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Mathematical Problems in Engineering
Volume 2017, Article ID 3930957, 12 pages
https://doi.org/10.1155/2017/3930957
Research Article

Robust L-Isomap with a Novel Landmark Selection Method

1Department of Automation, University of Science and Technology of China, Hefei, China
2College of Computer and Information Engineering, Henan University of Economics and Law, Zhengzhou, China
3Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei, China

Correspondence should be addressed to Hao Shi; nc.ude.ctsu.liam@ihsoah

Received 17 October 2016; Accepted 16 March 2017; Published 24 May 2017

Academic Editor: Guangming Xie

Copyright © 2017 Hao Shi 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. D. W. Scott, “The curse of dimensionality and dimension reduction,” in Multivariate Density Estimation: Theory, Practice, and Visualization, pp. 195–217, 2008. View at Google Scholar
  2. I. T. Jolliffe, Principal Component Analysis, Wiley Online Library, 2nd edition, 2002.
  3. M. A. A. Cox. and T. F. Cox, Multidimensional scaling, vol. 59 of Monographs on Statistics and Applied Probability, Chapman and Hall, London, UK, 1994. View at MathSciNet
  4. 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
  5. S. T. Roweis and L. K. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science, vol. 290, no. 5500, pp. 2323–2326, 2000. View at Publisher · View at Google Scholar · View at Scopus
  6. Z. Zhang and H. Zha, “Principal manifolds and nonlinear dimensionality reduction via tangent space alignment,” SIAM Journal on Scientific Computing, vol. 26, no. 1, pp. 313–338, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. V. D. Silva and J. B. Tenebaum, “Global versus local methods in nonlinear dimensionality reduction,” Advances in Neural Information Processing Systems 15, pp. 705–712, 2003. View at Google Scholar
  8. Y.-K. Lei, Z.-H. You, T. Dong, Y.-X. Jiang, and J.-A. Yang, “Increasing reliability of protein interactome by fast manifold embedding,” Pattern Recognition Letters, vol. 34, no. 4, pp. 372–379, 2013. View at Publisher · View at Google Scholar · View at Scopus
  9. D. Liang, C. Qiao, and Z. Xu, “Enhancing both efficiency and representational capability of isomap by extensive landmark selection,” Mathematical Problems in Engineering, vol. 2015, 18 pages, Article ID 241436, 2015. View at Publisher · View at Google Scholar · View at Scopus
  10. M. Balasubramanian, E. L. Schwartz, J. B. Tenenbaum et al., “The isomap algorithm and topological stability,” Science, vol. 295, no. 5552, Article 7, 2002. View at Google Scholar
  11. J. A. Lee and M. Verleysen, “Nonlinear dimensionality reduction of data manifolds with essential loops,” Neurocomputing, vol. 67, pp. 29–53, 2005. View at Publisher · View at Google Scholar · View at Scopus
  12. H. Choi and S. Choi, “Robust kernel Isomap,” Pattern Recognition, vol. 40, no. 3, pp. 853–862, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. E. W. Dijkstra, “A note on two problems in connexion with graphs,” Numerische Mathematik, vol. 1, pp. 269–271, 1959. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. R. W. Floyd, “Algorithm 97: shortest path,” Communications of the ACM, vol. 5, no. 6, article 345, 1962. View at Publisher · View at Google Scholar
  15. D. S. Johnson, “Approximation algorithms for combinatorial problems,” Journal of Computer and System Sciences, vol. 9, pp. 256–278, 1974. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. V. Chvatal, “A greedy heuristic for the set-covering problem,” Mathematics of Operations Research, vol. 4, no. 3, pp. 233–235, 1979. View at Publisher · View at Google Scholar · View at MathSciNet
  17. H. Shi, B. Yin, Y. Bao, and Y. Lei, “A novel landmark point selection method for L-ISOMAP,” in 12th IEEE International Conference on Control and Automation ICCA '16, pp. 621–625, Nepal, June 2016. View at Publisher · View at Google Scholar · View at Scopus
  18. M. P. Wand and M. C. Jones, “Kernel smoothing,” Crc Press. View at Publisher · View at Google Scholar · View at MathSciNet
  19. B. W. Silverman, Density Estimation for Statistics and Data Analysis, Chapman & Hall, London, UK, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  20. B. A. Turlach, Bandwidth Selection in Kernel Density Estimation: A Review, Universit catholique de Louvain, Louvain-la-Neuve, Belgium, 1993.
  21. H. Shi, B. Yin, X. Zhang, Y. Kang, and Y. Lei, “A landmark selection method for L-Isomap based on greedy algorithm and its application,” in 54th IEEE CDC 2015 Conference on Decision and Control, pp. 7371–7376, Japan, December 2015. View at Publisher · View at Google Scholar · View at Scopus
  22. P. Tune and M. Roughan, “Internet traffic matrices: a primer,” Recent Advances in Networking, vol. 1, pp. 1–41, 2013. View at Google Scholar
  23. S. Uhlig, B. Quoitin, J. Lepropre, and S. Balon, “Providing public intradomain traffic matrices to the research community,” ACM SIGCOMM Computer Communication Review, vol. 36, pp. 83–86, 2006. View at Publisher · View at Google Scholar · View at Scopus
  24. A. Lakhina, K. Papagiannaki, M. Crovella, C. Diot, E. D. Kolaczyk, and N. Taft, “Structural analysis of network traffic flows,” SIGMETRICS Performance Evaluation Review, vol. 32, pp. 61–72, 2004. View at Google Scholar · View at Scopus