Hypergraph Clustering Using a New Laplacian Tensor with Applications in Image Processing

Authors:
  • JCJingya Chang
    Jingya Chang
  • YCYannan Chen
    Yannan Chen
  • LQLiqun Qi
    Liqun Qi
  • HYHong Yan
    Hong Yan
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Abstract
In this paper, we consider the multiclass clustering problem involving a hypergraph model. Fundamentally, we study a new normalized Laplacian tensor of an even-uniform weighted hypergraph. The hypergraph's connectivity is related with the second smallest Z-eigenvalue of the proposed Laplacian tensor. Particularly, an analogue of fractional Cheeger inequality holds. Next, we generalize the Laplacian tensor based approach from biclustering to multiclass clustering. A tensor optimization model with an orthogonal constraint is established and analyzed. Finally, we apply our hypergraph clustering approach to image segmentation and motion segmentation problems. Experimental results demonstrate that our method is effective.
Funding Information
  • Hong Kong Research Grants Council (PolyU 15302114, 15300715, 15301716, 15300717)
  • Hong Kong Research Grants Council (C1007-15G)
  • City University of Hong Kong (9610308)
  • National Natural Science Foundation of China (11901118)
  • National Natural Science Foundation of China (11771405)
  • Guangdong Basic and Applied Basic Research Foundation (2020B1515310001, 2020A1515010489)

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