Hypergraph Clustering Using a New Laplacian Tensor with Applications in Image Processing
Jingya Chang, Yannan Chen, Liqun Qi, Hong Yan
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.