About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 259863, 11 pages
http://dx.doi.org/10.1155/2013/259863
Research Article

Dictionary Learning Based on Nonnegative Matrix Factorization Using Parallel Coordinate Descent

1Graduate School of Computer Science and Engineering, University of Aizu, Aizu-Wakamatsu City, Fukushima 965-8580, Japan
2School of Computer Science and Engineering, University of Aizu, Aizu-Wakamatsu City, Fukushima 965-8580, Japan
3Department for Student Affairs, University of Aizu, Aizu-Wakamatsu City, Fukushima 965-8580, Japan

Received 28 February 2013; Accepted 16 May 2013

Academic Editor: Yong Zhang

Copyright © 2013 Zunyi Tang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. V. P. Pauca, J. Piper, and R. J. Plemmons, “Nonnegative matrix factorization for spectral data analysis,” Linear Algebra and its Applications, vol. 416, no. 1, pp. 29–47, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. L. Miao and H. Qi, “Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization,” IEEE Transactions on Geoscience and Remote Sensing, vol. 45, pp. 765–777, 2007.
  3. S. Li, X. Hou, H. Zhang, and Q. Cheng, “Learning spatially localized, parts-based representation,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR '01), pp. 207–212, 2001.
  4. I. Kotsia, S. Zafeiriou, and I. Pitas, “A novel discriminant non-negative matrix factorization algorithm with applications to facial image characterization problems,” IEEE Transactions on Information Forensics and Security, vol. 2, pp. 588–595, 2007.
  5. F. Shahnaz, M. W. Berry, V. P. Pauca, and R. J. Plemmons, “Document clustering using nonnegative matrix factorization,” Information Processing & Management, vol. 42, pp. 373–386, 2006.
  6. M. Wang, W. Xu, and A. Tang, “A unique “nonnegative” solution to an underdetermined system: from vectors to matrices,” IEEE Transactions on Signal Processing, vol. 59, no. 3, pp. 1007–1016, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  7. M. Plumbley, T. Blumensath, L. Daudet, R. Gribonval, and M. Davies, “Sparse representations in audio and music: from coding to source separation,” Proceedings of the IEEE, pp. 995–1005, 2010.
  8. M. Elad, M. Figueiredo, and Y. Ma, “On the role of sparse and redundant representations in image processing,” Proceedings of the IEEE, vol. 98, pp. 972–982, 2010.
  9. D. L. Donoho and M. Elad, “Optimally sparse representation in general (nonorthogonal) dictionaries via 1 minimization,” Proceedings of the National Academy of Sciences of the United States of America, vol. 100, no. 5, pp. 2197–2202, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, “Least angle regression,” The Annals of Statistics, vol. 32, no. 2, pp. 407–499, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation,” IEEE Transaction on Signal Processing, vol. 54, pp. 4311–4322, 2006.
  12. K. Engan, K. Skretting, and J. H. Husoy, “Family of iterative LS-based dictionary learning algorithms, ILS-DLA, for sparse signal representation,” Digital Signal Processing, vol. 17, pp. 32–49, 2007.
  13. J. Mairal, F. Bach, J. Ponce, and G. Sapiro, “Online learning for matrix factorization and sparse coding,” Journal of Machine Learning Research, vol. 11, pp. 19–60, 2010. View at Zentralblatt MATH · View at MathSciNet
  14. K. Skretting and K. Engan, “Recursive least squares dictionary learning algorithm,” IEEE Transactions on Signal Processing, vol. 58, no. 4, pp. 2121–2130, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  15. M. Aharon, M. Elad, and A. M. Bruckstein, “K-SVD and its non-negative variant for dictionary design,” in Proceedings of the SPIE Conference Wavelets, pp. 327–339.
  16. D. D. Lee and H. S. Seung, “Learning the parts of objects by nonnegative matrix factorization,” Nature, vol. 401, pp. 788–791, 1999.
  17. D. D. Lee and H. S. Seung, “Algorithms for non-negative matrix factorization,” in Advances in Neural Information Processing Systems, pp. 556–562, 2000.
  18. P. O. Hoyer, “Non-negative sparse coding,” in Proceedings of the IEEE Workshop on Neural Networks for Signal Processing, pp. 557–565.
  19. J. Eggert and E. Korner, “Sparse coding and NMF,” in Proceedings of IEEE International Joint Conference on Neural Networks, pp. 2529–2533.
  20. W. Liu, N. Zheng, and X. Lu, “Non-negative matrix factorization for visual coding,” in IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP ’03), pp. 293–296, 2003.
  21. P. O. Hoyer, “Non-negative matrix factorization with sparseness constraints,” Journal of Machine Learning Research, vol. 5, pp. 1457–1469, 2004. View at MathSciNet
  22. V. P. Pauca, F. Shahnaz, M. W. Berry, and R. J. Plemmons, “Text mining using non-negative matrix factorizations,” in Proceedings of the Fourth SIAM International Conference on Data Mining, pp. 452–456, SIAM, Philadelphia, Pa, USA, 2004. View at MathSciNet
  23. Y. Gao and G. Church, “Improving molecular cancer class discovery through sparse non-negative matrix factorization,” Bioinformatics, vol. 21, pp. 3970–3975, 2005.
  24. R. Peharz, M. Stark, and F. Pernkopf, “Sparse nonnegative matrix factorization using 0-constraints,” in IEEE International Workshop on Machine Learning for Signal Processing (MLSP '10), pp. 83–88, 2010.
  25. R. Peharz and F. Pernkopf, “Sparse nonnegative matrix factorization using 0-constraints,” Neurocomputing, vol. 80, pp. 38–46, 2012.
  26. A. Pascual-Montano, J. M. Carazo, K. Kochi, D. Lehmann, and R. D. Pascual-Marqui, “Nonsmooth nonnegative matrix factorization (nsNMF),” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, pp. 403–415, 2006.
  27. H. Kim and H. Park, “Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis,” Bioinformatics, vol. 23, pp. 1495–1502, 2007.
  28. R. Tandon and S. Sra, “Sparse nonnegative matrix approximation: new formulations and algorithms,” Tech. Rep. 193, MPI, 2010.
  29. J. Friedman, T. Hastie, H. Höfling, and R. Tibshirani, “Pathwise coordinate optimization,” The Annals of Applied Statistics, vol. 1, no. 2, pp. 302–332, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  30. L. Grippo and M. Sciandrone, “On the convergence of the block nonlinear Gauss-Seidel method under convex constraints,” Operations Research Letters, vol. 26, no. 3, pp. 127–136, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. M. Elad and M. Aharon, “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Transactions on Image Processing, vol. 15, no. 12, pp. 3736–3745, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  32. W. Dong, X. Li, L. Zhang, and G. Shi, “Sparsity-based image denoising via dictionary learning and structural clustering,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR '11), pp. 457–464, 2011.
  33. J. Mairal, M. Elad, and G. Sapiro, “Sparse representation for color image restoration,” IEEE Transactions on Image Processing, vol. 17, no. 1, pp. 53–69, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  34. Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Transactions on Image Processing, vol. 13, pp. 600–612, 2004.
  35. R. Baraniuk, H. Choi, R. Neelamani, and V. Ribeiro, “Rice Wavelet Toolbox,” 2011, http://dsp.rice.edu/software/rice-wavelet-toolbox/.
  36. A. Buades, B. Coll, and J.-M. Morel, “A non-local algorithm for image denoising,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR '05), pp. 60–65, 2005.