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Supervised by Ministry of Industry and Information Technology of The People's Republic of China Sponsored by Harbin Institute of Technology Editor-in-chief Yu Zhou ISSNISSN 1005-9113 CNCN 23-1378/T

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Related citation:Lin Ma,Cai-Fa Zhou,Xi Liu,Yu-Bin Xu.Adaptive Neighboring Selection Algorithm Based on Curvature Prediction in Manifold Learning[J].Journal of Harbin Institute Of Technology(New Series),2013,20(3):119-123.DOI:10.11916/j.issn.1005-9113.2013.03.020.
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Adaptive Neighboring Selection Algorithm Based on Curvature Prediction in Manifold Learning
Author NameAffiliation
Lin Ma Communication Research Center, Harbin Institute of Technology, Harbin 150080, China 
Cai-Fa Zhou Communication Research Center, Harbin Institute of Technology, Harbin 150080, China 
Xi Liu Communication Research Center, Harbin Institute of Technology, Harbin 150080, China 
Yu-Bin Xu Communication Research Center, Harbin Institute of Technology, Harbin 150080, China 
Abstract:
Recently manifold learning algorithm for dimensionality reduction attracts more and more interests, and various linear and nonlinear, global and local algorithms are proposed. The key step of manifold learning algorithm is the neighboring region selection. However, so far for the references we know, few of which propose a generally accepted algorithm to well select the neighboring region. So in this paper, we propose an adaptive neighboring selection algorithm, which successfully applies the LLE and ISOMAP algorithms in the test. It is an algorithm that can find the optimal K nearest neighbors of the data points on the manifold. And the theoretical basis of the algorithm is the approximated curvature of the data point on the manifold. Based on Riemann Geometry, Jacob matrix is a proper mathematical concept to predict the approximated curvature. By verifying the proposed algorithm on embedding Swiss roll from R3 to R2 based on LLE and ISOMAP algorithm, the simulation results show that the proposed adaptive neighboring selection algorithm is feasible and able to find the optimal value of K, making the residual variance relatively small and better visualization of the results. By quantitative analysis, the embedding quality measured by residual variance is increased 45.45% after using the proposed algorithm in LLE.
Key words:  manifold learning  curvature prediction  adaptive neighboring selection  residual variance
DOI:10.11916/j.issn.1005-9113.2013.03.020
Clc Number:S7
Fund:

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