About eigenvalues from embedding data complex in low dimension

Authors:
Jiun-Wei Liou;Cheng-Yuan Liou
Affiliations:
Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan, Republic of China;Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan, Republic of China
Venue:
ICSI'12 Proceedings of the Third international conference on Advances in Swarm Intelligence - Volume Part II
Year:
2012

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Abstract

LLE(Local linear embedding) and Isomap are widely used approaches for dimension reduction on data complex. The embedding results from the two methods are eigenvectors from solving specific matrices. The corresponding eigenvalues for the selected eigenvectors have important meaning for the embedding results. In this paper, the k-nn method and ε-distance approach are used for neighborhood function with parameters. Then, different datasets and parameters will be applied to obtain the embedding results and eigenvalues. The main change of eigenvalues and the corresponding embedding results will be shown in this paper.