In this paper, we propose a general framework for incomplete multiview clustering. The proposed method is the first work that exploits the graph learning and spectral clustering techniques to learn the common representation for incomplete multiview clustering. First, owing to the good performance of low-rank representation in discovering the intrinsic subspace structure of data, we adopt it to adaptively construct the graph of each view. Second, a spectral constraint is used to achieve the low-dimensional representation of each view based on the spectral clustering. Third, we further introduce a co-regularization term to learn the common representation of samples for all views, and then use the k-means to partition the data into their respective groups. An efficient iterative algorithm is provided to optimize the model. Experimental results conducted on seven incomplete multiview datasets show that the proposed method achieves the best performance in comparison with some state-of-the-art methods, which proves the effectiveness of the proposed method in incomplete multiview clustering.

Conventional multiview clustering seeks to partition data into respective groups based on the assumption that all views are fully observed. However, in practical applications, such as disease diagnosis, multimedia analysis, and recommendation system, it is common to observe that not all views of samples are available in many cases, which leads to the failure of the conventional multiview clustering methods. Clustering on such incomplete multiview data is referred to as incomplete multiview clustering (IMC). In view of the promising application prospects, the research of IMC has noticeable advances in recent years. However, there is no survey to summarize the current progresses and point out the future research directions. To this end, we review the recent studies of IMC. Importantly, we provide some frameworks to unify the corresponding IMC methods and make an in-depth comparative analysis for some representative methods from theoretical and experimental perspectives. Finally, some open problems in the IMC field are offered for researchers. The related codes are released at https://github.com/DarrenZZhang/Survey_IMC .

In real-world applications, it is often that the collected multi-view data are incomplete, i.e., some views of samples are absent. Existing clustering methods for incomplete multi-view data all focus on obtaining a common representation or graph from the available views but neglect the hidden information of missing views and information imbalance of different views. To solve these problems, a novel method, called adaptive graph completion based incomplete multi-view clustering (AGC_IMC), is proposed in this paper. Specifically, AGC_IMC develops a joint framework for graph completion and consensus representation learning, which mainly contains three components, i.e., within-view preservation, between-view inferring, and consensus representation learning. To reduce the negative influence of information imbalance, AGC_IMC introduces some adaptive weights to balance the importance of different views during the consensus representation learning. Importantly, AGC_IMC has the potential to recover the similarity graphs of all views with the optimal cluster structure, which encourages it to obtain a more discriminative consensus representation. Experimental results on five well-known datasets show that AGC_IMC significantly outperforms the state-of-the-art methods.