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.

基于稀疏表示的拉普拉斯稀疏字典图像分类

[1]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.

[2]Bąk, S., Corvee, E., Bremond, F., et al., 2012. Boosted human re-identification using Riemannian manifolds. Image Vis. Comput., 30(6):443-452.

[3]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.

[4]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.

[5]Chapelle, O., Schölkopf, B., Zien, A., 2006. Semi-supervised Learning. MIT Press, Cambridge, MA.

[6]Elhamifar, E., Vidal, R., 2013. Sparse subspace clustering: algorithm, theory, and applications. IEEE Trans. Patt. Anal. Mach. Intell., 35(11):2765-2781.

[7]Gangeh, M.J., Ghodsi, A., Kamel, M.S., 2013. Kernelized supervised dictionary learning. IEEE Trans. Signal Process., 61(19):4753-4767.

[8]Gao, S., Tsang, I.W.H., Ma, Y., 2014. Learning category-specific dictionary and shared dictionary for fine-grained image categorization. IEEE Trans. Image Process., 23(2): 623-634.

[9]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.

[10]He, X., Niyogi, P., 2003. Locality preserving projections. 17th Annual Conf. on Neural Information Processing Systems, p.186-197.

[11]He, X., Yan, S., Hu, Y., et al., 2005. Face recognition using Laplacian faces. IEEE Trans. Patt. Anal. Mach. Intell., 27(3):328-340.

[12]Huang, M., Yang, W., Jiang, J., et al., 2014. Brain extraction based on locally linear representation-based classification. NeuroImage, 92:322-339.

[13]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.

[14]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.

[15]Lu, X., Li, X., 2014. Group sparse reconstruction for image segmentation. Neurocomputing, 136:41-48.

[16]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.

[17]Lu, Y., Lai, Z., Fan, Z., et al., 2015. Manifold discriminant regression learning for image classification. Neurocomputing, 166:475-486.

[18]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.

[19]Peleg, T., Elad, M., 2014. A statistical prediction model based on sparse representations for single image super- resolution. IEEE Trans. Image Process., 23(6):2569-2582.

[20]Qiao, L., Chen, S., Tan, X., 2010. Sparsity preserving projections with applications to face recognition. Patt. Recogn., 43(1):331-341.

[21]Roweis, S.T., Saul, L.K., 2000. Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500): 2323-2326.

[22]Rubinstein, R., Bruckstein, A.M., Elad, M., 2010a. Dictionaries for sparse representation modeling. Proc. IEEE, 98(6):1045-1057.

[23]Rubinstein, R., Zibulevsky, M., Elad, M., 2010b. Double sparsity: learning sparse dictionaries for sparse signal approximation. IEEE Trans. Signal Process., 58(3): 1553-1564.

[24]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.

[25]Tenenbaum, J.B., de Silva, V., Langford, J.C., 2000. A global geometric framework for nonlinear dimensionality reduction. Science, 290(5500):2319-2323.

[26]Tibshirani, R., 1996. Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B (Methodol.), 58(2):267-288.

[27]Turk, M., Pentland, A., 1991. Eigenfaces for recognition. J. Cogn. Neurosci., 3(1):71-86.

[28]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.

[29]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.

[30]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.

[31]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.

[32]Yang, J.F., Zhang, Y., 2011. Alternating direction algorithms for -problems in compressive sensing. SIAM J. Sci. Comput., 33(1):250-278.

[33]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.

[34]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.

[35]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.

[36]Zhang, Z., Xu, Y., Yang, J., et al., 2015. A survey of sparse representation: algorithms and applications. IEEE Access, 3:490-530.

[37]Zheng, M., Bu, J., Chen, C., et al., 2011. Graph regularized sparse coding for image representation. IEEE Trans. Image Process., 20(5):1327-1336.

[38]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.