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Fast hypergraph regularized nonnegative tensor ring decomposition based on low-rank approximation

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Abstract

Tensor ring (TR) decomposition is a highly effective tool for obtaining the low-rank character of multi-way data. Recently, nonnegative tensor ring (NTR) decomposition combined with manifold learning has emerged as a promising approach for exploiting the multi-dimensional structure and extracting features from tensor data. However, an existing method such as graph regularized tensor ring (GNTR) decomposition only models the pair-wise similarities of objects. The graph cannot precisely encode similarity relationships for tensor data with a complex manifold structure. In this paper, to sufficiently utilize the high-dimensional and complex similarities among objects, we add a novel hypergraph regulation into the NTR framework to further enhance feature extraction. Based on this, we propose a hypergraph regularized nonnegative tensor ring decomposition (HGNTR) model. To reduce computational complexity and suppress noise, we apply the low-rank approximation trick to accelerate HGNTR (called LraHGNTR). Our experiment results demonstrate that the proposed HGNTR and LraHGNTR algorithms outperform other state-of-the-art algorithms; additionally, LraHGNTR significantly reduces running time without sacrificing accuracy.

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Acknowledgements

This work was supported in part by the Guangdong Key R&D Project of China (Grant 2019B010121001) and the National Natural Science Foundation of China (Grant 62073087, Grant U1911401, Grant 62071132, and Grant 61973090).

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Authors and Affiliations

  1. School of Automation, Guangdong University of Technology, Guangzhou, China

    Xinhai Zhao, Yuyuan Yu, Guoxu Zhou, Qibin Zhao & Weijun Sun

  2. RIKEN Center for Advanced Intelligence Project, RIKEN, Tokyo, Japan

    Qibin Zhao

  3. Guangdong Key Laboratory of IoT Information Technology, Guangzhou, China

    Weijun Sun

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  1. Xinhai Zhao
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  2. Yuyuan Yu
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  3. Guoxu Zhou
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  4. Qibin Zhao
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  5. Weijun Sun
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Correspondence to Guoxu Zhou or Qibin Zhao.

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Zhao, X., Yu, Y., Zhou, G. et al. Fast hypergraph regularized nonnegative tensor ring decomposition based on low-rank approximation. Appl Intell 52, 17684–17707 (2022). https://doi.org/10.1007/s10489-022-03346-1

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