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Automatic Choice of the Number of Nearest Neighbors in Locally Linear Embedding

  • Juliana Valencia-Aguirre
  • Andrés Álvarez-Mesa
  • Genaro Daza-Santacoloma
  • Germán Castellanos-Domínguez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5856)

Abstract

Locally linear embedding (LLE) is a method for nonlinear dimensionality reduction, which calculates a low dimensional embedding with the property that nearby points in the high dimensional space remain nearby and similarly co-located with respect to one another in the low dimensional space [1]. LLE algorithm needs to set up a free parameter, the number of nearest neighbors k. This parameter has a strong influence in the transformation. In this paper is proposed a cost function that quantifies the quality of the embedding results and computes an appropriate k. Quality measure is tested on artificial and real-world data sets, which allow us to visually confirm whether the embedding was correctly calculated.

Keywords

Locally Linear Embedding Linear Embedding Nonlinear Dimensionality Reduction Embed Space Automatic Choice 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Juliana Valencia-Aguirre
    • 1
  • Andrés Álvarez-Mesa
    • 1
  • Genaro Daza-Santacoloma
    • 1
  • Germán Castellanos-Domínguez
    • 1
  1. 1.Control and Digital Signal Processing GroupUniversidad Nacional de ColombiaManizalesColombia

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