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International Conference of Pioneering Computer Scientists, Engineers and Educators

ICPCSEE 2017: Data Science pp 520–533Cite as

Nonlinear Dimensionality Reduction via Homeomorphic Tangent Space and Compactness

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 727))

Abstract

This paper establishes the geometric framework of manifold learning. After summarizing the requirements of the classical manifold learning methods, we construct the smooth homeomorphism between the manifold and its tangent space. Then we propose a new algorithm via homeomorphic tangent space (LHTS). We also present another algorithm via compactness (CSLI) by analyzing the topological properties of manifolds. We illustrate our algorithm on the completed manifold and non-completed manifold. We also address several theoretical issues for further research and improvements.

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Author information

Authors and Affiliations

  1. Sichuan University, Chengdu, 610024, China

    Shaoqun Zhang & Wanyun Xie

Authors
  1. Shaoqun Zhang
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  2. Wanyun Xie
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Corresponding author

Correspondence to Shaoqun Zhang .

Editor information

Editors and Affiliations

  1. Central South University, Changsha, China

    Beiji Zou

  2. Central South University, Changsha, China

    Min Li

  3. Harbin Institute of Technology, Harbin, China

    Hongzhi Wang

  4. Harbin University of Science and Technology, Harbin, China

    Xianhua Song

  5. Harbin University of Science and Technology, Harbin, China

    Wei Xie

  6. Harbin Sea of Clouds and Computer Technology, Harbin, China

    Zeguang Lu

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© 2017 Springer Nature Singapore Pte Ltd.

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Zhang, S., Xie, W. (2017). Nonlinear Dimensionality Reduction via Homeomorphic Tangent Space and Compactness. In: Zou, B., Li, M., Wang, H., Song, X., Xie, W., Lu, Z. (eds) Data Science. ICPCSEE 2017. Communications in Computer and Information Science, vol 727. Springer, Singapore. https://doi.org/10.1007/978-981-10-6385-5_44

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  • DOI: https://doi.org/10.1007/978-981-10-6385-5_44

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-6384-8

  • Online ISBN: 978-981-10-6385-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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