Multi-view data may lose some instances in real applications. Most existing methods for clustering such incomplete multi-view data still have at least one of the following limitations: 1) The common relations among data points across all views are ignored. 2) The complementary multi-view information of original data representation is not well exploited. 3) Arbitrary incomplete scenarios or data with negative entries cannot be handled. To address these limitations, in this paper, we propose a novel Consensus Learning approach to Incomplete Multi-view Clustering (CLIMC). Specifically, a low-dimensional consensus representation is introduced to exploit complementary multi-view information from the original feature representation of available instances by integrating index matrices into matrix factorization. In addition, by combining self-representation, index matrices, and consensus term, a consensus similarity graph is leveraged to explore the underlying cross-view relations among data points. Further, the key of the proposed CLIMC is that the consensus representation is correlated with the similarity graph by a graph Laplacian regularization. Consequently, the compactness of the low-dimensional representation and the accuracy of similarity degree of the graph are reciprocally promoted. Extensive experiments on several multi-view datasets demonstrate the effectiveness of CLIMC over state-of-the-arts.

在实际应用程序中，多视图数据可能会丢失一些实例。聚类这种不完整的多视图数据的大多数现有方法仍然至少具有以下限制之一：1）忽略所有视图中数据点之间的公共关系。2）原始数据表示的补充性多视图信息没有得到很好的利用。3）无法处理任意不完整的方案或带有否定条目的数据。为了解决这些限制，在本文中，我们提出了一种新颖的共识学习方法，用于不完整的多视图聚类（CLIMC）。具体而言，引入了低维共识表示，以通过将索引矩阵集成到矩阵分解中来从可用实例的原始特征表示中利用互补的多视图信息。此外，通过将自我表示，索引矩阵和共识项相结合，可以利用共识相似度图来探索数据点之间潜在的交叉视图关系。此外，提出的CLIMC的关键是通过图拉普拉斯正则化将共识表示与相似性图相关。因此，相互促进了低维表示的紧凑性和图形相似度的准确性。在多个多视图数据集上进行的广泛实验证明了CLIMC在最新技术方面的有效性。提出的CLIMC的关键是通过图拉普拉斯正则化将共识表示与相似图相关联。因此，相互促进了低维表示的紧凑性和图形相似度的准确性。在多个多视图数据集上进行的广泛实验证明了CLIMC在最新技术方面的有效性。提出的CLIMC的关键是通过图拉普拉斯正则化将共识表示与相似图相关联。因此，相互促进了低维表示的紧凑性和图形相似度的准确性。在多个多视图数据集上进行的广泛实验证明了CLIMC在最新技术方面的有效性。