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Mathematical Problems in Engineering Volume 2017 ,2017-05-24
Robust L-Isomap with a Novel Landmark Selection Method
Research Article
Hao Shi 1 Baoqun Yin 1 Yu Kang 1 Chao Shao 2 Jie Gui 3
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DOI:10.1155/2017/3930957
Received 2016-10-17, accepted for publication 2017-03-16, Published 2017-03-16
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摘要

Isomap is a widely used nonlinear method for dimensionality reduction. Landmark-Isomap (L-Isomap) has been proposed to improve the scalability of Isomap. In this paper, we focus on two important issues that were not taken into account in L-Isomap, landmark point selection and topological stability. At first, we present a novel landmark point selection method. It first uses a greedy strategy to select some points as landmark candidates and then removes the candidate points that are neighbours of other candidates. The remaining candidate points are the landmark points. The selection method can promote the computation efficiency without sacrificing accuracy. For the topological stability, we define edge density for each edge in the neighbourhood graph. According to the geometrical characteristic of the short-circuit edges, we provide a method to eliminate the short-circuit edge without breaking the data integrity. The approach that integrates L-Isomap with these two improvements is referred to as Robust L-Isomap (RL-Isomap). The effective performance of RL-Isomap is confirmed through several numerical experiments.

授权许可

Copyright © 2017 Hao Shi et al. 2017
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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通讯作者

Hao Shi.Department of Automation, University of Science and Technology of China, Hefei, China, ustc.edu.haoshi@mail.ustc.edu.cn

推荐引用方式

Hao Shi,Baoqun Yin,Yu Kang,Chao Shao,Jie Gui. Robust L-Isomap with a Novel Landmark Selection Method. Mathematical Problems in Engineering ,Vol.2017(2017)

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