Using locally estimated geodesic distance to optimize neighborhood graph for isometric data embedding |
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| Authors: | Guihua Wen Lijun Jiang Jun Wen |
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| Affiliation: | 1. South China University of Technology, Guangzhou 510641, China;2. Hubei Institute for Nationalities, Ensi 445000, China;1. School of Energy and Environment, Inner Mongolia University of Science and Technology, Baotou 014010, China;2. Mining Research Institute, Inner Mongolia University of Science and Technology, Baotou 014010, China;3. Inner Mongotia Key Laboratory of Efficient and Clean Combustion, Baotou 014030, China;1. College of Material Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China;2. Shandong Inspection and Quarantine Technology Center, Qingdao 266590, China |
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| Abstract: | To deal with the highly twisted and folded manifold, this paper propose a geodesic distance-based approach to build the neighborhood graph for isometric embedding. This approach assumes that the neighborhood of a point located at the highly twisted place of the manifold may not be linear so that its neighbors should be determined by geodesic distance. This approach firstly determines the neighborhood for each point using Euclidean distance and then applies the locally estimated geodesic distances to optimize the neighborhood. It increases only linear time complexity. Furthermore the optimized neighborhood can speed up the subsequent embedding process. The proposed approach is simple, general and easy to deal with a wider range of data. The conducted experiments on both synthetic and real data sets validate the approach. |
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