Incomplete multi-view clustering, which aims to solve the clustering problem on the incomplete multi-view data with partial view missing, has received more and more attention in recent years. Although numerous methods have been developed, most of the methods either cannot flexibly handle the incomplete multi-view data with arbitrary missing views or do not consider the negative factor of information imbalance among views. Moreover, some methods do not fully explore the local structure of all incomplete views. To tackle these problems, this paper proposes a simple but effective method, named localized sparse incomplete multi-view clustering (LSIMVC). Different from the existing methods, LSIMVC intends to learn a sparse and structured consensus latent representation from the incomplete multi-view data by optimizing a sparse regularized and novel graph embedded multi-view matrix factorization model. Specifically, in such a novel model based on the matrix factorization, a l1 norm based sparse constraint is introduced to obtain the sparse low-dimensional individual representations and the sparse consensus representation. Moreover, a novel local graph embedding term is introduced to learn the structured consensus representation. Different from the existing works, our local graph embedding term aggregates the graph embedding task and consensus representation learning task into a concise term. Furthermore, to reduce the imbalance factor of incomplete multi-view learning, an adaptive weighted learning scheme is introduced to LSIMVC. Finally, an efficient optimization strategy is given to solve the optimization problem of our proposed model. Comprehensive experimental results performed on six incomplete multi-view databases verify that the performance of our LSIMVC is superior to the state-of-the-art IMC approaches. The code is available in https://github.com/justsmart/LSIMVC.

翻译：不完整多视图聚类旨在解决部分视图缺失的不完整多视图数据上的聚类问题，近年来受到越来越多的关注。尽管已有众多方法被提出，但大多数方法要么无法灵活处理存在任意视图缺失的不完整多视图数据，要么未考虑视图间信息不平衡这一负面因素。此外，部分方法未能充分探索所有不完整视图的局部结构。为解决这些问题，本文提出一种简单有效的方法，称为局部稀疏不完整多视图聚类（LSIMVC）。与现有方法不同，LSIMVC通过优化一个稀疏正则化且嵌入新颖图结构的多视图矩阵分解模型，旨在从不完整多视图数据中学习稀疏且结构化的共识潜在表示。具体而言，在该基于矩阵分解的新颖模型中，引入了基于ℓ1范数的稀疏约束，以获得稀疏的低维个体表示和稀疏共识表示。此外，引入了一种新颖的局部图嵌入项来学习结构化的共识表示。与现有工作不同，我们的局部图嵌入项将图嵌入任务和共识表示学习任务整合为一个简洁的项。进一步地，为降低不完整多视图学习的不平衡因子，LSIMVC引入了自适应加权学习方案。最后，给出了一种高效的优化策略来求解所提模型的优化问题。在六个不完整多视图数据库上进行的全面实验结果验证了我们的LSIMVC性能优于最先进的不完整多视图聚类方法。代码可在 https://github.com/justsmart/LSIMVC 获取。