Automatic selection of parameters in LLE

• Published in: Revista Facultad de Ingeniería no. 56; pp. 170 - 181
• Main Authors: Valencia Aguirre, Juliana, Álvarez Meza, Andrés Marino, Daza Santacoloma, Genaro, Acosta Medina, Carlos Daniel, Castellanos Domínguez, Germán
• Format: Journal Article
• Language: English
• Published: Universidad de Antioquia 28.02.2013
• Subjects: automatic regularization; dimensionality reduction; locally linear embedding; number of nearest neighbors
• ISSN: 0120-6230; 2422-2844
• DOI: 10.17533/udea.redin.14665

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 kand a, 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.