Abstract
The sparse representation based classification (SRC) was initially proposed for face recognition problems. However, SRC was found to excel in a variety of classification tasks. There have been many extensions to SRC, of which group SRC, kernel SRC being the prominent ones. Prior methods in kernel SRC used greedy methods like Orthogonal Matching Pursuit (OMP). It is well known that for solving a sparse recovery problem, both in theory and in practice, l 1 -minimization is a better approach compared to OMP. The standard l 1 -minimization is a solved problem. For the first time in this work, we propose a technique for Kernel l 1 -minimization. Through simulation results we show that our proposed method outperforms prior kernelised greedy sparse recovery techniques.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Natarajan, B.: Sparse approximate solutions to linear systems. SIAM J. Comput. 24, 227–234 (1995)
Tropp, J., Gilbert, A.C., Strauss, M.: Algorithms for simultaneous sparse approximations; Part I: greedy pursuit. Sig. Proc. 86, 572–588 (2006). Special Issue on Sparse approximations in signal and image processing.
Tibshirani, R.: Regression shrinkage and selection via the lasso. J. Royal. Statist. Soc B. 58(1), 267–288 (1996)
Daubechies, I., Defrise, M., De Mol, C.: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 57(11), 1413–1457 (2004)
Zhang, L., Zhou, W.-D., Chang, P.-C., Liu, J., Yan, Z., Wang, T., Li, F.-Z.: Kernel sparse representation-based classifier. IEEE Trans. Signal Process. 60(4), 1684–1695 (2012)
Chen, Y., Nasrabadi, N., Tran, T.: Hyperspectral image classification via kernel sparse representation. IEEE Trans. Geosci. Remote Sens. 51(1), 217–231 (2013)
Yin, J., Liu, Z., Jin, Z., Yang, W.: Kernel sparse representation based classification. Neurocomputing 77(1), 120–128 (2012)
Majumdar, A., Ward, R.K.: Robust classifiers for data reduced via random projections. IEEE Trans. Syst. Man Cybern. B 40(5), 1359–1371 (2010)
Yuan, X.T., Liu, X., Yan, S.: visual classification with multitask joint sparse representation. IEEE Trans. Image Process. 21(10), 4349–4360 (2012)
Elhamifar, E., Vidal, R.: Robust Classification using Structured Sparse Representation. In: IEEE CVPR (2011)
Goswami, G., Mittal, P., Majumdar, A., Singh, R., Vatsa, M.: Group sparse representation based classification for multi-feature multimodal biometrics. Inf. Fus 32(B), 3–12 (2016)
Sparse signal restoration. cnx.org/content/m32168/
Bredies, K., Lorenz, D.A.: Iterated hard shrinkage for minimization problems with sparsity constraints. SIAM J. Sci. Comput. 30(2), 657–683 (2008)
Wright, J., Yang, A., Ganesh, A., Sastry, S., Ma, Y.: Robust face recognition via sparse representation. IEEE Trans. Pattern Anal. Mach. Intell. 31(2), 210–227 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Gogna, A., Majumdar, A. (2016). Kernel L1-Minimization: Application to Kernel Sparse Representation Based Classification. In: Hirose, A., Ozawa, S., Doya, K., Ikeda, K., Lee, M., Liu, D. (eds) Neural Information Processing. ICONIP 2016. Lecture Notes in Computer Science(), vol 9948. Springer, Cham. https://doi.org/10.1007/978-3-319-46672-9_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-46672-9_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-46671-2
Online ISBN: 978-3-319-46672-9
eBook Packages: Computer ScienceComputer Science (R0)