-regularized low-rank representation for destriping of hyperspectral images,” IEEE Trans. Geosci. Remote Sens. 51, 4009–4018 (2013).
[Crossref]

Xia, J.

J. Xia, J. Chanussot, P. Du, and X. He, “(Semi-) supervised probabilistic principal component analysis for hyperspectral remote sensing image classification,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 7, 2224–2236 (2014).
[Crossref]

Xu, Y.

L. Fei, Y. Xu, X. Fang, and J. Yang, “Low rank representation with adaptive distance penalty for semi-supervised subspace classification,” Pattern Recogn. 67, 252–262 (2017).
[Crossref]

Xue, Z.

Z. Xue, P. Du, J. Li, and H. Su, “Simultaneous sparse graph embedding for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 53, 6114–6133 (2015).
[Crossref]

Yan, S.

S. Yang, S. Yan, C. Zhang, and X. Tang, “Bilinear analysis for kernel selection and nonlinear feature extraction,” IEEE Trans. Neural Netw. 18, 1442–1452 (2007).
[Crossref]

Yang, J.

L. Fei, Y. Xu, X. Fang, and J. Yang, “Low rank representation with adaptive distance penalty for semi-supervised subspace classification,” Pattern Recogn. 67, 252–262 (2017).
[Crossref]

J. Chen and J. Yang, “Robust subspace segmentation via low-rank representation,” IEEE Trans. Cybern. 44, 1432–1445 (2014).
[Crossref]

Yang, S.

S. Yang, S. Yan, C. Zhang, and X. Tang, “Bilinear analysis for kernel selection and nonlinear feature extraction,” IEEE Trans. Neural Netw. 18, 1442–1452 (2007).
[Crossref]

Yu, J.

P. Li, J. Yu, M. Wang, L. Zhang, D. Cai, and X. Li, “Constrained low-rank learning using least squares-based regularization,” IEEE Trans. Cybern. 47, 4250–4262 (2017).
[Crossref]

Yuan, Y.

X. Lu, Y. Wang, and Y. Yuan, “Graph-regularized low-rank representation for destriping of hyperspectral images,” IEEE Trans. Geosci. Remote Sens. 51, 4009–4018 (2013).
[Crossref]

Zhang, C.

S. Yang, S. Yan, C. Zhang, and X. Tang, “Bilinear analysis for kernel selection and nonlinear feature extraction,” IEEE Trans. Neural Netw. 18, 1442–1452 (2007).
[Crossref]

Zhang, L.

P. Li, J. Yu, M. Wang, L. Zhang, D. Cai, and X. Li, “Constrained low-rank learning using least squares-based regularization,” IEEE Trans. Cybern. 47, 4250–4262 (2017).
[Crossref]

Zhang, Z.

L. Huo, P. Tang, Z. Zhang, and D. Tuia, “Semisupervised classification of remote sensing images with hierarchical spatial similarity,” IEEE Geosci. Remote Sens. Lett. 12, 150–154 (2015).
[Crossref]

Zoej, M. J. V.

B. Mojaradi, H. Abrishami-Moghaddam, M. J. V. Zoej, and R. P. W. Duin, “Dimensionality reduction of hyperspectral data via spectral feature extraction,” IEEE Trans. Geosci. Remote Sens. 47, 2091–2105 (2009).
[Crossref]

Found. Comput. Math. (1)

E. J. Candès and B. Recht, “Exact matrix completion via convex optimization,” Found. Comput. Math. 9, 717–772 (2009).
[Crossref]

IEEE Geosci. Remote Sens. Lett. (5)

X. Wang and F. Liu, “Weighted low-rank representation-based dimension reduction for hyperspectral image classification,” IEEE Geosci. Remote Sens. Lett. 14, 1938–1942 (2017).
[Crossref]

L. Huo, P. Tang, Z. Zhang, and D. Tuia, “Semisupervised classification of remote sensing images with hierarchical spatial similarity,” IEEE Geosci. Remote Sens. Lett. 12, 150–154 (2015).
[Crossref]

D. Tuia and G. Camps-Valls, “Semisupervised remote sensing image classification with cluster kernels,” IEEE Geosci. Remote Sens. Lett. 6, 224–228 (2009).
[Crossref]

L. Pan, H. Li, H. Meng, W. Li, Q. Du, and W. J. Emery, “Hyperspectral image classification via low-rank and sparse representation with spectral consistency constraint,” IEEE Geosci. Remote Sens. Lett. 14, 2117–2121 (2017).
[Crossref]

W. Du, M. Lv, Q. Hou, and L. Jing, “Semisupervised dimension reduction based on pairwise constraint propagation for hyperspectral images,” IEEE Geosci. Remote Sens. Lett. 13, 1880–1884 (2016).
[Crossref]

IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. (6)

P. Quesada-Barriuso, F. Argüello, and D. B. Heras, “Spectral–spatial classification of hyperspectral images using wavelets and extended morphological profiles,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 7, 1177–1185 (2014).
[Crossref]

Y. Gu and K. Feng, “Optimized Laplacian SVM with distance metric learning for hyperspectral image classification,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 6, 1109–1117 (2013).
[Crossref]

M. Borhani and H. Ghassemian, “Kernel multivariate spectral–spatial analysis of hyperspectral data,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 8, 2418–2426 (2015).
[Crossref]

R. Luo, W. Liao, X. Huang, Y. Pi, and W. Philips, “Feature extraction of hyperspectral images with semisupervised graph learning,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 9, 4389–4399 (2016).
[Crossref]

W. Liao, R. Bellens, A. Pizurica, W. Philips, and Y. Pi, “Classification of hyperspectral data over urban areas using directional morphological profiles and semi-supervised feature extraction,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 5, 1177–1190 (2012).
[Crossref]

J. Xia, J. Chanussot, P. Du, and X. He, “(Semi-) supervised probabilistic principal component analysis for hyperspectral remote sensing image classification,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 7, 2224–2236 (2014).
[Crossref]

IEEE Signal Process. Mag. (1)

J. Arenas-Garcia, K. B. Petersen, G. Camps-Valls, and L. K. Hansen, “Kernel multivariate analysis framework for supervised subspace learning: a tutorial on linear and kernel multivariate methods,” IEEE Signal Process. Mag. 30(4), 16–29 (2013).
[Crossref]

IEEE Trans. Cybern. (2)

J. Chen and J. Yang, “Robust subspace segmentation via low-rank representation,” IEEE Trans. Cybern. 44, 1432–1445 (2014).
[Crossref]

P. Li, J. Yu, M. Wang, L. Zhang, D. Cai, and X. Li, “Constrained low-rank learning using least squares-based regularization,” IEEE Trans. Cybern. 47, 4250–4262 (2017).
[Crossref]

IEEE Trans. Geosci. Remote Sens. (12)

X. Lu, Y. Wang, and Y. Yuan, “Graph-regularized low-rank representation for destriping of hyperspectral images,” IEEE Trans. Geosci. Remote Sens. 51, 4009–4018 (2013).
[Crossref]

L. Fang, S. Li, X. Kang, and J. A. Benediktsson, “Spectral–spatial classification of hyperspectral images with a superpixel-based discriminative sparse model,” IEEE Trans. Geosci. Remote Sens. 53, 4186–4201 (2015).
[Crossref]

F. Melgani and L. Bruzzone, “Classification of hyperspectral remote sensing images with support vector machines,” IEEE Trans. Geosci. Remote Sens. 42, 1778–1790 (2004).
[Crossref]

E. Izquierdo-Verdiguier, L. Gómez-Chova, L. Bruzzone, and G. Camps-Valls, “Semisupervised kernel feature extraction for remote sensing image analysis,” IEEE Trans. Geosci. Remote Sens. 52, 5567–5578 (2014).
[Crossref]

Z. Xue, P. Du, J. Li, and H. Su, “Simultaneous sparse graph embedding for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 53, 6114–6133 (2015).
[Crossref]

A. Soltani-Farani, H. R. Rabiee, and S. A. Hosseini, “Spatial-aware dictionary learning for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 53, 527–541 (2015).
[Crossref]

Y. Chen, H. Jiang, C. Li, X. Jia, and P. Ghamisi, “Deep feature extraction and classification of hyperspectral images based on convolutional neural networks,” IEEE Trans. Geosci. Remote Sens. 54, 6232–6251 (2016).
[Crossref]

B. Mojaradi, H. Abrishami-Moghaddam, M. J. V. Zoej, and R. P. W. Duin, “Dimensionality reduction of hyperspectral data via spectral feature extraction,” IEEE Trans. Geosci. Remote Sens. 47, 2091–2105 (2009).
[Crossref]

L. Bruzzone, M. Chi, and M. Marconcini, “A novel transductive SVM for semisupervised classification of remote-sensing images,” IEEE Trans. Geosci. Remote Sens. 44, 3363–3373 (2006).
[Crossref]

G. Camps-Valls and L. Bruzzone, “Kernel-based methods for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 43, 1351–1362 (2005).
[Crossref]

X. Jin, Y. Gu, and T. Liu, “Intrinsic image recovery from remote sensing hyperspectral images,” IEEE Trans. Geosci. Remote Sens. 57, 224–238 (2019).
[Crossref]

J. Li, P. R. Marpu, A. Plaza, J. M. Bioucas-Dias, and J. A. Benediktsson, “Generalized composite kernel framework for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 51, 4816–4829 (2013).
[Crossref]

IEEE Trans. Neural Netw. (1)

S. Yang, S. Yan, C. Zhang, and X. Tang, “Bilinear analysis for kernel selection and nonlinear feature extraction,” IEEE Trans. Neural Netw. 18, 1442–1452 (2007).
[Crossref]

IEEE Trans. Neural Netw. Learn. Syst. (1)

Y. Motai, “Kernel association for classification and prediction: a survey,” IEEE Trans. Neural Netw. Learn. Syst. 26, 208–223 (2015).
[Crossref]

Imag. Sci. J. (1)

S. A. Ahmadi, N. Mehrshad, and S. M. Razavi, “Semisupervised dimensionality reduction for hyperspectral images based on the combination of semisupervised learning and metric learning,” Imag. Sci. J. 66, 320–327 (2018).
[Crossref]

J. Mach. Learn. Res. (1)

M. Belkin, P. Niyogi, and V. Sindhwani, “Manifold regularization: a geometric framework for learning from labeled and unlabeled examples,” J. Mach. Learn. Res. 7, 2399–2434 (2006).

J. Opt. Soc. Am. A (1)

Pattern Recogn. (1)

L. Fei, Y. Xu, X. Fang, and J. Yang, “Low rank representation with adaptive distance penalty for semi-supervised subspace classification,” Pattern Recogn. 67, 252–262 (2017).
[Crossref]

Proc. IEEE (2)

E. J. Candes and Y. Plan, “Matrix completion with noise,” Proc. IEEE 98, 925–936 (2010).
[Crossref]

X. Jia, B. Kuo, and M. M. Crawford, “Feature mining for hyperspectral image classification,” Proc. IEEE 101, 676–697 (2013).
[Crossref]

Other (1)

Z. Lin, R. Liu, and Z. Su, “Linearized alternating direction method with adaptive penalty for low-rank representation,” in 24th International Conference on Neural Information Processing Systems, Granada, Spain (Curran Associates Inc., 2011), pp. 612–620.

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Figures (3)

Fig. 1.
Fig. 1. Best OA% of the kernel functions versus the number of labeled samples based on a SVM classifier for the (a) Indiana Pines data set and (b) University of Pavia data set.
Fig. 2.
Fig. 2. Best classification maps of the different kernel functions used by a SVM classifier for Indian Pines data set (top row) and University of Pavia data set (bottom row): (a) ground truth, (b)  ${{\textbf{K}}_{{\rm LLE}}}$ , (c)  ${{\textbf{K}}_{{\ell _1}}}$ , (d)  ${{\textbf{K}}_{\rm RBF}}$ , (e)  ${{\textbf{K}}_{{\rm bag}}}$ , (f)  ${{\textbf{K}}_{{\rm MS} - {\rm bag}}}$ , (g)  ${{\textbf{K}}_{{\rm LRR}}}$ , and (h)  ${{\textbf{K}}_{{\rm S} - {\rm LRR}}}$ .
Fig. 3.
Fig. 3. OA% versus the number of unlabeled samples for both data sets.

Tables (3)

Tables Icon

Table 1. Procedure of LRR Kernel Construction

Tables Icon

Table 2. Name and Number of Samples in Both Data Sets

Tables Icon

Table 3. Best OA% (Kappa Statistic) of Different Kernel Construction Methods Used by SVM versus the Number of Labeled Samples for the Indiana Pines Data Set and the University of Pavia Data Set

Equations (6)

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min Z , E Z + γ E 2 , 1 , s . t . X = AZ + E ,
min Z , E Z + P ( Z , E ) , s . t . X = XZ + E ,
S i j ( i , j ) = e x i x j 2 σ ,
1 2 i , j = 1 n z i z j 2 2 S i j = i = 1 n z i T z i D i i i , j = 1 n z i T z j S i j = t r a c e ( ZD Z T ) t r a c e ( ZS Z T ) = t r a c e ( ZL Z T ) ,
min Z , E Z + λ 1 E 1 + + λ 2 t r a c e ( Z L Z T ) s . t . X = XZ + E , Z = Z T , Z > 0 ,
K s - L R R = ρ K R B F + ( 1 ρ ) K L R R ,

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