SIAM Journal on Imaging Sciences, Volume 13, Issue 3, Page 1157-1178, January 2020.
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.

中文翻译：

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使用新拉普拉斯张量的超图聚类及其在图像处理中的应用

SIAM影像科学杂志，第13卷，第3期，第1157-1178页，2020
年1月。在本文中，我们考虑涉及超图模型的多类聚类问题。从根本上讲，我们研究了加权均匀超图的新规范化拉普拉斯张量。超图的连通性与拟议的Laplacian张量的第二个最小Z特征值有关。特别地，分数奇格不等式的类似物成立。接下来，我们将基于拉普拉斯张量的方法从双聚类化到多类聚类。建立并分析了具有正交约束的张量优化模型。最后，我们将超图聚类方法应用于图像分割和运动分割问题。实验结果表明，该方法是有效的。