About this Journal Submit a Manuscript Table of Contents
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 683053, 8 pages
http://dx.doi.org/10.1155/2013/683053
Research Article

Split-and-Combine Singular Value Decomposition for Large-Scale Matrix

Department of Mathematical Sciences, National Chengchi University, No. 64, Section 2, ZhiNan Road, Wenshan District, Taipei City 11605, Taiwan

Received 16 November 2012; Revised 17 January 2013; Accepted 22 January 2013

Academic Editor: Nicola Mastronardi

Copyright © 2013 Jengnan Tzeng. 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. D. J. Hand, Discrimination and Classification, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, Chichester, UK, 1981. View at Zentralblatt MATH · View at MathSciNet
  2. M. Cox and T. Cox, Multidimensional Scaling, Handbook of Data Visualization, Springer, Berlin, Germany, 2008.
  3. G. H. Golub and C. Reinsch, “Singular value decomposition and least squares solutions,” Numerische Mathematik, vol. 14, no. 5, pp. 403–420, 1970. View at Publisher · View at Google Scholar · View at MathSciNet
  4. T. F. Chan, “An improved algorithm for computing the singular value decomposition,” ACM Transactions on Mathematical Software, vol. 8, no. 1, pp. 72–83, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. P. Deift, J. Demmel, L. C. Li, and C. Tomei, “The bidiagonal singular value decomposition and Hamiltonian mechanics,” SIAM Journal on Numerical Analysis, vol. 28, no. 5, pp. 1463–1516, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. L. Eldén, “Partial least-squares vs. Lanczos bidiagonalization. I. Analysis of a projection method for multiple regression,” Computational Statistics & Data Analysis, vol. 46, no. 1, pp. 11–31, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  7. J. Baglama and L. Reichel, “Augmented implicitly restarted Lanczos bidiagonalization methods,” SIAM Journal on Scientific Computing, vol. 27, no. 1, pp. 19–42, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. Baglama and L. Reichel, “Restarted block Lanczos bidiagonalization methods,” Numerical Algorithms, vol. 43, no. 3, pp. 251–272, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. Brand, “Fast low-rank modifications of the thin singular value decomposition,” Linear Algebra and Its Applications, vol. 415, no. 1, pp. 20–30, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. W. S. Torgerson, “Multidimensional scaling. I. Theory and method,” Psychometrika, vol. 17, pp. 401–419, 1952. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. M. Chalmers, “Linear iteration time layout algorithm for visualizing high-dimensional data,” in Proceedings of the 7th Conference on Visualization, pp. 127–132, November 1996. View at Scopus
  12. J. B. Tenenbaum, V. de Silva, and J. C. Langford, “A global geometric framework for nonlinear dimensionality reduction,” Science, vol. 290, no. 5500, pp. 2319–2323, 2000. View at Publisher · View at Google Scholar · View at Scopus
  13. J. Tzeng, H. Lu, and W. H. Li, “Multidimensional scaling for large genomic data sets,” BMC Bioinformatics, vol. 9, article 179, 2008. View at Publisher · View at Google Scholar · View at Scopus
  14. A. Morrison, G. Ross, and M. Chalmers, “Fast multidimensional scaling through sampling, springs and interpolation,” Information Visualization, vol. 2, no. 1, pp. 68–77, 2003.