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Abstract

In this chapter, locally linear embedding (LLE) method for dimensionality reduction is introduced. The method is based on simple geometric intuitions: If a data set is sampled from a smooth manifold, then neighbors of each point remain nearby and are similarly co-located in the low-dimensional space. In LLE, each point in the data set is linearly embedded into a locally linear patch of the manifold. Then low-dimensional data is constructed such that the locally linear relations of the original data are preserved. The chapter is organized as follows. In Section 10.1, we geometrically describe LLE method and its algorithm. The experiments of LLE are presented in Section 10.2 and some applications are introduced in Section 10.3. The mathematical justification of LLE is given in Section 10.4.

Keywords

Weight Matrix Neighborhood Size Locally Linear Embedding Linear Embedding Noise Standard Deviation 
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References

  1. [1]
    Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000).CrossRefGoogle Scholar
  2. [2]
    Saul, L.K., Roweis, S.T.: Think globally, fit locally: Unsupervised learning of low dimensional manifolds. Journal of Machine Learning Research 4, 119–155 (2003).MathSciNetGoogle Scholar
  3. [3]
    Dyken, C. Floater, M.: Transfinite mean value interpolation. Computer Aided Geometric Design 26(1), 117–134 (2009).MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    Cosatto, E., Graf, H.P.: Sample-based synthesis of photo-realistic talking-heads. In: Proceedings of Computer Animation, IEEE Computer Society, pp. 103–110 (1998).Google Scholar
  5. [5]
    de Ridder, D., Kouropteva, O., Okun, O., PietikŁinen, M., Duin, R.P.: Supervised locally linear embedding. In: Proceedings of the 2003 joint international conference on Artificial neural networks and neural information processing, pp. 333–341 (2003).Google Scholar

Copyright information

© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jianzhong Wang
    • 1
  1. 1.Department of Mathematics and StatisticsSam Houston State UniversityHuntsvilleUSA

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