Abstract

VALENCIA AGUIRRE, Juliana et al. Automatic selection of parameters in LLE. Rev.fac.ing.univ. Antioquia [online]. 2010, n.56, pp.170-181. ISSN 0120-6230.

Locally Linear Embedding (LLE) is a nonlinear dimensionality reduction technique, which preserves the local geometry of high dimensional space performing an embedding to low dimensional space. LLE algorithm has 3 free parameters that must be set to calculate the embedding: the number of nearest neighbors k, the output space dimensionality m and the regularization parameter a. The last one only is necessary when the value of k is greater than the dimensionality of input space or data are not located in general position, and it plays an important role in the embedding results. In this paper we propose a pair of criteria to find the optimum value for the parameters k and α, to obtain an embedding that faithfully represent the input data space. Our approaches are tested on 2 artificial data sets and 2 real world data sets to verify the effectiveness of the proposed criteria, besides the results are compared against methods found in the state of art.

Keywords : Dimensionality reduction; locally linear embedding; number of nearest neighbors; automatic regularization.

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