Selección automática de parámetros en LLE / Automatic selection of parameters in LLE

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 κ, the output space dimensionality m and the regularization parameter α. The last one only is necessary when the value of κ 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 κ 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.