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.
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Keywords
- Locally Linear Embedding
- Linear Embedding
- Nonlinear Dimensionality Reduction
- Embed Space
- Automatic Choice
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Valencia-Aguirre, J., Álvarez-Mesa, A., Daza-Santacoloma, G., Castellanos-Domínguez, G. (2009). Automatic Choice of the Number of Nearest Neighbors in Locally Linear Embedding. In: Bayro-Corrochano, E., Eklundh, JO. (eds) Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications. CIARP 2009. Lecture Notes in Computer Science, vol 5856. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10268-4_9
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DOI: https://doi.org/10.1007/978-3-642-10268-4_9
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