Abstract
Over the past few years, nonlinear manifold learning has been widely exploited in data analysis and machine learning. This paper presents a novel manifold learning algorithm, named atlas compatibility transformation (ACT). It solves two problems which correspond to two key points in the manifold definition: how to chart a given manifold and how to align the patches to a global coordinate space based on compatibility. For the first problem, we divide the manifold into maximal linear patch (MLP) based on normal vector field of the manifold. For the second problem, we align patches into an optimal global system by solving a generalized eigenvalue problem. Compared with the traditional method, the ACT could deal with noise datasets and fragment datasets. Moreover, the mappings between high dimensional space and low dimensional space are given. Experiments on both synthetic data and real-world data indicate the effection of the proposed algorithm.
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This work was supported by National Natural Science Foundation of China (No. 61171145) and Shanghai Educational Development Fundation (No. 12ZZ083).
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Zhong-Hua Hao received the B. Sc. degree in automation from Three Gorges University, China in 2007. He received the M. Sc. degree in control theory and control engineering from Kunming University of Science and Technology, China in 2000. Now, he is a Ph. D. candidate in Shanghai University, China.
His research interests include digital image processing, data mining, machine learning and pattern recognition.
ORCID iD0000-0002-8309-0333
Shi-Wei Ma received B. Sc. and M. Sc. degrees in electronics from Lanzhou University, China in 1986 and 1991, respectively, and received the Ph.D. degree in control theory and engineering from Shanghai University, China in 2000. From 2001 to 2003, he was a Japan Science and Technology research fellow at the National Institute of Industrial Safety of Japan. From 2003 to 2008, he was an associate professor. Since 2008, he has been a professor, both in the Department of Automation in Shanghai University, China.
His research interests include signal processingpattern recognition and intelligent system.
ORCID iD0000-0001-6039-5030
Fan Zhao received the B. Sc. degree in information engineering from Northwestern Polytechnical University, China in 2012. She is a master student in control science and engineering at Shanghai University, China.
Her research interests include digital image processing and machine learning.
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Hao, ZH., Ma, SW. & Zhao, F. Atlas compatibility transformation: A normal manifold learning algorithm. Int. J. Autom. Comput. 12, 382–392 (2015). https://doi.org/10.1007/s11633-014-0854-x
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DOI: https://doi.org/10.1007/s11633-014-0854-x