Skip to main content

DC Programming and DCA for Dictionary Learning

  • Conference paper
  • First Online:
Computational Collective Intelligence

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9329))

Abstract

Sparse representations of signals based on learned dictionaries have drawn considerable interest in recent years. However, the design of dictionaries adapting well to a set of training signals is still a challenging problem. For this task, we propose a novel algorithm based on DC (Difference of Convex functions) programming and DCA (DC Algorithm). The efficiency of proposed algorithm will be demonstrated in image denoising application.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aharon, M., Elad, M., Bruckstein, A.: K-SVD: An algorithm for designing of overcomplete dictionaries for sparse representation. IEEE Transactions on Signal Processing 54(11), 4311–4322 (2006)

    Article  Google Scholar 

  2. Chen, S., Donoho, D., Saunders, M.: Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing 20, 33–61 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  3. Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. Image Process. 54(12), 3736–3745 (2006)

    Article  MathSciNet  Google Scholar 

  4. Fan, J., Li, R.: Variable selection via nonconcave penalized likelihood and its oracle properties. J. Am. Stat. Assoc. 96(456), 1348–1360 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. Thi, L.: H.A. and Pham Dinh, T.: The DC (difference of convex functions) Programming and DCA revisited with DC models of real world nonconvex optimization problems. Annals of Operations Research 133, 23–46 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Le Thi, H.A., Pham Dinh, T., Le, H.M., Vo, X.T.: DC approximation approaches for sparse optimization. Eur. J. Oper. Res. 244(1), 26–46 (2015)

    Google Scholar 

  7. Le Thi, H.A., Nguyen, V.V., Ouchani, S.: Gene selection for cancer classification using DCA. In: Tang, C., Ling, C.X., Zhou, X., Cercone, N.J., Li, X. (eds.) ADMA 2008. LNCS (LNAI), vol. 5139, pp. 62–72. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  8. Le Thi, H.A., Le, H.M., Nguyen, V.V., Pham Dinh, T.: A DC Programming approach for feature selection in support vector machines learning. Adv. Data Analysis and Classification 2(3), 259–278 (2008)

    Google Scholar 

  9. Le Thi, H.A., Nguyen Thi, B.T., Le, H.M.: Sparse signal recovery by difference of convex functions algorithms. In: Selamat, A., Nguyen, N.T., Haron, H. (eds.) ACIIDS 2013, Part II. LNCS, vol. 7803, pp. 387–397. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  10. Le, H.M., Le Thi, H.A., Nguyen, M.C.: Sparse Semi-Supervised Support Vector Machines by DC Programming and DCA. Neurocomputing 153(4), 62–76 (2015)

    Article  Google Scholar 

  11. Le Thi, H.A., Nguyen, M.C., Pham Dinh, T.: A DC programming approach for finding Communities in networks. Neural Computation 26(12), 2827–2854 (2014)

    Google Scholar 

  12. Le Thi, H.A., Vo, X.T., Pham Dinh, T.: Feature Selection for linear SVMs under Uncertain Data: Robust optimization based on Difference of Convex functions Algorithms. Neural Networks 59, 36–50 (2014)

    Article  MATH  Google Scholar 

  13. Mallat, S., Zhang, Z.: Matching pursuits with time-frequency dictionaries. IEEE Trans. Signal Process. 41(12), 3397–3415 (1993)

    Article  MATH  Google Scholar 

  14. Mallat, S.: A wavelet tour of signal processing, 2nd edn. Academic Press, New York (1999)

    MATH  Google Scholar 

  15. Mairal, J., Bach, F., Ponce, J., Sapiro, G.: Online learning for matrix factorization and sparse coding. Journal of Machine Learning Research 11, 19–60 (2010)

    MathSciNet  MATH  Google Scholar 

  16. Olshausen, B.A., Field, D.J.: Sparse coding with an overcomplete basis set: A strategy employed by V1? Vision Research 37, 3311–3325 (1997)

    Article  Google Scholar 

  17. Ong, C.S., Le Thi, H.A.: Learning sparse classifiers with difference of convex functions algorithms. Optimization Methods and Software 28(4), 830–854 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  18. Pati, Y.C., Rezaiifar, R., Krishnaprasad, P.S.: Orthogonal Matching Pursuit: recursive function approximation with application to wavelet decomposition. In: Asilomar Conf. on Signals, Systems and Comput., pp. 40–41 (1993)

    Google Scholar 

  19. Peleg, D., Meir, R.: A bilinear formulation for vector sparsity optimization. Signal Processing 88(2), 375–389 (2008)

    Article  MATH  Google Scholar 

  20. Pham Dinh, T., Le Thi, H.A.: Convex analysis approach to DC programming: Theory, algorithms and applications. Acta Math. Vietnamica 22(1), 289–357 (1997)

    Google Scholar 

  21. Pham Dinh, T., Le Thi, H.A.: Dc optimization algorithms for solving the trust region subproblem. SIAM. J Optimization 8, 476–505 (1998)

    Google Scholar 

  22. Skretting, K., Engan, K.: Recursive least squares dictionary learning algorithm. IEEE Transactions on Signal Processing 58(4), 2121–2130 (2010)

    Article  MathSciNet  Google Scholar 

  23. Tibshirani, R.: Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B 58(1), 267–288 (1996)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xuan Thanh Vo .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Vo, X.T., An Le Thi, H., Dinh, T.P., Nguyen, T.B.T. (2015). DC Programming and DCA for Dictionary Learning. In: Núñez, M., Nguyen, N., Camacho, D., Trawiński, B. (eds) Computational Collective Intelligence. Lecture Notes in Computer Science(), vol 9329. Springer, Cham. https://doi.org/10.1007/978-3-319-24069-5_28

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-24069-5_28

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24068-8

  • Online ISBN: 978-3-319-24069-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics