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Kernel L1-Minimization: Application to Kernel Sparse Representation Based Classification

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Neural Information Processing (ICONIP 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9948))

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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.

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References

  1. Natarajan, B.: Sparse approximate solutions to linear systems. SIAM J. Comput. 24, 227–234 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  2. 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.

    Article  MATH  Google Scholar 

  3. Tibshirani, R.: Regression shrinkage and selection via the lasso. J. Royal. Statist. Soc B. 58(1), 267–288 (1996)

    MathSciNet  MATH  Google Scholar 

  4. 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)

    Article  MathSciNet  MATH  Google Scholar 

  5. 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)

    Article  MathSciNet  Google Scholar 

  6. Chen, Y., Nasrabadi, N., Tran, T.: Hyperspectral image classification via kernel sparse representation. IEEE Trans. Geosci. Remote Sens. 51(1), 217–231 (2013)

    Article  Google Scholar 

  7. Yin, J., Liu, Z., Jin, Z., Yang, W.: Kernel sparse representation based classification. Neurocomputing 77(1), 120–128 (2012)

    Article  Google Scholar 

  8. Majumdar, A., Ward, R.K.: Robust classifiers for data reduced via random projections. IEEE Trans. Syst. Man Cybern. B 40(5), 1359–1371 (2010)

    Article  Google Scholar 

  9. Yuan, X.T., Liu, X., Yan, S.: visual classification with multitask joint sparse representation. IEEE Trans. Image Process. 21(10), 4349–4360 (2012)

    Article  MathSciNet  Google Scholar 

  10. Elhamifar, E., Vidal, R.: Robust Classification using Structured Sparse Representation. In: IEEE CVPR (2011)

    Google Scholar 

  11. 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)

    Article  Google Scholar 

  12. Sparse signal restoration. cnx.org/content/m32168/

  13. Bredies, K., Lorenz, D.A.: Iterated hard shrinkage for minimization problems with sparsity constraints. SIAM J. Sci. Comput. 30(2), 657–683 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. 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)

    Article  Google Scholar 

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Correspondence to Angshul Majumdar .

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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

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  • DOI: https://doi.org/10.1007/978-3-319-46672-9_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46671-2

  • Online ISBN: 978-3-319-46672-9

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