Abstract

Face recognition is one of the most important applications of machine learning and computer vision. The traditional supervised learning methods require a large amount of labeled face images to achieve good performance. In practice, however, labeled images are usually scarce while unlabeled ones may be abundant. In this paper, we introduce a semi-supervised face recognition method, in which semi-supervised linear discriminant analysis (SDA) and affinity propagation (AP) are integrated into a self-training framework. In particular, SDA is employed to compute the face subspace using both labeled and unlabeled images, and AP is used to identify the exemplars of different face classes in the subspace. The unlabeled data can then be classified according to the exemplars and the newly labeled data with the highest confidence are added to the labeled data, and the whole procedure iterates until convergence. A series of experiments on four face datasets are carried out to evaluate the performance of our algorithm. Experimental results illustrate that our algorithm outperforms the other unsupervised, semi-supervised, and supervised methods.

© 2013 Optical Society of America

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    [CrossRef]
  2. R. Jafri and H. R. Arabnia, “A survey of face recognition techniques,” J. Inf. Process. Syst. 5, 41–68 (2009).
    [CrossRef]
  3. D. Cai, X. He, Y. Hu, J. Han, and T. Huang, “Learning a spatially smooth subspace for face recognition,” in Proceedings of IEEE Conference Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–7.
  4. X. He, S. Yan, Y. Hu, P. Niyogi, and H.-J. Zhang, “Face recognition using laplacianfaces,” IEEE Trans. Patt. Analysis Mach. Intell. 27, 328–340 (2005).
    [CrossRef]
  5. J. Lu, Y.-P. Tan, and G. Wang, “Discriminative multimanifold analysis for face recognition from a single training sample per person,” IEEE Trans. Patt. Analysis Mach. Intell. 35, 39–51 (2013).
    [CrossRef]
  6. R. Gross, I. Matthews, and S. Baker, “Appearance-based face recognition and light-fields,” IEEE Trans. Patt. Analysis Mach. Intell. 26, 449–465 (2004).
    [CrossRef]
  7. H. K. Ekenel and R. Stiefelhagen, “Local appearance-based face recognition using discrete cosine transform,” in 13th European Signal Processing Conference (EUSIPCO, 2005).
  8. H. Murase and S. K. Nayar, “Visual learning and recognition of 3D objects from appearance,” Int. J. Comput. Vis. 14, 5–24 (1995).
    [CrossRef]
  9. Z. Lei, S. Liao, M. Pietikainen, and S. Z. Li, “Face recognition by exploring information jointly in space, scale and orientation,” IEEE Trans. Image Process. 20, 247–256 (2011).
    [CrossRef]
  10. W. Yu, X. Teng, and C. Liu, “Face recognition using discriminant locality preserving projections,” Image Vis. Comput. 24, 239–248 (2006).
    [CrossRef]
  11. C. Rosenberg, M. Hebert, and H. Schneiderman, “Semi-supervised self-training of object detection models,” in Proceedings of the Seventh IEEE Workshops on Application of Computer Vision (IEEE, 2005), pp. 29–36.
  12. A. Blum and T. Mitchell, “Combining labeled and unlabeled data with co-training,” in Proceedings of the Eleventh Annual Conference on Computational Learning Theory (ACM, 1998), pp. 92–100.
  13. T. Joachims, “Transductive inference for text classification using support vector machines,” in Proceedings of the Sixteenth International Conference on Machine Learning (Morgan Kaufmann Publishers, 1999), pp. 200–209.
  14. K. P. Nigam, “Using unlabeled data to improve text classification,” Ph.D. thesis (Carnegie Mellon University, 2001). AAI3040487.
  15. X. Zhu, Z. Ghahramani, and J. Lafferty, “Semi-supervised learning using Gaussian fields and harmonic functions,” in Proceedings of the 20th International Conference on Machine Learning (Morgan Kaufmann Publishers, 2003), pp. 912–919.
  16. X. Zhu, “Semi-supervised learning literature survey,” (Computer Sciences, University of Wisconsin-Madison, 2005).
  17. F. Roli and G. Marcialis, “Semi-supervised PCA-based face recognition using self-training,” in Structural, Syntactic, and Statistical Pattern Recognition, Vol. 4109 of Lecture Notes in Computer Science (Springer, 2006), pp. 560–568.
  18. A. M. Martinez and A. Kak, “PCA versus LDA,” IEEE Trans. Patt. Analysis Mach. Intell. 23, 228–233 (2001).
    [CrossRef]
  19. X. Zhao, N. W. D. Evans, and J.-L. Dugelay, “Semi-supervised face recognition with LDA self-training,” in IEEE International Conference on Image Processing (IEEE, 2011), pp. 3102–3105.
  20. D. Cai, X. He, and J. Han, “Semi-supervised discriminant analysis,” in Proceedings of International Conference Computer Vision (IEEE, 2007).
  21. B. J. Frey and D. Dueck, “Clustering by passing messages between data points,” Science 315, 972–976 (2007).
    [CrossRef]
  22. Y. Fujiwara, G. Irie, and T. Kitahara, “Fast algorithm for affinity propagation,” in Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence (AAAI, 2011), pp. 2238–2243.
  23. F. Kschischang, B. Frey, and H.-A. Loeliger, “Factor graphs and the sum-product algorithm,” IEEE Trans. Inf. Theory 47, 498–519 (2001).
    [CrossRef]
  24. P. Belhumeur, J. Hespanha, and D. Kriegman, “Eigenfaces versus fisherfaces: recognition using class specific linear projection,” IEEE Trans. Patt. Analysis Mach. Intell. 19, 711–720 (1997).
    [CrossRef]
  25. M. Turk and A. Pentland, “Eigenfaces for recognition,” J. Cogn. Neurosci. 3, 71–86 (1991).
  26. ORL face dataset, http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html .
  27. Yale face dataset, http://cvc.yale.edu/projects/yalefaces/yalefaces.html .
  28. Extended Yale face dataset B, http://www.cad.zju.edu.cn/home/dengcai/Data/FaceData.html .
  29. D. Cai, X. He, J. Han, and H.-J. Zhang, “Orthogonal laplacianfaces for face recognition,” IEEE Trans. Image Process. 15, 3608–3614 (2006).
    [CrossRef]
  30. D. Cai, X. He, and J. Han, “Spectral regression for efficient regularized subspace learning,” in IEEE 11th International Conference on Computer Vision (IEEE, 2007), pp. 1–8.
  31. CMU PIE face dataset, http://vasc.ri.cmu.edu/idb/html/face/ .

2013

J. Lu, Y.-P. Tan, and G. Wang, “Discriminative multimanifold analysis for face recognition from a single training sample per person,” IEEE Trans. Patt. Analysis Mach. Intell. 35, 39–51 (2013).
[CrossRef]

2011

Z. Lei, S. Liao, M. Pietikainen, and S. Z. Li, “Face recognition by exploring information jointly in space, scale and orientation,” IEEE Trans. Image Process. 20, 247–256 (2011).
[CrossRef]

2009

R. Jafri and H. R. Arabnia, “A survey of face recognition techniques,” J. Inf. Process. Syst. 5, 41–68 (2009).
[CrossRef]

2007

B. J. Frey and D. Dueck, “Clustering by passing messages between data points,” Science 315, 972–976 (2007).
[CrossRef]

A. F. Abate, M. Nappi, D. Riccio, and G. Sabatino, “2D and 3D face recognition: a survey,” Pattern Recogn. Lett. 28, 1885–1906 (2007).
[CrossRef]

2006

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

W. Yu, X. Teng, and C. Liu, “Face recognition using discriminant locality preserving projections,” Image Vis. Comput. 24, 239–248 (2006).
[CrossRef]

2005

X. He, S. Yan, Y. Hu, P. Niyogi, and H.-J. Zhang, “Face recognition using laplacianfaces,” IEEE Trans. Patt. Analysis Mach. Intell. 27, 328–340 (2005).
[CrossRef]

2004

R. Gross, I. Matthews, and S. Baker, “Appearance-based face recognition and light-fields,” IEEE Trans. Patt. Analysis Mach. Intell. 26, 449–465 (2004).
[CrossRef]

2001

F. Kschischang, B. Frey, and H.-A. Loeliger, “Factor graphs and the sum-product algorithm,” IEEE Trans. Inf. Theory 47, 498–519 (2001).
[CrossRef]

A. M. Martinez and A. Kak, “PCA versus LDA,” IEEE Trans. Patt. Analysis Mach. Intell. 23, 228–233 (2001).
[CrossRef]

1997

P. Belhumeur, J. Hespanha, and D. Kriegman, “Eigenfaces versus fisherfaces: recognition using class specific linear projection,” IEEE Trans. Patt. Analysis Mach. Intell. 19, 711–720 (1997).
[CrossRef]

1995

H. Murase and S. K. Nayar, “Visual learning and recognition of 3D objects from appearance,” Int. J. Comput. Vis. 14, 5–24 (1995).
[CrossRef]

1991

M. Turk and A. Pentland, “Eigenfaces for recognition,” J. Cogn. Neurosci. 3, 71–86 (1991).

Abate, A. F.

A. F. Abate, M. Nappi, D. Riccio, and G. Sabatino, “2D and 3D face recognition: a survey,” Pattern Recogn. Lett. 28, 1885–1906 (2007).
[CrossRef]

Arabnia, H. R.

R. Jafri and H. R. Arabnia, “A survey of face recognition techniques,” J. Inf. Process. Syst. 5, 41–68 (2009).
[CrossRef]

Baker, S.

R. Gross, I. Matthews, and S. Baker, “Appearance-based face recognition and light-fields,” IEEE Trans. Patt. Analysis Mach. Intell. 26, 449–465 (2004).
[CrossRef]

Belhumeur, P.

P. Belhumeur, J. Hespanha, and D. Kriegman, “Eigenfaces versus fisherfaces: recognition using class specific linear projection,” IEEE Trans. Patt. Analysis Mach. Intell. 19, 711–720 (1997).
[CrossRef]

Blum, A.

A. Blum and T. Mitchell, “Combining labeled and unlabeled data with co-training,” in Proceedings of the Eleventh Annual Conference on Computational Learning Theory (ACM, 1998), pp. 92–100.

Cai, D.

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

D. Cai, X. He, and J. Han, “Semi-supervised discriminant analysis,” in Proceedings of International Conference Computer Vision (IEEE, 2007).

D. Cai, X. He, Y. Hu, J. Han, and T. Huang, “Learning a spatially smooth subspace for face recognition,” in Proceedings of IEEE Conference Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–7.

D. Cai, X. He, and J. Han, “Spectral regression for efficient regularized subspace learning,” in IEEE 11th International Conference on Computer Vision (IEEE, 2007), pp. 1–8.

Dueck, D.

B. J. Frey and D. Dueck, “Clustering by passing messages between data points,” Science 315, 972–976 (2007).
[CrossRef]

Dugelay, J.-L.

X. Zhao, N. W. D. Evans, and J.-L. Dugelay, “Semi-supervised face recognition with LDA self-training,” in IEEE International Conference on Image Processing (IEEE, 2011), pp. 3102–3105.

Ekenel, H. K.

H. K. Ekenel and R. Stiefelhagen, “Local appearance-based face recognition using discrete cosine transform,” in 13th European Signal Processing Conference (EUSIPCO, 2005).

Evans, N. W. D.

X. Zhao, N. W. D. Evans, and J.-L. Dugelay, “Semi-supervised face recognition with LDA self-training,” in IEEE International Conference on Image Processing (IEEE, 2011), pp. 3102–3105.

Frey, B.

F. Kschischang, B. Frey, and H.-A. Loeliger, “Factor graphs and the sum-product algorithm,” IEEE Trans. Inf. Theory 47, 498–519 (2001).
[CrossRef]

Frey, B. J.

B. J. Frey and D. Dueck, “Clustering by passing messages between data points,” Science 315, 972–976 (2007).
[CrossRef]

Fujiwara, Y.

Y. Fujiwara, G. Irie, and T. Kitahara, “Fast algorithm for affinity propagation,” in Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence (AAAI, 2011), pp. 2238–2243.

Ghahramani, Z.

X. Zhu, Z. Ghahramani, and J. Lafferty, “Semi-supervised learning using Gaussian fields and harmonic functions,” in Proceedings of the 20th International Conference on Machine Learning (Morgan Kaufmann Publishers, 2003), pp. 912–919.

Gross, R.

R. Gross, I. Matthews, and S. Baker, “Appearance-based face recognition and light-fields,” IEEE Trans. Patt. Analysis Mach. Intell. 26, 449–465 (2004).
[CrossRef]

Han, J.

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

D. Cai, X. He, and J. Han, “Semi-supervised discriminant analysis,” in Proceedings of International Conference Computer Vision (IEEE, 2007).

D. Cai, X. He, Y. Hu, J. Han, and T. Huang, “Learning a spatially smooth subspace for face recognition,” in Proceedings of IEEE Conference Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–7.

D. Cai, X. He, and J. Han, “Spectral regression for efficient regularized subspace learning,” in IEEE 11th International Conference on Computer Vision (IEEE, 2007), pp. 1–8.

He, X.

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

X. He, S. Yan, Y. Hu, P. Niyogi, and H.-J. Zhang, “Face recognition using laplacianfaces,” IEEE Trans. Patt. Analysis Mach. Intell. 27, 328–340 (2005).
[CrossRef]

D. Cai, X. He, Y. Hu, J. Han, and T. Huang, “Learning a spatially smooth subspace for face recognition,” in Proceedings of IEEE Conference Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–7.

D. Cai, X. He, and J. Han, “Semi-supervised discriminant analysis,” in Proceedings of International Conference Computer Vision (IEEE, 2007).

D. Cai, X. He, and J. Han, “Spectral regression for efficient regularized subspace learning,” in IEEE 11th International Conference on Computer Vision (IEEE, 2007), pp. 1–8.

Hebert, M.

C. Rosenberg, M. Hebert, and H. Schneiderman, “Semi-supervised self-training of object detection models,” in Proceedings of the Seventh IEEE Workshops on Application of Computer Vision (IEEE, 2005), pp. 29–36.

Hespanha, J.

P. Belhumeur, J. Hespanha, and D. Kriegman, “Eigenfaces versus fisherfaces: recognition using class specific linear projection,” IEEE Trans. Patt. Analysis Mach. Intell. 19, 711–720 (1997).
[CrossRef]

Hu, Y.

X. He, S. Yan, Y. Hu, P. Niyogi, and H.-J. Zhang, “Face recognition using laplacianfaces,” IEEE Trans. Patt. Analysis Mach. Intell. 27, 328–340 (2005).
[CrossRef]

D. Cai, X. He, Y. Hu, J. Han, and T. Huang, “Learning a spatially smooth subspace for face recognition,” in Proceedings of IEEE Conference Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–7.

Huang, T.

D. Cai, X. He, Y. Hu, J. Han, and T. Huang, “Learning a spatially smooth subspace for face recognition,” in Proceedings of IEEE Conference Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–7.

Irie, G.

Y. Fujiwara, G. Irie, and T. Kitahara, “Fast algorithm for affinity propagation,” in Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence (AAAI, 2011), pp. 2238–2243.

Jafri, R.

R. Jafri and H. R. Arabnia, “A survey of face recognition techniques,” J. Inf. Process. Syst. 5, 41–68 (2009).
[CrossRef]

Joachims, T.

T. Joachims, “Transductive inference for text classification using support vector machines,” in Proceedings of the Sixteenth International Conference on Machine Learning (Morgan Kaufmann Publishers, 1999), pp. 200–209.

Kak, A.

A. M. Martinez and A. Kak, “PCA versus LDA,” IEEE Trans. Patt. Analysis Mach. Intell. 23, 228–233 (2001).
[CrossRef]

Kitahara, T.

Y. Fujiwara, G. Irie, and T. Kitahara, “Fast algorithm for affinity propagation,” in Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence (AAAI, 2011), pp. 2238–2243.

Kriegman, D.

P. Belhumeur, J. Hespanha, and D. Kriegman, “Eigenfaces versus fisherfaces: recognition using class specific linear projection,” IEEE Trans. Patt. Analysis Mach. Intell. 19, 711–720 (1997).
[CrossRef]

Kschischang, F.

F. Kschischang, B. Frey, and H.-A. Loeliger, “Factor graphs and the sum-product algorithm,” IEEE Trans. Inf. Theory 47, 498–519 (2001).
[CrossRef]

Lafferty, J.

X. Zhu, Z. Ghahramani, and J. Lafferty, “Semi-supervised learning using Gaussian fields and harmonic functions,” in Proceedings of the 20th International Conference on Machine Learning (Morgan Kaufmann Publishers, 2003), pp. 912–919.

Lei, Z.

Z. Lei, S. Liao, M. Pietikainen, and S. Z. Li, “Face recognition by exploring information jointly in space, scale and orientation,” IEEE Trans. Image Process. 20, 247–256 (2011).
[CrossRef]

Li, S. Z.

Z. Lei, S. Liao, M. Pietikainen, and S. Z. Li, “Face recognition by exploring information jointly in space, scale and orientation,” IEEE Trans. Image Process. 20, 247–256 (2011).
[CrossRef]

Liao, S.

Z. Lei, S. Liao, M. Pietikainen, and S. Z. Li, “Face recognition by exploring information jointly in space, scale and orientation,” IEEE Trans. Image Process. 20, 247–256 (2011).
[CrossRef]

Liu, C.

W. Yu, X. Teng, and C. Liu, “Face recognition using discriminant locality preserving projections,” Image Vis. Comput. 24, 239–248 (2006).
[CrossRef]

Loeliger, H.-A.

F. Kschischang, B. Frey, and H.-A. Loeliger, “Factor graphs and the sum-product algorithm,” IEEE Trans. Inf. Theory 47, 498–519 (2001).
[CrossRef]

Lu, J.

J. Lu, Y.-P. Tan, and G. Wang, “Discriminative multimanifold analysis for face recognition from a single training sample per person,” IEEE Trans. Patt. Analysis Mach. Intell. 35, 39–51 (2013).
[CrossRef]

Marcialis, G.

F. Roli and G. Marcialis, “Semi-supervised PCA-based face recognition using self-training,” in Structural, Syntactic, and Statistical Pattern Recognition, Vol. 4109 of Lecture Notes in Computer Science (Springer, 2006), pp. 560–568.

Martinez, A. M.

A. M. Martinez and A. Kak, “PCA versus LDA,” IEEE Trans. Patt. Analysis Mach. Intell. 23, 228–233 (2001).
[CrossRef]

Matthews, I.

R. Gross, I. Matthews, and S. Baker, “Appearance-based face recognition and light-fields,” IEEE Trans. Patt. Analysis Mach. Intell. 26, 449–465 (2004).
[CrossRef]

Mitchell, T.

A. Blum and T. Mitchell, “Combining labeled and unlabeled data with co-training,” in Proceedings of the Eleventh Annual Conference on Computational Learning Theory (ACM, 1998), pp. 92–100.

Murase, H.

H. Murase and S. K. Nayar, “Visual learning and recognition of 3D objects from appearance,” Int. J. Comput. Vis. 14, 5–24 (1995).
[CrossRef]

Nappi, M.

A. F. Abate, M. Nappi, D. Riccio, and G. Sabatino, “2D and 3D face recognition: a survey,” Pattern Recogn. Lett. 28, 1885–1906 (2007).
[CrossRef]

Nayar, S. K.

H. Murase and S. K. Nayar, “Visual learning and recognition of 3D objects from appearance,” Int. J. Comput. Vis. 14, 5–24 (1995).
[CrossRef]

Nigam, K. P.

K. P. Nigam, “Using unlabeled data to improve text classification,” Ph.D. thesis (Carnegie Mellon University, 2001). AAI3040487.

Niyogi, P.

X. He, S. Yan, Y. Hu, P. Niyogi, and H.-J. Zhang, “Face recognition using laplacianfaces,” IEEE Trans. Patt. Analysis Mach. Intell. 27, 328–340 (2005).
[CrossRef]

Pentland, A.

M. Turk and A. Pentland, “Eigenfaces for recognition,” J. Cogn. Neurosci. 3, 71–86 (1991).

Pietikainen, M.

Z. Lei, S. Liao, M. Pietikainen, and S. Z. Li, “Face recognition by exploring information jointly in space, scale and orientation,” IEEE Trans. Image Process. 20, 247–256 (2011).
[CrossRef]

Riccio, D.

A. F. Abate, M. Nappi, D. Riccio, and G. Sabatino, “2D and 3D face recognition: a survey,” Pattern Recogn. Lett. 28, 1885–1906 (2007).
[CrossRef]

Roli, F.

F. Roli and G. Marcialis, “Semi-supervised PCA-based face recognition using self-training,” in Structural, Syntactic, and Statistical Pattern Recognition, Vol. 4109 of Lecture Notes in Computer Science (Springer, 2006), pp. 560–568.

Rosenberg, C.

C. Rosenberg, M. Hebert, and H. Schneiderman, “Semi-supervised self-training of object detection models,” in Proceedings of the Seventh IEEE Workshops on Application of Computer Vision (IEEE, 2005), pp. 29–36.

Sabatino, G.

A. F. Abate, M. Nappi, D. Riccio, and G. Sabatino, “2D and 3D face recognition: a survey,” Pattern Recogn. Lett. 28, 1885–1906 (2007).
[CrossRef]

Schneiderman, H.

C. Rosenberg, M. Hebert, and H. Schneiderman, “Semi-supervised self-training of object detection models,” in Proceedings of the Seventh IEEE Workshops on Application of Computer Vision (IEEE, 2005), pp. 29–36.

Stiefelhagen, R.

H. K. Ekenel and R. Stiefelhagen, “Local appearance-based face recognition using discrete cosine transform,” in 13th European Signal Processing Conference (EUSIPCO, 2005).

Tan, Y.-P.

J. Lu, Y.-P. Tan, and G. Wang, “Discriminative multimanifold analysis for face recognition from a single training sample per person,” IEEE Trans. Patt. Analysis Mach. Intell. 35, 39–51 (2013).
[CrossRef]

Teng, X.

W. Yu, X. Teng, and C. Liu, “Face recognition using discriminant locality preserving projections,” Image Vis. Comput. 24, 239–248 (2006).
[CrossRef]

Turk, M.

M. Turk and A. Pentland, “Eigenfaces for recognition,” J. Cogn. Neurosci. 3, 71–86 (1991).

Wang, G.

J. Lu, Y.-P. Tan, and G. Wang, “Discriminative multimanifold analysis for face recognition from a single training sample per person,” IEEE Trans. Patt. Analysis Mach. Intell. 35, 39–51 (2013).
[CrossRef]

Yan, S.

X. He, S. Yan, Y. Hu, P. Niyogi, and H.-J. Zhang, “Face recognition using laplacianfaces,” IEEE Trans. Patt. Analysis Mach. Intell. 27, 328–340 (2005).
[CrossRef]

Yu, W.

W. Yu, X. Teng, and C. Liu, “Face recognition using discriminant locality preserving projections,” Image Vis. Comput. 24, 239–248 (2006).
[CrossRef]

Zhang, H.-J.

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

X. He, S. Yan, Y. Hu, P. Niyogi, and H.-J. Zhang, “Face recognition using laplacianfaces,” IEEE Trans. Patt. Analysis Mach. Intell. 27, 328–340 (2005).
[CrossRef]

Zhao, X.

X. Zhao, N. W. D. Evans, and J.-L. Dugelay, “Semi-supervised face recognition with LDA self-training,” in IEEE International Conference on Image Processing (IEEE, 2011), pp. 3102–3105.

Zhu, X.

X. Zhu, Z. Ghahramani, and J. Lafferty, “Semi-supervised learning using Gaussian fields and harmonic functions,” in Proceedings of the 20th International Conference on Machine Learning (Morgan Kaufmann Publishers, 2003), pp. 912–919.

X. Zhu, “Semi-supervised learning literature survey,” (Computer Sciences, University of Wisconsin-Madison, 2005).

IEEE Trans. Image Process.

Z. Lei, S. Liao, M. Pietikainen, and S. Z. Li, “Face recognition by exploring information jointly in space, scale and orientation,” IEEE Trans. Image Process. 20, 247–256 (2011).
[CrossRef]

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

IEEE Trans. Inf. Theory

F. Kschischang, B. Frey, and H.-A. Loeliger, “Factor graphs and the sum-product algorithm,” IEEE Trans. Inf. Theory 47, 498–519 (2001).
[CrossRef]

IEEE Trans. Patt. Analysis Mach. Intell.

P. Belhumeur, J. Hespanha, and D. Kriegman, “Eigenfaces versus fisherfaces: recognition using class specific linear projection,” IEEE Trans. Patt. Analysis Mach. Intell. 19, 711–720 (1997).
[CrossRef]

A. M. Martinez and A. Kak, “PCA versus LDA,” IEEE Trans. Patt. Analysis Mach. Intell. 23, 228–233 (2001).
[CrossRef]

X. He, S. Yan, Y. Hu, P. Niyogi, and H.-J. Zhang, “Face recognition using laplacianfaces,” IEEE Trans. Patt. Analysis Mach. Intell. 27, 328–340 (2005).
[CrossRef]

J. Lu, Y.-P. Tan, and G. Wang, “Discriminative multimanifold analysis for face recognition from a single training sample per person,” IEEE Trans. Patt. Analysis Mach. Intell. 35, 39–51 (2013).
[CrossRef]

R. Gross, I. Matthews, and S. Baker, “Appearance-based face recognition and light-fields,” IEEE Trans. Patt. Analysis Mach. Intell. 26, 449–465 (2004).
[CrossRef]

Image Vis. Comput.

W. Yu, X. Teng, and C. Liu, “Face recognition using discriminant locality preserving projections,” Image Vis. Comput. 24, 239–248 (2006).
[CrossRef]

Int. J. Comput. Vis.

H. Murase and S. K. Nayar, “Visual learning and recognition of 3D objects from appearance,” Int. J. Comput. Vis. 14, 5–24 (1995).
[CrossRef]

J. Cogn. Neurosci.

M. Turk and A. Pentland, “Eigenfaces for recognition,” J. Cogn. Neurosci. 3, 71–86 (1991).

J. Inf. Process. Syst.

R. Jafri and H. R. Arabnia, “A survey of face recognition techniques,” J. Inf. Process. Syst. 5, 41–68 (2009).
[CrossRef]

Pattern Recogn. Lett.

A. F. Abate, M. Nappi, D. Riccio, and G. Sabatino, “2D and 3D face recognition: a survey,” Pattern Recogn. Lett. 28, 1885–1906 (2007).
[CrossRef]

Science

B. J. Frey and D. Dueck, “Clustering by passing messages between data points,” Science 315, 972–976 (2007).
[CrossRef]

Other

Y. Fujiwara, G. Irie, and T. Kitahara, “Fast algorithm for affinity propagation,” in Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence (AAAI, 2011), pp. 2238–2243.

X. Zhao, N. W. D. Evans, and J.-L. Dugelay, “Semi-supervised face recognition with LDA self-training,” in IEEE International Conference on Image Processing (IEEE, 2011), pp. 3102–3105.

D. Cai, X. He, and J. Han, “Semi-supervised discriminant analysis,” in Proceedings of International Conference Computer Vision (IEEE, 2007).

ORL face dataset, http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html .

Yale face dataset, http://cvc.yale.edu/projects/yalefaces/yalefaces.html .

Extended Yale face dataset B, http://www.cad.zju.edu.cn/home/dengcai/Data/FaceData.html .

D. Cai, X. He, and J. Han, “Spectral regression for efficient regularized subspace learning,” in IEEE 11th International Conference on Computer Vision (IEEE, 2007), pp. 1–8.

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Figures (6)

Fig. 1.
Fig. 1.

Results obtained by mean templates and AP after 10 iterations.

Fig. 2.
Fig. 2.

Flow chart of our algorithm.

Fig. 3.
Fig. 3.

Face images from the four face datasets.

Fig. 4.
Fig. 4.

Recognition accuracy on ORL dataset.

Fig. 5.
Fig. 5.

Recognition accuracy on Yale dataset.

Fig. 6.
Fig. 6.

Recognition accuracy on Yale_B dataset.

Tables (6)

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Algorithm 1 Label the unlabeled images

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Table 1. Description of Experimental Face Datasets

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Table 2. Recognition Accuracy of the Five Algorithms on Testing Face Set in Three Face Datasets

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Table 3. Recognition Accuracy of the Two Algorithms on the Unlabeled Set in Three Face Datasets

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Table 4. Recognition Accuracy of the Two Algorithms on the Testing Set in Three Face Datasets with Different Selected Images in Each Iteration

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Table 5. Recognition Accuracies of the Four Algorithms on the CMU PIE Face Dataset with One Labeled Image per Individual

Equations (10)

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

J1(a)=aTXWXTa.
J2(a)=aTXI˜XTa,
I˜=[I000]
Sij={1ifxiNp(xj)orxjNp(xi)0otherwise,
J3(a)=ij(aTxiaTxj)2Sij=2aTXLXTa,
maxaaTXWXTaaT(X(I˜+αL)XT+βI)a.
XWXTa=λ(X(I˜+αL)XT+βI)a.
rij=(1λ)ρij+λrijaij=(1λ)αij+λaij,
ρij={sijmaxkj{aik+sik}ijsijmaxkj{sik}i=j
αij={min{0,rjj+Σki,jmax{0,rkj}}ijΣkjmax{0,rkj}i=j.

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