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A Survey of Graph Curvature and Embedding in Non-Euclidean Spaces

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Book cover Neural Information Processing (ICONIP 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12533))

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Abstract

Interest has been growing lately towards learning representations for non-Euclidean geometric data structures. Such kinds of data are found everywhere ranging from social network graphs, brain images, sensor networks to 3-dimensional objects. To understand the underlying geometry and functions of these high dimensional discrete data with non-Euclidean structure, it requires their representations in non-Euclidean spaces. Recently, graph embedding in Riemannian spaces has been explored to successfully capture the geometric properties of networks and achieve the state-of-the-art quality in graph representation learning tasks. In this survey, we provide an overview on graph embeddings based on Riemannian geometry with different curvature spaces. We further present recent developments in various application areas using graph embedding models in non-Euclidean domains.

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Acknowledgements

The work described in this paper was supported by the Research Grants Council of the Hong Kong Special Administrative Region, China (CUHK 2410021, Research Impact Fund, No. R5034-18).

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Authors and Affiliations

  1. Department of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, NT, Hong Kong

    Chandni Saxena, Tianyu Liu & Irwin King

Authors
  1. Chandni Saxena
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  2. Tianyu Liu
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  3. Irwin King
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Corresponding author

Correspondence to Chandni Saxena .

Editor information

Editors and Affiliations

  1. Department of AI, Ping An Life, Shenzhen, China

    Haiqin Yang

  2. Faculty of Information Technology, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand

    Kitsuchart Pasupa

  3. City University of Hong Kong, Kowloon, China

    Andrew Chi-Sing Leung

  4. Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Hong Kong, Hong Kong

    James T. Kwok

  5. School of Information Technology, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand

    Jonathan H. Chan

  6. The Chinese University of Hong Kong, New Territories, Hong Kong

    Irwin King

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Saxena, C., Liu, T., King, I. (2020). A Survey of Graph Curvature and Embedding in Non-Euclidean Spaces. In: Yang, H., Pasupa, K., Leung, A.CS., Kwok, J.T., Chan, J.H., King, I. (eds) Neural Information Processing. ICONIP 2020. Lecture Notes in Computer Science(), vol 12533. Springer, Cham. https://doi.org/10.1007/978-3-030-63833-7_11

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  • DOI: https://doi.org/10.1007/978-3-030-63833-7_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-63832-0

  • Online ISBN: 978-3-030-63833-7

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