Abstract
Manifold learning is a novel approach in non-linear dimensionality reduction that has shown great potential in numerous applications and has gained ground compared to linear techniques. In addition, sparse representations have been recently applied on computer vision problems with success, demonstrating promising results with respect to robustness in challenging scenarios. A key concept shared by both approaches is the notion of sparsity. In this paper we investigate how the framework of sparse representations can be applied in various stages of manifold learning. We explore the use of sparse representations in two major components of manifold learning: construction of the weight matrix and classification of test data. In addition, we investigate the benefits that are offered by introducing a weighting scheme on the sparse representations framework via the weighted LASSO algorithm. The underlying manifold learning approach is based on the recently proposed spectral regression framework that offers significant benefits compared to previously proposed manifold learning techniques. We present experimental results on these techniques in three challenging face recognition datasets.
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References
Baraniuk, R.G., Cevher, V., Wakin, M.B.: Low-dimensional models for dimensionality reduction and signal recovery: A geometric perspective. To appear in Proceedings of the IEEE (2010)
Cover, T.M.: Estimation by the nearest neighbor rule. IEEE Trans. on Information Theory 14(1), 50–55 (1968)
Tenenbaum, J.B., Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)
Saul, L.K., Roweis, S.T.: Think globally, fit locally: unsupervised learning of low dimensional manifolds. Journal of Machine Learning Research 4, 119–155 (2003)
Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation 15(6), 1373–1396 (2006)
Qiao, L., Chen, S., Tan, X.: Sparsity preserving discriminant analysis for single training image face recognition. Pattern Recognition Letters (2009)
He, X., Niyogi, P.: Locality preserving projections. In: Advances in Neural Information Processing Systems, vol. 16, pp. 153–160 (2003)
He, X., Cai, D., Yan, S., Zhang, H.J.: Neighborhood preserving embedding. In: IEEE Int. Conf. on Computer Vision, pp. 1208–1213 (2005)
Qiao, L., Chen, S., Tan, X.: Sparsity preserving projections with applications to face recognition. Pattern Recognition 43(1), 331–341 (2010)
Cheng, B., Yang, J., Yan, S., Fu, Y., Huang, T.: Learning with L1-Graph for Image Analysis. IEEE Transactions on Image Processing (2010) (accepted for publication)
Wright, J., Yang, A.Y., Ganesh, A., Sastry, S.S., Ma, Y.: Robust face recognition via sparse representation. IEEE Trans. on Pattern Analysis and Machine Intelligence 31(2), 210–227 (2009)
Belhumeur, P., Hespanda, J., Kriegman, D.: Eigenfaces versus Fisherfaces: Recognition Using Class Specific Linear Projection. IEEE Trans. Pattern Analysis and Machine Intelligence 19(7), 711–720 (1997)
Andoni, A., Indyk, P.: Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions. Communications of the ACM 51(1), 117–122 (2008)
He, X., Yan, S., Hu, Y., Niyogi, P., Zhang, H.J.: Face recognition using laplacianfaces. IEEE Trans. on Pattern Analysis and Machine Intelligence, 328–340 (2005)
Candès, E., Romberg, J., Tao, T.: Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. on Information Theory 52(2), 489–509 (2006)
Donoho, D.: Compressed sensing. IEEE Trans. on Information Theory 52(4), 1289–1306 (2006)
Mairal, J., Bach, F., Ponce, J., Sapiro, G., Zisserman, A.: Supervised dictionary learning. In: Advances in Neural Information Processing Systems, vol. 21 (2009)
Elgammal, A., Lee, C.S.: Inferring 3D body pose from silhouettes using activity manifold learning. In: IEEE Conf. on Computer Vision and Pattern Recognition, vol. 2 (2004)
Tuzel, O., Porikli, F., Meer, P.: Pedestrian detection via classification on Riemannian manifolds. IEEE Trans. on Pattern Analysis and Machine Intelligence, 1713–1727 (2008)
Rabaud, V., Belongie, S.: Linear Embeddings in Non-Rigid Structure from Motion. In: IEEE Conf. on Computer Vision and Pattern Recognition (2008)
AT&T face database, http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html
Yale Univ. Face Database, http://cvc.yale.edu/projects/yalefaces/yalefaces.html
Cai, D., He, X., Han, J.: Spectral regression for efficient regularized subspace learning. In: Proc. Int. Conf. Computer Vision, pp. 1–8 (2007)
Georghiades, A.S., Belhumeur, P.N., Kriegman, D.J.: From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose. IEEE Trans. Pattern Analysis and Machine Intelligence 23(6), 643–660 (2001)
Zou, H.: The adaptive Lasso and its oracle properties. Journal of the American Statistical Association 101(476), 1418–1429 (2006)
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Tsagkatakis, G., Savakis, A. (2010). Face Recognition Using Sparse Representations and Manifold Learning. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2010. Lecture Notes in Computer Science, vol 6453. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17289-2_49
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DOI: https://doi.org/10.1007/978-3-642-17289-2_49
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