Abstract

This paper investigates the use of feature dimensionality reduction approaches for high-dimensional data analysis. Most of the existing preserving projection methods are based on similarity, such as the well-known locality-preserving projections, neighborhood-preserving embedding, and sparsity-preserving projections. Here, we propose a simple yet very efficient preserving projection method based on sparsity and dissimilarity for feature extraction, named dissimilarity sparsity-preserving projections, which is an extended version of sparsity-preserving projections. Both projection coefficients and reconstructive residuals are considered in our proposed framework. We give an idea of a “dissimilarity metric” as the measurement of the relationship among the object data. If the value of the dissimilarity metric of two samples is large, the possibility of them belonging to the same class is small. The proposed methods do not have to preset the number of neighbors and heat kernel width, which is one of the important differences from other projection methods. In practical applications, an approximately direct and complete solution is obtained for the proposed algorithm. Experimental results on three widely used face datasets demonstrate that the proposed framework could achieve competitive performance in terms of accuracy and efficiency.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2012 (3)

Y. D. Leeuw and D. Cohen, “Diffusion in sparse networks: linear to semilinear crossover,” Phys. Rev. E 86, 051120 (2012).
[CrossRef]

H. Wang, C. Yuan, W. Hub, and C. Sun, “Supervised class-specific dictionary learning or sparse modeling in action recognition,” Pattern Recogn. 45, 3902–3911 (2012).
[CrossRef]

N. Gu, M. Fan, H. Qiao, and B. Zhang, “Discriminative sparsity preserving projections for semi-supervised dimensionality reduction,” IEEE Signal Process. Lett. 19, 391–394 (2012).
[CrossRef]

2011 (2)

Y. Sun, J. Zhao, and Y. Hu, “Supervised sparsity preserving projections for face recognition,” Proc. SPIE 8009, 80092D (2011).
[CrossRef]

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50, 072601 (2011).
[CrossRef]

2010 (4)

J. Wright, Y. Ma, J. Mairal, G. Spairo, T. Huang, and S. Yan, “Sparse representation for computer vision and pattern recognition,” Proc. IEEE 98, 1031–1044 (2010).
[CrossRef]

L. Qiao, S. Chen, and X. Tan, “Sparsity preserving discriminant analysis for single training image face recognition,” Pattern Recogn. Lett. 31, 422–429 (2010).
[CrossRef]

Y. Lu, C. Lu, M. Qi, and S. Wang, “A supervised locality preserving projections based local matching algorithm for face recognition,” Lect. Notes Comput. Sci. 6059, 28–37 (2010).
[CrossRef]

L. Qiao, S. Chen, and X. Tan, “Sparsity preserving projections with applications to face recognition,” Pattern Recogn. 43, 331–341 (2010).
[CrossRef]

2009 (2)

J. Wright, A. Yang, A. Ganesh, S. Shastry, and Y. Ma, “Robust face recognition via sparse representation,” IEEE Trans. Pattern Anal. Mach. Intell. 31, 210–227 (2009).
[CrossRef]

J. Ma and F.-X. L. Dimet, “Deblurring from highly incomplete measurements for remote sensing,” IEEE Trans. Geosci. Remote Sens. 47, 792–802 (2009).
[CrossRef]

2008 (2)

G. Feng, D. Hu, and Z. Zhou, “A direct locality preserving projections (DLPP) algorithm for image recognition,” Neural Process. Lett. 27, 247–255 (2008).

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25 (2), 21–30 (2008).
[CrossRef]

2007 (3)

J. Yang, D. Zhang, and J.-Y. Yang, “Globally maximizing, locally minimizing: unsupervised discriminant projection with applications to face and palm biometrics,” IEEE Trans. Pattern Anal. Mach. Intell. 29, 650–664 (2007).
[CrossRef]

Z. L. Zhang, F. Yang, W. Tan, J. Jia, and J. Yang, “Gabor feature based face recognition using supervised locality preserving projection,” Signal Process. 87, 2473–2483 (2007).
[CrossRef]

D. Hu, G. Feng, and Z. Zhou, “Two-dimensional locality preserving projections (2DLPP) with its application to palmprint recognition,” Pattern Recogn. 40, 339–342 (2007).
[CrossRef]

2006 (2)

M. Elad and M. Aharon, “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Trans. Image Process. 15, 3736–3745 (2006).
[CrossRef]

D. Cai, X. He, and L. Han, “Orthogonal Laplacianfaces for face recognition,” IEEE Trans. Image Process. 15, 3608–3614 (2006).
[CrossRef]

2005 (2)

J. Yang, A. F. Frangi, J. Y. Yang, D. Zhang, and Z. Jin, “Kernel PCA plus LDA: a complete kernel Fisher discriminant framework for feature extraction and representation,” IEEE Trans. Pattern Anal. Mach. Intell. 27, 230–244 (2005).
[CrossRef]

J. Cheng, Q. Liu, H. Lu, and Y.-W. Chen, “Supervised kernel locality preserving projections for face recognition,” Neurocomputing 67, 443–449 (2005).
[CrossRef]

2003 (2)

L. K. Saul and S. T. Roweis, “Think globally, fit locally: unsupervised learning of low dimensional manifolds,” J. Mach. Learn. Res. 4, 119–155 (2003).
[CrossRef]

X. He and P. Niyogi, “Locality preserving projections,” Adv. Neural Inf. Process. Syst. 16, 1–8 (2003).

2001 (1)

H. Yu and J. Yang, “A direct LDA algorithm for high-dimensional data with application to face recognition,” Pattern Recogn. 34, 2067–2070 (2001).
[CrossRef]

2000 (2)

A. K. Jain, R. P. W. Duin, and J. Mao, “Statistical pattern recognition: a review,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 4–37 (2000).
[CrossRef]

S. T. Roweis and L. K. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science 290, 2323–2326 (2000).
[CrossRef]

1998 (1)

B. Scholkopf, A. Smola, and K. R. Muller, “Nonlinear component analysis as a kernel eigenvalues problem,” Neural Comput. 10, 1299–1319 (1998).
[CrossRef]

1997 (1)

P. Belhumeur, J. Hesanha, and D. Kreigman, “Eigenfaces vs. Fisherfaces: recognition using class specific linear projection,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 711–720 (1997).
[CrossRef]

Aharon, M.

M. Elad and M. Aharon, “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Trans. Image Process. 15, 3736–3745 (2006).
[CrossRef]

Ahuja, N.

M. H. Yang, N. Ahuja, and D. Kriegman, “Face recognition using kernel eigenfaces,” in Proceedings of International Conf. on Image Processing, Vancouver, Canada (2000), pp. 1–4.

Belhumeur, P.

P. Belhumeur, J. Hesanha, and D. Kreigman, “Eigenfaces vs. Fisherfaces: recognition using class specific linear projection,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 711–720 (1997).
[CrossRef]

Belkin, M.

M. Belkin and P. Niyogi, “Laplacian eigenmaps and spectral techniques for embedding and clustering,” in Advances in Neural Information Processing Systems 14, Vancouver, Canada (2001), pp. 585–591.

Bengio, Y.

Y. Bengio, J. Palement, and P. Vincent, “Out-of-sample extensions for LLE, isomap, MOS, eigenmaps, and spectral clustering,” in Advances in Neural Information Processing Systems 6, Cambridge, MA (2003), p. 117.

Cai, D.

D. Cai, X. He, and L. Han, “Orthogonal Laplacianfaces for face recognition,” IEEE Trans. Image Process. 15, 3608–3614 (2006).
[CrossRef]

D. Cai, X. He, and K. Zhou, “Locality sensitive discriminant analysis,” in Proc. of International Joint Conf. on Artificial Intelligence, Hyderabad, India (2007), pp. 1–6.

D. Cai, X. He, and J. Han, “Semi-supervised discriminant analysis,” in Tenth IEEE International Conf. on Computer Vision (IEEE, 2007), pp. 1–7.

X. He, D. Cai, S. Yan, and H.-J. Zhang, “Neighborhood preserving embedding,” in Tenth IEEE International Conf. on Computer Vision, Beijing, China (2005), pp. 1–8.

Candès, E. J.

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25 (2), 21–30 (2008).
[CrossRef]

Chen, S.

L. Qiao, S. Chen, and X. Tan, “Sparsity preserving projections with applications to face recognition,” Pattern Recogn. 43, 331–341 (2010).
[CrossRef]

L. Qiao, S. Chen, and X. Tan, “Sparsity preserving discriminant analysis for single training image face recognition,” Pattern Recogn. Lett. 31, 422–429 (2010).
[CrossRef]

Chen, Y.-W.

J. Cheng, Q. Liu, H. Lu, and Y.-W. Chen, “Supervised kernel locality preserving projections for face recognition,” Neurocomputing 67, 443–449 (2005).
[CrossRef]

Cheng, J.

J. Cheng, Q. Liu, H. Lu, and Y.-W. Chen, “Supervised kernel locality preserving projections for face recognition,” Neurocomputing 67, 443–449 (2005).
[CrossRef]

Cohen, D.

Y. D. Leeuw and D. Cohen, “Diffusion in sparse networks: linear to semilinear crossover,” Phys. Rev. E 86, 051120 (2012).
[CrossRef]

Dimet, F.-X. L.

J. Ma and F.-X. L. Dimet, “Deblurring from highly incomplete measurements for remote sensing,” IEEE Trans. Geosci. Remote Sens. 47, 792–802 (2009).
[CrossRef]

Duin, R. P. W.

A. K. Jain, R. P. W. Duin, and J. Mao, “Statistical pattern recognition: a review,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 4–37 (2000).
[CrossRef]

R. P. W. Duin and E. Pekalska, “On refining dissimilarity matrices for an improved NN learning,” in Proceedings of 19th International Conf. on Pattern Recognition (IEEE, 2008), pp. 1–4.

Elad, M.

M. Elad and M. Aharon, “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Trans. Image Process. 15, 3736–3745 (2006).
[CrossRef]

Fan, M.

N. Gu, M. Fan, H. Qiao, and B. Zhang, “Discriminative sparsity preserving projections for semi-supervised dimensionality reduction,” IEEE Signal Process. Lett. 19, 391–394 (2012).
[CrossRef]

Feng, G.

G. Feng, D. Hu, and Z. Zhou, “A direct locality preserving projections (DLPP) algorithm for image recognition,” Neural Process. Lett. 27, 247–255 (2008).

D. Hu, G. Feng, and Z. Zhou, “Two-dimensional locality preserving projections (2DLPP) with its application to palmprint recognition,” Pattern Recogn. 40, 339–342 (2007).
[CrossRef]

Feng, X.

L. Zhang, M. Yang, and X. Feng, “Sparse representation or collaborative representation: which helps face recognition?,” in Tenth IEEE International Conf. on Computer Vision (IEEE, 2011), pp. 1–8.

Frangi, A. F.

J. Yang, A. F. Frangi, J. Y. Yang, D. Zhang, and Z. Jin, “Kernel PCA plus LDA: a complete kernel Fisher discriminant framework for feature extraction and representation,” IEEE Trans. Pattern Anal. Mach. Intell. 27, 230–244 (2005).
[CrossRef]

Ganesh, A.

J. Wright, A. Yang, A. Ganesh, S. Shastry, and Y. Ma, “Robust face recognition via sparse representation,” IEEE Trans. Pattern Anal. Mach. Intell. 31, 210–227 (2009).
[CrossRef]

Gong, Y.

J. Wang, J. Yang, K. Yu, F. Lv, T. Huang, and Y. Gong, “Locality-constrained linear coding for image classification,” in 2010 IEEE Conf. on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 3360–3367.

Gu, N.

N. Gu, M. Fan, H. Qiao, and B. Zhang, “Discriminative sparsity preserving projections for semi-supervised dimensionality reduction,” IEEE Signal Process. Lett. 19, 391–394 (2012).
[CrossRef]

Han, J.

D. Cai, X. He, and J. Han, “Semi-supervised discriminant analysis,” in Tenth IEEE International Conf. on Computer Vision (IEEE, 2007), pp. 1–7.

Han, L.

D. Cai, X. He, and L. Han, “Orthogonal Laplacianfaces for face recognition,” IEEE Trans. Image Process. 15, 3608–3614 (2006).
[CrossRef]

He, X.

D. Cai, X. He, and L. Han, “Orthogonal Laplacianfaces for face recognition,” IEEE Trans. Image Process. 15, 3608–3614 (2006).
[CrossRef]

X. He and P. Niyogi, “Locality preserving projections,” Adv. Neural Inf. Process. Syst. 16, 1–8 (2003).

X. He, D. Cai, S. Yan, and H.-J. Zhang, “Neighborhood preserving embedding,” in Tenth IEEE International Conf. on Computer Vision, Beijing, China (2005), pp. 1–8.

D. Cai, X. He, and J. Han, “Semi-supervised discriminant analysis,” in Tenth IEEE International Conf. on Computer Vision (IEEE, 2007), pp. 1–7.

D. Cai, X. He, and K. Zhou, “Locality sensitive discriminant analysis,” in Proc. of International Joint Conf. on Artificial Intelligence, Hyderabad, India (2007), pp. 1–6.

Hesanha, J.

P. Belhumeur, J. Hesanha, and D. Kreigman, “Eigenfaces vs. Fisherfaces: recognition using class specific linear projection,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 711–720 (1997).
[CrossRef]

Hou, B.

F. Yin, L. C. Jiao, F. Shang, S. Wang, and B. Hou, “Fast Fisher sparsity preserving projections,” Neural Comput. Appl.1–15 (2012).
[CrossRef]

Hu, D.

G. Feng, D. Hu, and Z. Zhou, “A direct locality preserving projections (DLPP) algorithm for image recognition,” Neural Process. Lett. 27, 247–255 (2008).

D. Hu, G. Feng, and Z. Zhou, “Two-dimensional locality preserving projections (2DLPP) with its application to palmprint recognition,” Pattern Recogn. 40, 339–342 (2007).
[CrossRef]

Hu, Y.

Y. Sun, J. Zhao, and Y. Hu, “Supervised sparsity preserving projections for face recognition,” Proc. SPIE 8009, 80092D (2011).
[CrossRef]

Huang, T.

J. Wright, Y. Ma, J. Mairal, G. Spairo, T. Huang, and S. Yan, “Sparse representation for computer vision and pattern recognition,” Proc. IEEE 98, 1031–1044 (2010).
[CrossRef]

J. Wang, J. Yang, K. Yu, F. Lv, T. Huang, and Y. Gong, “Locality-constrained linear coding for image classification,” in 2010 IEEE Conf. on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 3360–3367.

Hub, W.

H. Wang, C. Yuan, W. Hub, and C. Sun, “Supervised class-specific dictionary learning or sparse modeling in action recognition,” Pattern Recogn. 45, 3902–3911 (2012).
[CrossRef]

Jain, A. K.

A. K. Jain, R. P. W. Duin, and J. Mao, “Statistical pattern recognition: a review,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 4–37 (2000).
[CrossRef]

Jia, J.

Z. L. Zhang, F. Yang, W. Tan, J. Jia, and J. Yang, “Gabor feature based face recognition using supervised locality preserving projection,” Signal Process. 87, 2473–2483 (2007).
[CrossRef]

Jiao, L. C.

F. Yin, L. C. Jiao, F. Shang, S. Wang, and B. Hou, “Fast Fisher sparsity preserving projections,” Neural Comput. Appl.1–15 (2012).
[CrossRef]

Jin, Z.

J. Yang, A. F. Frangi, J. Y. Yang, D. Zhang, and Z. Jin, “Kernel PCA plus LDA: a complete kernel Fisher discriminant framework for feature extraction and representation,” IEEE Trans. Pattern Anal. Mach. Intell. 27, 230–244 (2005).
[CrossRef]

Jolloffe, J. T.

J. T. Jolloffe, Principal Component Analysis (Springer-Verlag, 1986).

Joseph, N. W.

M. Raazia, D. G. Paul, and N. W. Joseph, “A matching pursuit based similarity measure for fuzzy clustering and classification of signals,” in Proceedings of IEEE International Conference on Fuzzy Systems, Hong Kong, China (2008), pp. 1950–1955.

Kreigman, D.

P. Belhumeur, J. Hesanha, and D. Kreigman, “Eigenfaces vs. Fisherfaces: recognition using class specific linear projection,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 711–720 (1997).
[CrossRef]

Kriegman, D.

M. H. Yang, N. Ahuja, and D. Kriegman, “Face recognition using kernel eigenfaces,” in Proceedings of International Conf. on Image Processing, Vancouver, Canada (2000), pp. 1–4.

Leeuw, Y. D.

Y. D. Leeuw and D. Cohen, “Diffusion in sparse networks: linear to semilinear crossover,” Phys. Rev. E 86, 051120 (2012).
[CrossRef]

Liu, Q.

J. Cheng, Q. Liu, H. Lu, and Y.-W. Chen, “Supervised kernel locality preserving projections for face recognition,” Neurocomputing 67, 443–449 (2005).
[CrossRef]

Lu, C.

Y. Lu, C. Lu, M. Qi, and S. Wang, “A supervised locality preserving projections based local matching algorithm for face recognition,” Lect. Notes Comput. Sci. 6059, 28–37 (2010).
[CrossRef]

Lu, H.

J. Cheng, Q. Liu, H. Lu, and Y.-W. Chen, “Supervised kernel locality preserving projections for face recognition,” Neurocomputing 67, 443–449 (2005).
[CrossRef]

Lu, Y.

Y. Lu, C. Lu, M. Qi, and S. Wang, “A supervised locality preserving projections based local matching algorithm for face recognition,” Lect. Notes Comput. Sci. 6059, 28–37 (2010).
[CrossRef]

Lv, F.

J. Wang, J. Yang, K. Yu, F. Lv, T. Huang, and Y. Gong, “Locality-constrained linear coding for image classification,” in 2010 IEEE Conf. on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 3360–3367.

Ma, J.

J. Ma and F.-X. L. Dimet, “Deblurring from highly incomplete measurements for remote sensing,” IEEE Trans. Geosci. Remote Sens. 47, 792–802 (2009).
[CrossRef]

Ma, Y.

J. Wright, Y. Ma, J. Mairal, G. Spairo, T. Huang, and S. Yan, “Sparse representation for computer vision and pattern recognition,” Proc. IEEE 98, 1031–1044 (2010).
[CrossRef]

J. Wright, A. Yang, A. Ganesh, S. Shastry, and Y. Ma, “Robust face recognition via sparse representation,” IEEE Trans. Pattern Anal. Mach. Intell. 31, 210–227 (2009).
[CrossRef]

Mairal, J.

J. Wright, Y. Ma, J. Mairal, G. Spairo, T. Huang, and S. Yan, “Sparse representation for computer vision and pattern recognition,” Proc. IEEE 98, 1031–1044 (2010).
[CrossRef]

Mao, J.

A. K. Jain, R. P. W. Duin, and J. Mao, “Statistical pattern recognition: a review,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 4–37 (2000).
[CrossRef]

Marcia, R. F.

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50, 072601 (2011).
[CrossRef]

Muller, K. R.

B. Scholkopf, A. Smola, and K. R. Muller, “Nonlinear component analysis as a kernel eigenvalues problem,” Neural Comput. 10, 1299–1319 (1998).
[CrossRef]

Murase, H.

S. A. Nene, S. K. Nayar, and H. Murase, “Columbia Object Image Library (COIL100),” Department of Computer Science, Columbia University Tech. Rep. No.  (1996).

Nayar, S. K.

S. A. Nene, S. K. Nayar, and H. Murase, “Columbia Object Image Library (COIL100),” Department of Computer Science, Columbia University Tech. Rep. No.  (1996).

Nene, S. A.

S. A. Nene, S. K. Nayar, and H. Murase, “Columbia Object Image Library (COIL100),” Department of Computer Science, Columbia University Tech. Rep. No.  (1996).

Nichols, J. M.

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50, 072601 (2011).
[CrossRef]

Niyogi, P.

X. He and P. Niyogi, “Locality preserving projections,” Adv. Neural Inf. Process. Syst. 16, 1–8 (2003).

M. Belkin and P. Niyogi, “Laplacian eigenmaps and spectral techniques for embedding and clustering,” in Advances in Neural Information Processing Systems 14, Vancouver, Canada (2001), pp. 585–591.

Palement, J.

Y. Bengio, J. Palement, and P. Vincent, “Out-of-sample extensions for LLE, isomap, MOS, eigenmaps, and spectral clustering,” in Advances in Neural Information Processing Systems 6, Cambridge, MA (2003), p. 117.

Paul, D. G.

M. Raazia, D. G. Paul, and N. W. Joseph, “A matching pursuit based similarity measure for fuzzy clustering and classification of signals,” in Proceedings of IEEE International Conference on Fuzzy Systems, Hong Kong, China (2008), pp. 1950–1955.

Pekalska, E.

R. P. W. Duin and E. Pekalska, “On refining dissimilarity matrices for an improved NN learning,” in Proceedings of 19th International Conf. on Pattern Recognition (IEEE, 2008), pp. 1–4.

Qi, M.

Y. Lu, C. Lu, M. Qi, and S. Wang, “A supervised locality preserving projections based local matching algorithm for face recognition,” Lect. Notes Comput. Sci. 6059, 28–37 (2010).
[CrossRef]

Qiao, H.

N. Gu, M. Fan, H. Qiao, and B. Zhang, “Discriminative sparsity preserving projections for semi-supervised dimensionality reduction,” IEEE Signal Process. Lett. 19, 391–394 (2012).
[CrossRef]

Qiao, L.

L. Qiao, S. Chen, and X. Tan, “Sparsity preserving discriminant analysis for single training image face recognition,” Pattern Recogn. Lett. 31, 422–429 (2010).
[CrossRef]

L. Qiao, S. Chen, and X. Tan, “Sparsity preserving projections with applications to face recognition,” Pattern Recogn. 43, 331–341 (2010).
[CrossRef]

Raazia, M.

M. Raazia, D. G. Paul, and N. W. Joseph, “A matching pursuit based similarity measure for fuzzy clustering and classification of signals,” in Proceedings of IEEE International Conference on Fuzzy Systems, Hong Kong, China (2008), pp. 1950–1955.

Roweis, S. T.

L. K. Saul and S. T. Roweis, “Think globally, fit locally: unsupervised learning of low dimensional manifolds,” J. Mach. Learn. Res. 4, 119–155 (2003).
[CrossRef]

S. T. Roweis and L. K. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science 290, 2323–2326 (2000).
[CrossRef]

Saul, L. K.

L. K. Saul and S. T. Roweis, “Think globally, fit locally: unsupervised learning of low dimensional manifolds,” J. Mach. Learn. Res. 4, 119–155 (2003).
[CrossRef]

S. T. Roweis and L. K. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science 290, 2323–2326 (2000).
[CrossRef]

Scholkopf, B.

B. Scholkopf, A. Smola, and K. R. Muller, “Nonlinear component analysis as a kernel eigenvalues problem,” Neural Comput. 10, 1299–1319 (1998).
[CrossRef]

Shang, F.

F. Yin, L. C. Jiao, F. Shang, S. Wang, and B. Hou, “Fast Fisher sparsity preserving projections,” Neural Comput. Appl.1–15 (2012).
[CrossRef]

Shastry, S.

J. Wright, A. Yang, A. Ganesh, S. Shastry, and Y. Ma, “Robust face recognition via sparse representation,” IEEE Trans. Pattern Anal. Mach. Intell. 31, 210–227 (2009).
[CrossRef]

Smola, A.

B. Scholkopf, A. Smola, and K. R. Muller, “Nonlinear component analysis as a kernel eigenvalues problem,” Neural Comput. 10, 1299–1319 (1998).
[CrossRef]

Spairo, G.

J. Wright, Y. Ma, J. Mairal, G. Spairo, T. Huang, and S. Yan, “Sparse representation for computer vision and pattern recognition,” Proc. IEEE 98, 1031–1044 (2010).
[CrossRef]

Sugiyama, M.

M. Sugiyama, “Local Fisher discriminant analysis for supervised dimensionality reduction,” in Proc. of the 23th International Conf. on Machine Learning, Pittsburgh, USA (2006), pp. 1–8.

Sun, C.

H. Wang, C. Yuan, W. Hub, and C. Sun, “Supervised class-specific dictionary learning or sparse modeling in action recognition,” Pattern Recogn. 45, 3902–3911 (2012).
[CrossRef]

Sun, Y.

Y. Sun, J. Zhao, and Y. Hu, “Supervised sparsity preserving projections for face recognition,” Proc. SPIE 8009, 80092D (2011).
[CrossRef]

Tan, W.

Z. L. Zhang, F. Yang, W. Tan, J. Jia, and J. Yang, “Gabor feature based face recognition using supervised locality preserving projection,” Signal Process. 87, 2473–2483 (2007).
[CrossRef]

Tan, X.

L. Qiao, S. Chen, and X. Tan, “Sparsity preserving projections with applications to face recognition,” Pattern Recogn. 43, 331–341 (2010).
[CrossRef]

L. Qiao, S. Chen, and X. Tan, “Sparsity preserving discriminant analysis for single training image face recognition,” Pattern Recogn. Lett. 31, 422–429 (2010).
[CrossRef]

Vincent, P.

Y. Bengio, J. Palement, and P. Vincent, “Out-of-sample extensions for LLE, isomap, MOS, eigenmaps, and spectral clustering,” in Advances in Neural Information Processing Systems 6, Cambridge, MA (2003), p. 117.

Wakin, M. B.

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25 (2), 21–30 (2008).
[CrossRef]

Wang, H.

H. Wang, C. Yuan, W. Hub, and C. Sun, “Supervised class-specific dictionary learning or sparse modeling in action recognition,” Pattern Recogn. 45, 3902–3911 (2012).
[CrossRef]

Wang, J.

J. Wang, J. Yang, K. Yu, F. Lv, T. Huang, and Y. Gong, “Locality-constrained linear coding for image classification,” in 2010 IEEE Conf. on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 3360–3367.

Wang, S.

Y. Lu, C. Lu, M. Qi, and S. Wang, “A supervised locality preserving projections based local matching algorithm for face recognition,” Lect. Notes Comput. Sci. 6059, 28–37 (2010).
[CrossRef]

F. Yin, L. C. Jiao, F. Shang, S. Wang, and B. Hou, “Fast Fisher sparsity preserving projections,” Neural Comput. Appl.1–15 (2012).
[CrossRef]

Wang, Z.

F. Xiang, Z. Wang, and X. Yuan, “Image reconstruction based on sparse and redundant representation model: local vs nonlocal,” Optik (2012).
[CrossRef]

Willett, R. M.

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50, 072601 (2011).
[CrossRef]

Wright, J.

J. Wright, Y. Ma, J. Mairal, G. Spairo, T. Huang, and S. Yan, “Sparse representation for computer vision and pattern recognition,” Proc. IEEE 98, 1031–1044 (2010).
[CrossRef]

J. Wright, A. Yang, A. Ganesh, S. Shastry, and Y. Ma, “Robust face recognition via sparse representation,” IEEE Trans. Pattern Anal. Mach. Intell. 31, 210–227 (2009).
[CrossRef]

Xiang, F.

F. Xiang, Z. Wang, and X. Yuan, “Image reconstruction based on sparse and redundant representation model: local vs nonlocal,” Optik (2012).
[CrossRef]

Yan, S.

J. Wright, Y. Ma, J. Mairal, G. Spairo, T. Huang, and S. Yan, “Sparse representation for computer vision and pattern recognition,” Proc. IEEE 98, 1031–1044 (2010).
[CrossRef]

X. He, D. Cai, S. Yan, and H.-J. Zhang, “Neighborhood preserving embedding,” in Tenth IEEE International Conf. on Computer Vision, Beijing, China (2005), pp. 1–8.

Yang, A.

J. Wright, A. Yang, A. Ganesh, S. Shastry, and Y. Ma, “Robust face recognition via sparse representation,” IEEE Trans. Pattern Anal. Mach. Intell. 31, 210–227 (2009).
[CrossRef]

Yang, F.

Z. L. Zhang, F. Yang, W. Tan, J. Jia, and J. Yang, “Gabor feature based face recognition using supervised locality preserving projection,” Signal Process. 87, 2473–2483 (2007).
[CrossRef]

Yang, J.

Z. L. Zhang, F. Yang, W. Tan, J. Jia, and J. Yang, “Gabor feature based face recognition using supervised locality preserving projection,” Signal Process. 87, 2473–2483 (2007).
[CrossRef]

J. Yang, D. Zhang, and J.-Y. Yang, “Globally maximizing, locally minimizing: unsupervised discriminant projection with applications to face and palm biometrics,” IEEE Trans. Pattern Anal. Mach. Intell. 29, 650–664 (2007).
[CrossRef]

J. Yang, A. F. Frangi, J. Y. Yang, D. Zhang, and Z. Jin, “Kernel PCA plus LDA: a complete kernel Fisher discriminant framework for feature extraction and representation,” IEEE Trans. Pattern Anal. Mach. Intell. 27, 230–244 (2005).
[CrossRef]

H. Yu and J. Yang, “A direct LDA algorithm for high-dimensional data with application to face recognition,” Pattern Recogn. 34, 2067–2070 (2001).
[CrossRef]

J. Wang, J. Yang, K. Yu, F. Lv, T. Huang, and Y. Gong, “Locality-constrained linear coding for image classification,” in 2010 IEEE Conf. on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 3360–3367.

Yang, J. Y.

J. Yang, A. F. Frangi, J. Y. Yang, D. Zhang, and Z. Jin, “Kernel PCA plus LDA: a complete kernel Fisher discriminant framework for feature extraction and representation,” IEEE Trans. Pattern Anal. Mach. Intell. 27, 230–244 (2005).
[CrossRef]

Yang, J.-Y.

J. Yang, D. Zhang, and J.-Y. Yang, “Globally maximizing, locally minimizing: unsupervised discriminant projection with applications to face and palm biometrics,” IEEE Trans. Pattern Anal. Mach. Intell. 29, 650–664 (2007).
[CrossRef]

Yang, M.

L. Zhang, M. Yang, and X. Feng, “Sparse representation or collaborative representation: which helps face recognition?,” in Tenth IEEE International Conf. on Computer Vision (IEEE, 2011), pp. 1–8.

Yang, M. H.

M. H. Yang, N. Ahuja, and D. Kriegman, “Face recognition using kernel eigenfaces,” in Proceedings of International Conf. on Image Processing, Vancouver, Canada (2000), pp. 1–4.

Yin, F.

F. Yin, L. C. Jiao, F. Shang, S. Wang, and B. Hou, “Fast Fisher sparsity preserving projections,” Neural Comput. Appl.1–15 (2012).
[CrossRef]

Yu, H.

H. Yu and J. Yang, “A direct LDA algorithm for high-dimensional data with application to face recognition,” Pattern Recogn. 34, 2067–2070 (2001).
[CrossRef]

Yu, K.

J. Wang, J. Yang, K. Yu, F. Lv, T. Huang, and Y. Gong, “Locality-constrained linear coding for image classification,” in 2010 IEEE Conf. on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 3360–3367.

Yuan, C.

H. Wang, C. Yuan, W. Hub, and C. Sun, “Supervised class-specific dictionary learning or sparse modeling in action recognition,” Pattern Recogn. 45, 3902–3911 (2012).
[CrossRef]

Yuan, X.

F. Xiang, Z. Wang, and X. Yuan, “Image reconstruction based on sparse and redundant representation model: local vs nonlocal,” Optik (2012).
[CrossRef]

Zhang, B.

N. Gu, M. Fan, H. Qiao, and B. Zhang, “Discriminative sparsity preserving projections for semi-supervised dimensionality reduction,” IEEE Signal Process. Lett. 19, 391–394 (2012).
[CrossRef]

Zhang, D.

J. Yang, D. Zhang, and J.-Y. Yang, “Globally maximizing, locally minimizing: unsupervised discriminant projection with applications to face and palm biometrics,” IEEE Trans. Pattern Anal. Mach. Intell. 29, 650–664 (2007).
[CrossRef]

J. Yang, A. F. Frangi, J. Y. Yang, D. Zhang, and Z. Jin, “Kernel PCA plus LDA: a complete kernel Fisher discriminant framework for feature extraction and representation,” IEEE Trans. Pattern Anal. Mach. Intell. 27, 230–244 (2005).
[CrossRef]

Zhang, H.-J.

X. He, D. Cai, S. Yan, and H.-J. Zhang, “Neighborhood preserving embedding,” in Tenth IEEE International Conf. on Computer Vision, Beijing, China (2005), pp. 1–8.

Zhang, L.

L. Zhang, M. Yang, and X. Feng, “Sparse representation or collaborative representation: which helps face recognition?,” in Tenth IEEE International Conf. on Computer Vision (IEEE, 2011), pp. 1–8.

Zhang, S.

S. Zhang, “Semi-supervised locality preserving projections with compactness enhancement,” in 2010 International Conf. on Educational and Information Technology, Chongqing, China (2010), pp. 460–464.

Zhang, Z. L.

Z. L. Zhang, F. Yang, W. Tan, J. Jia, and J. Yang, “Gabor feature based face recognition using supervised locality preserving projection,” Signal Process. 87, 2473–2483 (2007).
[CrossRef]

Zhao, J.

Y. Sun, J. Zhao, and Y. Hu, “Supervised sparsity preserving projections for face recognition,” Proc. SPIE 8009, 80092D (2011).
[CrossRef]

Zhou, K.

D. Cai, X. He, and K. Zhou, “Locality sensitive discriminant analysis,” in Proc. of International Joint Conf. on Artificial Intelligence, Hyderabad, India (2007), pp. 1–6.

Zhou, Z.

G. Feng, D. Hu, and Z. Zhou, “A direct locality preserving projections (DLPP) algorithm for image recognition,” Neural Process. Lett. 27, 247–255 (2008).

D. Hu, G. Feng, and Z. Zhou, “Two-dimensional locality preserving projections (2DLPP) with its application to palmprint recognition,” Pattern Recogn. 40, 339–342 (2007).
[CrossRef]

Adv. Neural Inf. Process. Syst. (1)

X. He and P. Niyogi, “Locality preserving projections,” Adv. Neural Inf. Process. Syst. 16, 1–8 (2003).

IEEE Signal Process. Lett. (1)

N. Gu, M. Fan, H. Qiao, and B. Zhang, “Discriminative sparsity preserving projections for semi-supervised dimensionality reduction,” IEEE Signal Process. Lett. 19, 391–394 (2012).
[CrossRef]

IEEE Signal Process. Mag. (1)

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25 (2), 21–30 (2008).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

J. Ma and F.-X. L. Dimet, “Deblurring from highly incomplete measurements for remote sensing,” IEEE Trans. Geosci. Remote Sens. 47, 792–802 (2009).
[CrossRef]

IEEE Trans. Image Process. (2)

D. Cai, X. He, and L. Han, “Orthogonal Laplacianfaces for face recognition,” IEEE Trans. Image Process. 15, 3608–3614 (2006).
[CrossRef]

M. Elad and M. Aharon, “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Trans. Image Process. 15, 3736–3745 (2006).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (5)

J. Yang, A. F. Frangi, J. Y. Yang, D. Zhang, and Z. Jin, “Kernel PCA plus LDA: a complete kernel Fisher discriminant framework for feature extraction and representation,” IEEE Trans. Pattern Anal. Mach. Intell. 27, 230–244 (2005).
[CrossRef]

J. Wright, A. Yang, A. Ganesh, S. Shastry, and Y. Ma, “Robust face recognition via sparse representation,” IEEE Trans. Pattern Anal. Mach. Intell. 31, 210–227 (2009).
[CrossRef]

A. K. Jain, R. P. W. Duin, and J. Mao, “Statistical pattern recognition: a review,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 4–37 (2000).
[CrossRef]

J. Yang, D. Zhang, and J.-Y. Yang, “Globally maximizing, locally minimizing: unsupervised discriminant projection with applications to face and palm biometrics,” IEEE Trans. Pattern Anal. Mach. Intell. 29, 650–664 (2007).
[CrossRef]

P. Belhumeur, J. Hesanha, and D. Kreigman, “Eigenfaces vs. Fisherfaces: recognition using class specific linear projection,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 711–720 (1997).
[CrossRef]

J. Mach. Learn. Res. (1)

L. K. Saul and S. T. Roweis, “Think globally, fit locally: unsupervised learning of low dimensional manifolds,” J. Mach. Learn. Res. 4, 119–155 (2003).
[CrossRef]

Lect. Notes Comput. Sci. (1)

Y. Lu, C. Lu, M. Qi, and S. Wang, “A supervised locality preserving projections based local matching algorithm for face recognition,” Lect. Notes Comput. Sci. 6059, 28–37 (2010).
[CrossRef]

Neural Comput. (1)

B. Scholkopf, A. Smola, and K. R. Muller, “Nonlinear component analysis as a kernel eigenvalues problem,” Neural Comput. 10, 1299–1319 (1998).
[CrossRef]

Neural Process. Lett. (1)

G. Feng, D. Hu, and Z. Zhou, “A direct locality preserving projections (DLPP) algorithm for image recognition,” Neural Process. Lett. 27, 247–255 (2008).

Neurocomputing (1)

J. Cheng, Q. Liu, H. Lu, and Y.-W. Chen, “Supervised kernel locality preserving projections for face recognition,” Neurocomputing 67, 443–449 (2005).
[CrossRef]

Opt. Eng. (1)

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50, 072601 (2011).
[CrossRef]

Pattern Recogn. (4)

H. Wang, C. Yuan, W. Hub, and C. Sun, “Supervised class-specific dictionary learning or sparse modeling in action recognition,” Pattern Recogn. 45, 3902–3911 (2012).
[CrossRef]

D. Hu, G. Feng, and Z. Zhou, “Two-dimensional locality preserving projections (2DLPP) with its application to palmprint recognition,” Pattern Recogn. 40, 339–342 (2007).
[CrossRef]

L. Qiao, S. Chen, and X. Tan, “Sparsity preserving projections with applications to face recognition,” Pattern Recogn. 43, 331–341 (2010).
[CrossRef]

H. Yu and J. Yang, “A direct LDA algorithm for high-dimensional data with application to face recognition,” Pattern Recogn. 34, 2067–2070 (2001).
[CrossRef]

Pattern Recogn. Lett. (1)

L. Qiao, S. Chen, and X. Tan, “Sparsity preserving discriminant analysis for single training image face recognition,” Pattern Recogn. Lett. 31, 422–429 (2010).
[CrossRef]

Phys. Rev. E (1)

Y. D. Leeuw and D. Cohen, “Diffusion in sparse networks: linear to semilinear crossover,” Phys. Rev. E 86, 051120 (2012).
[CrossRef]

Proc. IEEE (1)

J. Wright, Y. Ma, J. Mairal, G. Spairo, T. Huang, and S. Yan, “Sparse representation for computer vision and pattern recognition,” Proc. IEEE 98, 1031–1044 (2010).
[CrossRef]

Proc. SPIE (1)

Y. Sun, J. Zhao, and Y. Hu, “Supervised sparsity preserving projections for face recognition,” Proc. SPIE 8009, 80092D (2011).
[CrossRef]

Science (1)

S. T. Roweis and L. K. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science 290, 2323–2326 (2000).
[CrossRef]

Signal Process. (1)

Z. L. Zhang, F. Yang, W. Tan, J. Jia, and J. Yang, “Gabor feature based face recognition using supervised locality preserving projection,” Signal Process. 87, 2473–2483 (2007).
[CrossRef]

Other (16)

D. Cai, X. He, and K. Zhou, “Locality sensitive discriminant analysis,” in Proc. of International Joint Conf. on Artificial Intelligence, Hyderabad, India (2007), pp. 1–6.

M. Sugiyama, “Local Fisher discriminant analysis for supervised dimensionality reduction,” in Proc. of the 23th International Conf. on Machine Learning, Pittsburgh, USA (2006), pp. 1–8.

D. Cai, X. He, and J. Han, “Semi-supervised discriminant analysis,” in Tenth IEEE International Conf. on Computer Vision (IEEE, 2007), pp. 1–7.

Y. Bengio, J. Palement, and P. Vincent, “Out-of-sample extensions for LLE, isomap, MOS, eigenmaps, and spectral clustering,” in Advances in Neural Information Processing Systems 6, Cambridge, MA (2003), p. 117.

J. T. Jolloffe, Principal Component Analysis (Springer-Verlag, 1986).

M. Belkin and P. Niyogi, “Laplacian eigenmaps and spectral techniques for embedding and clustering,” in Advances in Neural Information Processing Systems 14, Vancouver, Canada (2001), pp. 585–591.

M. H. Yang, N. Ahuja, and D. Kriegman, “Face recognition using kernel eigenfaces,” in Proceedings of International Conf. on Image Processing, Vancouver, Canada (2000), pp. 1–4.

X. He, D. Cai, S. Yan, and H.-J. Zhang, “Neighborhood preserving embedding,” in Tenth IEEE International Conf. on Computer Vision, Beijing, China (2005), pp. 1–8.

S. Zhang, “Semi-supervised locality preserving projections with compactness enhancement,” in 2010 International Conf. on Educational and Information Technology, Chongqing, China (2010), pp. 460–464.

F. Yin, L. C. Jiao, F. Shang, S. Wang, and B. Hou, “Fast Fisher sparsity preserving projections,” Neural Comput. Appl.1–15 (2012).
[CrossRef]

F. Xiang, Z. Wang, and X. Yuan, “Image reconstruction based on sparse and redundant representation model: local vs nonlocal,” Optik (2012).
[CrossRef]

L. Zhang, M. Yang, and X. Feng, “Sparse representation or collaborative representation: which helps face recognition?,” in Tenth IEEE International Conf. on Computer Vision (IEEE, 2011), pp. 1–8.

R. P. W. Duin and E. Pekalska, “On refining dissimilarity matrices for an improved NN learning,” in Proceedings of 19th International Conf. on Pattern Recognition (IEEE, 2008), pp. 1–4.

M. Raazia, D. G. Paul, and N. W. Joseph, “A matching pursuit based similarity measure for fuzzy clustering and classification of signals,” in Proceedings of IEEE International Conference on Fuzzy Systems, Hong Kong, China (2008), pp. 1950–1955.

S. A. Nene, S. K. Nayar, and H. Murase, “Columbia Object Image Library (COIL100),” Department of Computer Science, Columbia University Tech. Rep. No.  (1996).

J. Wang, J. Yang, K. Yu, F. Lv, T. Huang, and Y. Gong, “Locality-constrained linear coding for image classification,” in 2010 IEEE Conf. on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 3360–3367.

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Figures (6)

Fig. 1.
Fig. 1.

First six basis vectors of PCA, LDA, LPP, NPE, SPP, DSPP, and D2SPP calculated from the training set of the ORL database.

Fig. 2.
Fig. 2.

Samples from Extended Yale B database under various illumination controls of class 18 and 25.

Fig. 3.
Fig. 3.

Samples from AR database under various clothing and facial expression of one individual.

Fig. 4.
Fig. 4.

Comparison of the recognition error rate corresponding to different dimensions on Extended Yale B.

Fig. 5.
Fig. 5.

Recognition rate of our method influenced by the selection of parameter α on Extended Yale B.

Fig. 6.
Fig. 6.

Comparison of the recognition rate corresponding to different dimensions on AR_random setting.

Tables (3)

Tables Icon

Table 1. Algorithm of Proposed DSPP

Tables Icon

Table 3. Top Recognition Rate (%) and Corresponding Dimensionality of Compared Methods

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

X={x1,x2,,xi,,xn}={X1,X2,,Xr}Rm×n,
minijyiyj2Sij,
Sij={exp(xixj2/t),ifxiandxjare ink nearest neighbor mutually0,others.
XLXTw=λXDXTw,
minsisi1s.t.Xsixi<ε1=1Tsi
min[siTtT]T[siTtT]T1s.t.[xi1]=[XI1T0T][siti],
minwi=1nwTxiwTXsi2s.t.wTXXTw=1,
maxwwTXSβXTwwTXXTw,
XSβXTw=λXXTw.
ai=argmina{yXai22+λai1},
y^=aTX=a1X1+a2X2++arXr,
Ri=yXiai.
y=Xiai+Ri.
ζ(x1,x2)=[αR1(x1,X)R2(x2,X)2+(1α)a1(x1,X)a2(x2,X)2]1/2,
i,j(zizj)2Hij,
12i,j(zizj)2Hij=12i,j(wTxiwTxj)2Hij=iwTxiCiixiTwi,jwTxiHijxiTw=wTXKXTw,
J(w)=argwTXXTw=1maxwTXKXTw,
J(w)=argmaxwTXKXTwwTXXTw,
XKXTw=λXXTw.
AXXTAT=I,AXKXTA=Λ,

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