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Evolving Insight into High-Dimensional Data

  • Yiqing Tu
  • Gang Li
  • Honghua Dai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3644)

Abstract

ISOMap is a popular method for nonlinear dimensionality reduction in batch mode, but need to run its entirety inefficiently if the data comes sequentially. In this paper, we present an extension of ISOMap, namely I-ISOMap, augmenting the existing ISOMap framework to the situation where additional points become available after initial manifold is constructed. The MDS step, as a key component in ISOMap, is adapted by introducing Spring model and sampling strategy. As a result, it consumes only linear time to obtain a stable layout due to the Spring model’s iterative nature. The proposed method outperforms earlier work by Law [1], where their MDS step runs within quadratic time. Experimental results show that I-ISOMap is a precise and efficient technique for capturing evolving manifold.

Keywords

Feature Space Residual Variance Geodesic Distance Point Pair Neighborhood Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Law, M., Zhang, N., Jain, A.: Nonlinear manifold learning for data stream. In: Saim Data Mining (SDM) (2003) Google Scholar
  2. 2.
    Tenenbaum, J., de Silva, V., Langford, J.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)CrossRefGoogle Scholar
  3. 3.
    Roweis, S., Saul, L.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000)CrossRefGoogle Scholar
  4. 4.
    Belkin, M., Niyogi, P.: Laplacian eigenmaps and spectral techniques for embedding and clustering. In: Advances in Neural Information Processing Systems, NIPS (2002)Google Scholar
  5. 5.
    Vlachos, M., Domeniconi, C., Gunopulos, D.: Non-linear dimensionality reduction techniques for classi cation and visualization. In: Proceedings of the 8th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2002)Google Scholar
  6. 6.
    Cox, T., Cox, M.: Multidimensional Scaling. Chapman and Hall, London (1994)zbMATHGoogle Scholar
  7. 7.
    Eades, P.: Aheuristic for graph drawing. Congressus Numerantium 42 (1984)Google Scholar
  8. 8.
    Chalmers, M.: A linear iteration time layout algorithm for visualising high- dimensional data. IEEE Visualization, 127–132 (1996)Google Scholar
  9. 9.
  10. 10.
    Hull, J.J.: A database for handwritten text recognition research. IEEE Transacations on Pattern Analysis and Machine Intelligence (PAMI) 16, 49–67 (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Yiqing Tu
    • 1
  • Gang Li
    • 1
  • Honghua Dai
    • 1
  1. 1.School of Information TechnologyDeakin UniversityAustralia

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