Robust ISOMAP Based on Neighbor Ranking Metric

  • Chun Du
  • Shilin Zhou
  • Jixiang Sun
  • Jingjing Zhao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7389)


ISOMAP is one of classical manifold learning methods that can discover the low-dimensional nonlinear structure automatically in a high-dimensional data space. However, it is very sensitive to the outlier, which is a great disadvantage to its applications. To solve the noisy manifold learning problem, this paper proposes a robust ISOMAP based on neighbor ranking metric (NRM). Firstly, NRM is applied to remove outliers partially, then a two-step strategy is adopted to select suitable neighbors for each point to construct neighborhood graph. The experimental results indicate that the method can effectively improve robustness in noisy manifold learning both on synthetic and real-world data.


ISOMAP noisy manifold learning neighbor ranking metric 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Tenenbaum, J.B., de Silva, V., Langford, J.C.: A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science 290, 2319–2323 (2000)CrossRefGoogle Scholar
  2. 2.
    Roweis, S.T., Saul, L.K.: Nonlinear Dimensionality Reduction by Locally Linear Embedding. Science 290, 2323–2326 (2000)CrossRefGoogle Scholar
  3. 3.
    Zhang, Z., Zha, H.: Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment. SIAM J. Scientific Computing 26, 313–338 (2005)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Choi, H., Choi, S.: Robust kernel Isomap. Pattern Recognition 40, 853–862 (2007)zbMATHCrossRefGoogle Scholar
  5. 5.
    Chang, H., Yeung, D.Y.: Robust locally Linear Embedding. Pattern Recognition 39, 1053–1065 (2006)zbMATHCrossRefGoogle Scholar
  6. 6.
    Cox, T., Cox, M.: Multidimensional Scaling. Chapman and Hall, Boca Raton (1994)zbMATHGoogle Scholar
  7. 7.
    Mekuz, N., Tsotsos, J.K.: Parameterless Isomap with Adaptive Neighborhood Selection. In: Franke, K., Müller, K.-R., Nickolay, B., Schäfer, R. (eds.) DAGM 2006. LNCS, vol. 4174, pp. 364–373. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Zhan, Y., Yin, J., Liu, X., Zhang, G.: Adaptive Neighborhood Select Based on Local Linearity for Nonlinear Dimensionality Reduction. In: Cai, Z., Li, Z., Kang, Z., Liu, Y. (eds.) ISICA 2009. LNCS, vol. 5821, pp. 337–348. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Zhang, Z., Wang, J., Zha, H.: Adaptive Manifold Learning. IEEE Trans. Pattern Anal. Mach. Intell. 34, 253–265 (2012)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Chun Du
    • 1
  • Shilin Zhou
    • 1
  • Jixiang Sun
    • 1
  • Jingjing Zhao
    • 1
  1. 1.School of Electronic Science and EngineeringNational University of Defense TechnologyChangshaP.R. China

Personalised recommendations