Abstract In this paper, a new submodule clustering method for imaging (2-D) data is proposed. Unlike most existing clustering methods that first convert such data into vectors as preprocessing, the proposed method arranges the data samples as lateral slices of a third-order tensor. Our algorithm is based on the union-of-free-submodules model and the samples are represented using t-product in the third-order tensor space. First, we impose a low-rank constraint on the representation tensor to capture the principle information of data. By incorporating manifold regularization into the tensor factorization, the proposed method explicitly exploits the local manifold structure of data. Meanwhile, a segmentation dependent term is employed to integrate the two pipeline steps of affinity learning and spectral clustering into a unified optimization framework. The proposed method can be efficiently solved based on the alternating direction method of multipliers and spectral clustering. Finally, a nonlinear extension is proposed to handle data drawn from a mixture of nonlinear manifolds. Extensive experimental results on five real-world image datasets confirm the effectiveness of the proposed methods.

中文翻译：

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子模块聚类的图正则化低秩表示

摘要 本文提出了一种新的用于成像（二维）数据的子模块聚类方法。与大多数现有聚类方法首先将此类数据转换为向量作为预处理不同，所提出的方法将数据样本排列为三阶张量的横向切片。我们的算法基于自由子模块并集模型，样本在三阶张量空间中使用 t-product 表示。首先，我们对表示张量施加低秩约束以捕获数据的主要信息。通过将流形正则化合并到张量分解中，所提出的方法显式地利用了数据的局部流形结构。同时，使用分割相关项将亲和力学习和谱聚类的两个管道步骤集成到一个统一的优化框架中。基于乘法器和谱聚类的交替方向法，所提出的方法可以有效地求解。最后，提出了一种非线性扩展来处理从非线性流形混合中提取的数据。在五个真实世界图像数据集上的大量实验结果证实了所提出方法的有效性。