Multi-view subspace clustering methods used consensus and supplementary principles to learn the shared self-representation matrix or tensor have been applied to multiple fields. The existing advanced multi-view subspace clustering methods are mainly based on the extension of low-rank representation from matrix to tensor. However, the tensor optimization methods have two limitations: they cannot retain the local geometric structure of data features residing in multiple nonlinear subspaces; they represent the low-rank structure based on the tensor nuclear norm, which will cause undesirable low-rank approximation. To solve these problems, we propose a hyper-Laplacian regularized Nonconvex Low-rank Representation (HNLR) method for multi-view subspace clustering. HNLR uses hyper-Laplacian regularizer to capture the high-order local geometry structure of each view. In addition, by introducing a nonconvex Laplace function to replace the tensor nuclear norm, HNLR can greatly improve the approximate performance of the global low-rank structure. Based on the alternating direction method of multiplier, we design an effective alternate iteration strategy to optimize HNLR model. Experimental results on eight real datasets have proved the superiority of our proposed method.

中文翻译：

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多视图子空间聚类的超拉普拉斯正则化非凸低秩表示


多视图子空间聚类方法使用共识和补充原理来学习共享的自表示矩阵或张量，已应用于多个领域。现有的先进多视图子空间聚类方法主要基于低秩表示从矩阵到张量的扩展。然而，张量优化方法有两个局限性：它们不能保留驻留在多个非线性子空间中的数据特征的局部几何结构；它们代表基于张量核范数的低秩结构，这将导致不良的低秩近似。为了解决这些问题，我们提出了一种用于多视图子空间聚类的超拉普拉斯正则化非凸低秩表示（HNLR）方法。 HNLR 使用超拉普拉斯正则化器来捕获每个视图的高阶局部几何结构。此外，通过引入非凸拉普拉斯函数来替代张量核范数，HNLR可以极大地提高全局低秩结构的近似性能。基于乘子交替方向法，我们设计了一种有效的交替迭代策略来优化HNLR模型。在八个真实数据集上的实验结果证明了我们提出的方法的优越性。