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

Authors:
Juliana Valencia-Aguirre;Andrés Álvarez-Mesa;Genaro Daza-Santacoloma;Germán Castellanos-Domínguez
Affiliations:
Control and Digital Signal Processing Group, Universidad Nacional de Colombia, Manizales, Colombia;Control and Digital Signal Processing Group, Universidad Nacional de Colombia, Manizales, Colombia;Control and Digital Signal Processing Group, Universidad Nacional de Colombia, Manizales, Colombia;Control and Digital Signal Processing Group, Universidad Nacional de Colombia, Manizales, Colombia
Venue:
CIARP '09 Proceedings of the 14th Iberoamerican Conference on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
Year:
2009

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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.