Many works have proven that the consistency and differences in multi-view subspace clustering make the clustering results better than the single-view clustering. Therefore, this paper studies the multi-view clustering problem, which aims to divide data points into several groups using multiple features. However, existing multi-view clustering methods fail to capturing the grouping effect and local geometrical structure of the multiple features. In order to solve these problems, this paper proposes a novel multi-view subspace clustering model called graph-regularized least squares regression (GLSR), which uses not only the least squares regression instead of the nuclear norm to generate grouping effect, but also the manifold constraint to preserve the local geometrical structure of multiple features. Specifically, the proposed GLSR method adopts the least squares regression to learn the globally consensus information shared by multiple views and the column-sparsity norm to measure the residual information. Under the alternating direction method of multipliers framework, an effective method is developed by iteratively update all variables. Numerical studies on eight real databases demonstrate the effectiveness and superior performance of the proposed GLSR over eleven state-of-the-art methods.

许多工作证明，多视图子空间聚类的一致性和差异使得聚类结果优于单视图聚类。因此，本文研究了多视图聚类问题，该问题旨在使用多个特征将数据点分为几组。但是，现有的多视图聚类方法无法捕获多个特征的分组效果和局部几何结构。为了解决这些问题，本文提出了一种新颖的多视图子空间聚类模型，称为图规则化最小二乘回归（GLSR），该模型不仅使用最小二乘回归代替核范数来产生分组效应，而且流形约束，以保留多个特征的局部几何结构。特别，提出的GLSR方法采用最小二乘回归来学习多个视图共享的全局共识信息，并采用列稀疏范数来度量残差信息。在乘数的交替方向方法框架下，通过迭代更新所有变量来开发一种有效的方法。对八个真实数据库的数值研究表明，与11种最新方法相比，所建议的GLSR的有效性和优越的性能。