Owing to the presence of complex noise, it is extremely challenging to learn a low-dimensional subspace structure directly from the original data. In addition, the nonlinear structure of the data makes multi-view subspace clustering more difficult. In this paper, we propose a multiple kernel low-rank representation-based robust multi-view subspace clustering method (MKLR-RMSC) that combines a learnable low-rank multiple kernel trick with co-regularization. MKLR-RMSC mainly conducts the following four tasks: 1) fully mining the complementary information provided by the different views in the feature spaces, 2) the containment of multiple low-dimensional subspaces in the feature space data, 3) allowing all view-specific representations towards a common centroid, and 4) effectively dealing with non-Gaussian noise in data. In our model, the weighted Schatten p-norm is applied to fully explore the effects of different ranks while approaching the original low-rank hypothesis. Moreover, different predefined learning kernel matrices are designed for different views, which is more conducive to mining the unique and complementary information of different views. In addition, as a robust measure, correntropy is applied in MKLR-RMSC. Our method is more effective and robust than several of the most advanced methods on six commonly used datasets.

由于存在复杂的噪声，直接从原始数据中学习低维子空间结构非常具有挑战性。此外，数据的非线性结构使多视图子空间聚类更加困难。在本文中，我们提出了一种基于多核低秩表示的鲁棒多视图子空间聚类方法（MKLR-RMSC），该方法将可学习的低秩多核技巧与协规则化相结合。MKLR-RMSC主要执行以下四个任务：1）充分挖掘特征空间中不同视图提供的补充信息，2）在特征空间数据中包含多个低维子空间，3）允许所有特定于视图的4）有效处理数据中的非高斯噪声。在我们的模型中在接近原始的低秩假设的同时，应用p -norm来充分探索不同秩的影响。此外，针对不同的视图设计了不同的预定义学习内核矩阵，这更有利于挖掘不同视图的唯一且互补的信息。另外，作为一种可靠的措施，在MKLR-RMSC中应用了熵。与六个常用数据集上的几种最先进的方法相比，我们的方法更加有效和健壮。