Abstract
In this chapter, some concepts which are extensions of sparse properties are outlined. First, it describes some works about low-rank matrix approximation which include \(\ell _2\)-norm Wiberg algorithm and \(\ell _1\)-norm Wiberg algorithm. Second, it outlines the graphical models in compressed sensing which include message passing algorithm and approximate message passing algorithm. Third, it describes collaborative representation-based classifiers which use the \(\ell _2\)-norm to replace the \(\ell _1\)-norm in sparse representation model and the collaborative representation-based classifier (CRC). Lastly, it also describes some knowledge about high-dimensional nonlinear learning which includes kernel sparse representation, anchor points approaches, and sparse manifold learning.
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References
Buchanan, A.M., Fitzgibbon, A.W.: Damped newton algorithms for matrix factorization with missing data. In: IEEE CVPR (2005)
Chen, C.F., Wei, C.P., Wang, Y.C.: Low-rank matrix recovery with structural incoherence for robust face recognition. In: IEEE CVPR (2012)
Cheng, H., Liu, Z., Yang, L., Chen, X.: Sparse representation and learning in visual recognition: Theory and applications. Signal. Process. 93(6), 1408–1425 (2013)
Cristianini, N., Shawe-Taylor, J.: An introduction to support vector machines and other kernel-based learning methods. Cambridge University Press, Cambridge (2000)
Elhamifar, E., Vidal, R.: Sparse manifold clustering and embedding. In: NIPS (2011)
Eriksson, A., Van Den Hengel, A.: Efficient computation of robust low-rank matrix approximations in the presence of missing data using the l 1 norm. In: IEEE CVPR (2010)
Gao, S., Tsang, I.W.H., Chia, L.T.: Sparse representation with kernels. IEEE Trans. on Image Processing 22(2) (2013)
Ke, Q., Kanade, T.: Robust \(\ell _1\) norm factorization in the presence of outliers and missing data by alternative convex programming. In: IEEE CVPR (2005)
Maleki, M.A.: Approximate Message Passing Algorithms for Compressed Sensing. Stanford University (2010)
Montanari, A.: Graphical models concepts in compressed Sensing. Compressed sensing: Theory and Applications, pp. 394–438 (2012)
Okatani, T., Deguchi, K.: On the wiberg algorithm for matrix factorization in the presence of missing components. Int. J. Comput. Vis. 72(3), 329–337 (2007)
Olshausen, B.A., Field, D.J.: Sparse coding with an overcomplete basis set: A strategy employed by v1? Vis. Res. 37(23), 3311–3325 (1997)
Pei, D., Sun, F., Liu, H.: Low-rank matrix recovery for traffic sign recognition in image sequences. In: Foundations and Practical Applications of Cognitive Systems and Information Processing, pp. 857–865. Springer (2014)
Peng, Y., Ganesh, A., Wright, J., Xu, W., Ma, Y.: RASL: robust alignment by sparse and low-rank decomposition for linearly correlated images. IEEE Trans. Pattern Anal. mach. Intell.34(11) (2012)
Rigamonti, R., Brown, M.A., Lepetit, V.: Are sparse representations really relevant for image classification? In: IEEE CVPR (2011)
Schölkopf, B., Smola, A., Müller, K.R.: Nonlinear component analysis as a kernel eigenvalue problem. Neural. Comput. 10(5), 1299–1319 (1998)
Scholkopft, B., Mullert, K.R.: Fisher discriminant analysis with Kernels (1999)
Shi, Q., Eriksson, A., van den Hengel, A., Shen, C.: Is face recognition really a compressive sensing problem? In: IEEE CVPR (2011)
Silva, J., Marques, J.S., Lemos, J.M.: Selecting landmark points for sparse manifold learning. In: NIPS (2005)
Tax, D.M., Duin, R.P.: Support vector data description. Mach.Learn. 54(1), 45–66 (2004)
Turk, M., Pentland, A.: Eigenfaces for recognition. J. Cogn. Neurosci. 3(1), 71–86 (1991)
Vapnik, V.: The Nature of Statistical Learning Theory. springer, New York (2000)
Wiberg, T.: Computation of principal components when data are missing. In: Proceedings Second Symp. Computational statistics (1976)
Wright, J., Yang, A.Y., Ganesh, A., Sastry, S.S., Ma, Y.: Robust face recognition via sparse representation. IEEE Trans. on Pattern Anal. Mach. Intell. 31(2) (2009)
Yu, K., Zhang, T., Gong, Y.: Nonlinear learning using local coordinate coding. In: NIPS, vol. 9 (2009)
Zhang, C., Liu, J., Tian, Q., Xu, C., Lu, H., Ma, S.: Image classification by non-negative sparse coding, low-rank and sparse decomposition. In: IEEE CVPR (2011)
Zhang, D., Yang, M., Feng, X.: Sparse representation or collaborative representation: which helps face recognition? In: IEEE ICCV (2011)
Zhang, Y., Jiang, Z., Davis, L.S.: Learning structured low-rank representations for image classification. In: IEEE CVPR (2013)
Zhou, T., Tao, D., Wu, X.: Manifold elastic net: a unified framework for sparse dimension reduction. Data. Min. Knowl.Discov. 22(3), 340–371 (2011)
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Cheng, H. (2015). Beyond Sparsity. In: Sparse Representation, Modeling and Learning in Visual Recognition. Advances in Computer Vision and Pattern Recognition. Springer, London. https://doi.org/10.1007/978-1-4471-6714-3_9
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DOI: https://doi.org/10.1007/978-1-4471-6714-3_9
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