Abstract
Sparse representation is a mathematical model for data representation that has proved to be a powerful tool for solving problems in various fields such as pattern recognition, machine learning, and computer vision. As one of the building blocks of the sparse representation method, dictionary learning plays an important role in the minimization of the reconstruction error between the original signal and its sparse representation in the space of the learned dictionary. Although using training samples directly as dictionary bases can achieve good performance, the main drawback of this method is that it may result in a very large and inefficient dictionary due to noisy training instances. To obtain a smaller and more representative dictionary, in this paper, we propose an approach called Laplacian sparse dictionary (LSD) learning. Our method is based on manifold learning and double sparsity. We incorporate the Laplacian weighted graph in the sparse representation model and impose the l1-norm sparsity on the dictionary. An LSD is a sparse overcomplete dictionary that can preserve the intrinsic structure of the data and learn a smaller dictionary for each class. The learned LSD can be easily integrated into a classification framework based on sparse representation. We compare the proposed method with other methods using three benchmark-controlled face image databases, Extended Yale B, ORL, and AR, and one uncontrolled person image dataset, i-LIDS-MA. Results show the advantages of the proposed LSD algorithm over state-of-the-art sparse representation based classification methods.
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References
Aharon, M., Elad, M., Bruckstein, A., 2006. K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Signal Process., 54(11): 4311–4322. https://doi.org/10.1109/TSP.2006.881199
Bąk, S., Corvee, E., Bremond, F., et al., 2012. Boosted human re-identification using Riemannian manifolds. Image Vis. Comput., 30(6): 443–452. https://doi.org/10.1016/j.imavis.2011.08.008
Belhumeur, P.N., Hespanha, J.P., Kriegman, D.J., 1997. Eigenfaces vs. Fisherfaces: recognition using class specific linear projection. IEEE Trans. Patt. Anal. Mach. Intell., 19(7): 711–720. https://doi.org/10.1109/34.598228
Belkin, M., Niyogi, P., 2001. Laplacian eigenmaps and spectral techniques for embedding and clustering. In: Advances in Neural Information Processing Systems. MIT Press, Cambridge, MA, p.585–591.
Chapelle, O., Schölkopf, B., Zien, A., 2006. Semi-supervised Learning. MIT Press, Cambridge, MA.
Elhamifar, E., Vidal, R., 2013. Sparse subspace clustering: algorithm, theory, and applications. IEEE Trans. Patt. Anal. Mach. Intell., 35(11): 2765–2781. https://doi.org/10.1109/TPAMI.2013.57
Gangeh, M.J., Ghodsi, A., Kamel, M.S., 2013. Kernelized supervised dictionary learning. IEEE Trans. Signal Process., 61(19): 4753–4767. https://doi.org/10.1109/TSP.2013.2274276
Gao, S., Tsang, I.W.H., Ma, Y., 2014. Learning categoryspecific dictionary and shared dictionary for fine-grained image categorization. IEEE Trans. Image Process., 23(2): 623–634. https://doi.org/10.1109/TIP.2013.2290593
Georghiades, A.S., Belhumeur, P.N., Kriegman, D.J., 2001. From few to many: illumination cone models for face recognition under variable lighting and pose. IEEE Trans. Patt. Anal. Mach. Intell., 23(6): 643–660. https://doi.org/10.1109/34.927464
He, X., Niyogi, P., 2003. Locality preserving projections. 17th Annual Conf. on Neural Information Processing Systems, p.186–197.
He, X., Yan, S., Hu, Y., et al., 2005. Face recognition using Laplacian faces. IEEE Trans. Patt. Anal. Mach. Intell., 27(3): 328–340. https://doi.org/10.1109/TPAMI.2005.55
Huang, M., Yang, W., Jiang, J., et al., 2014. Brain extraction based on locally linear representation-based classification. NeuroImage, 92: 322–339. https://doi.org/10.1016/j.neuroimage.2014.01.059
Lee, H., Battle, A., Raina, R., et al., 2006. Efficient sparse coding algorithms. In: Advances in Neural Information Processing Systems. MIT Press, Cambridge, MA, p.801–808.
Lee, K.C., Ho, J., Kriegman, D.J., 2005. Acquiring linear subspaces for face recognition under variable lighting. IEEE Trans. Patt. Anal. Mach. Intell., 27(5): 684–698. https://doi.org/10.1109/TPAMI.2005.92
Lu, X., Li, X., 2014. Group sparse reconstruction for image segmentation. Neurocomputing, 136: 41–48. https://doi.org/10.1016/j.neucom.2014.01.034
Lu, X., Wu, H., Yuan, Y., et al., 2013. Manifold regularized sparse NMF for hyperspectral unmixing. IEEE Trans. Geosci. Remote Sens., 51(5): 2815–2826. https://doi.org/10.1109/TGRS.2012.2213825
Lu, Y., Lai, Z., Fan, Z., et al., 2015. Manifold discriminant regression learning for image classification. Neurocomputing, 166: 475–486. https://doi.org/10.1016/j.neucom.2015.03.031
Martinez, A.M., Benavente, R., 1998. The AR Face Database. CVC Technical Report, No. 24. Centre de Visió per Computador, Universitat Autònoma de Barcelona, Edifici O, Bellaterra, Barcelona.
Peleg, T., Elad, M., 2014. A statistical prediction model based on sparse representations for single image superresolution. IEEE Trans. Image Process., 23(6): 2569–2582. https://doi.org/10.1109/TIP.2014.2305844
Qiao, L., Chen, S., Tan, X., 2010. Sparsity preserving projections with applications to face recognition. Patt. Recogn., 43(1): 331–341. https://doi.org/10.1016/j.patcog.2009.05.005
Roweis, S.T., Saul, L.K., 2000. Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500): 2323–2326. https://doi.org/10.1126/science.290.5500.2323
Rubinstein, R., Bruckstein, A.M., Elad, M., 2010a. Dictionaries for sparse representation modeling. Proc. IEEE, 98(6): 1045–1057. https://doi.org/10.1109/JPROC.2010.2040551
Rubinstein, R., Zibulevsky, M., Elad, M., 2010b. Double sparsity: learning sparse dictionaries for sparse signal approximation. IEEE Trans. Signal Process., 58(3): 1553–1564. https://doi.org/10.1109/TSP.2009.2036477
Shao, L., Yan, R., Li, X., et al., 2014. From heuristic optimization to dictionary learning: a review and comprehensive comparison of image denoising algorithms. IEEE Trans. Cybern., 44(7): 1001–1013. https://doi.org/10.1109/TCYB.2013.2278548
Tenenbaum, J.B., de Silva, V., Langford, J.C., 2000. A global geometric framework for nonlinear dimensionality reduction. Science, 290(5500): 2319–2323. https://doi.org/10.1126/science.290.5500.2319
Tibshirani, R., 1996. Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B (Methodol.), 58(2): 267–288.
Turk, M., Pentland, A., 1991. Eigenfaces for recognition. J. Cogn. Neurosci., 3(1): 71–86.
Wang, W., Wang, R., Huang, Z., et al., 2015. Discriminant analysis on Riemannian manifold of Gaussian distributions for face recognition with image sets. Proc. IEEE Conf. on Computer Vision and Pattern Recognition, p.2048–2057. https://doi.org/10.1109/TCSVT.2014.2367357
Wright, J., Yang, A.Y., Ganesh, A., et al., 2009. Robust face recognition via sparse representation. IEEE Trans. Patt. Anal. Mach. Intell., 31(2): 210–227. https://doi.org/10.1109/TPAMI.2008.79
Yang, A.Y., Zhou, Z., Balasubramanian, A.G., et al., 2013. Fast-l1 minimization algorithms for robust face recognition. IEEE Trans. Image Process., 22(8): 3234–3246. https://doi.org/10.1109/TIP.2013.2262292
Yang, J., Zhang, L., Xu, Y., et al., 2012. Beyond sparsity: the role of l1-optimizer in pattern classification. Patt. Recogn., 45(3): 1104–1118. https://doi.org/10.1016/j.patcog.2011.08.022
Yang, J.F., Zhang, Y., 2011. Alternating direction algorithms for ℓ1-problems in compressive sensing. SIAM J. Sci. Comput., 33(1): 250–278. https://doi.org/10.1137/090777761
Yang, M., Zhang, L., Yang, J., et al., 2010. Metaface learning for sparse representation-based face recognition. 17th IEEE Int. Conf. on Image Processing, p.1601–1604. https://doi.org/10.1109/ICIP.2010.5652363
Yang, M., van Gool, L., Zhang, L., 2013. Sparse variation dictionary learning for face recognition with a single training sample per person. IEEE Int. Conf. on Computer Vision, p.689–696. https://doi.org/10.1109/ICCV.2013.91
Yang, M., Dai, D., Shen, L., et al., 2014. Latent dictionary learning for sparse representation-based classification. IEEE Conf. on Computer Vision and Pattern Recognition, p.4138–4145. https://doi.org/10.1109/CVPR.2014.527
Zhang, Z., Xu, Y., Yang, J., et al., 2015. A survey of sparse representation: algorithms and applications. IEEE Access, 3: 490–530. https://doi.org/10.1109/ACCESS.2015.2430359
Zheng, M., Bu, J., Chen, C., et al., 2011. Graph regularized sparse coding for image representation. IEEE Trans. Image Process., 20(5): 1327–1336. https://doi.org/10.1109/TIP.2010.2090535
Zhu, P., Zuo, W., Zhang, L., et al., 2014. Image set-based collaborative representation for face recognition. IEEE Trans. Inform. Forens. Secur., 9(7): 1120–1132. https://doi.org/10.1109/TIFS.2014.2324277
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Project supported by the National Natural Science Foundation of China (Nos. 61272304 and 61363029) and the Guangxi Key Laboratory of Trusted Software (No. kx201313)
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Li, F., Sheng, J. & Zhang, Sy. Laplacian sparse dictionary learning for image classification based on sparse representation. Frontiers Inf Technol Electronic Eng 18, 1795–1805 (2017). https://doi.org/10.1631/FITEE.1600039
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DOI: https://doi.org/10.1631/FITEE.1600039