Automatic selection of parameters in LLE
DOI:
https://doi.org/10.17533/udea.redin.14665Keywords:
dimensionality reduction, locally linear embedding, number of nearest neighbors, automatic regularizationAbstract
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.
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M. A. Carreira-Perpiñan. “A review of dimension reduction techniques”. Department of Computer Science. University of Sheffield. Tech. Rep. CS-96-09. 1997. pp 1-69.
S. T. Roweis, L. K. Saul. “Nonlinear dimensionality reduction by locally linear embedding”. Science. Vol. 290. 2000. pp. 2323-2326. DOI: https://doi.org/10.1126/science.290.5500.2323
L. K. Saul, S. T. Roweis. “An introduction to locally linear embedding”. AT&T Labs and Gatsby Computational Neuroscience Unit. Tech. Rep. 2000. pp 1-16.
L. K. Saul, S. T. Roweis. “Think globally, fit locally: Unsupervised learning of low dimensional manifolds”. Machine Learning Research. Vol. 4. 2003. pp. 119- 155.
M. Polito, P. Perona. “Grouping and dimensionality reduction by locally linear embedding”. NIPS. Vol. 14. 2001. pp. 1255-1262.
D. de Ridder, R. P. W. Duin. Locally linear embedding for classification. Pattern Recongnition Group. Delft University of Technology. Netherlands. Tech. Rep. 2002. pp. 1-15.
P. C. Hansen. Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion. SIAM. Philadelphia. 1998. DOI: https://doi.org/10.1137/1.9780898719697
Y. Goldberg, Y. Ritov. “Local procrustes for manifold embedding: a measure of embedding quality and embedding algorithms”. Machine learning. Vol. 77. 2009. pp 1-25. DOI: https://doi.org/10.1007/s10994-009-5107-9
O. Kouropteva, O. Okun, M. Pietikäinen. Selection of the optimal parameter value for the locally linear embedding algorithm. The 1st ICFSKD. 2002. pp. 359-363.
S. A. Nene, S. K. Nayar, H. Murase. Columbia object image library: Coil-100. Department of Computer Science, Columbia University. NY.Tech. Rep. 1996. pp. 1-16.
A. Tank. Daily dataset of 20th-century surface air temperature and precipitation series for the European climate assessment. Int. Jour. Climatology. Vol. 22. 2002. pp. 1441-1453. DOI: https://doi.org/10.1002/joc.773
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