Incomplete multi-view clustering optimally integrates a group of pre-specified incomplete views to improve clustering performance. Among various excellent solutions, multiple kernel $k$k-means with incomplete kernels forms a benchmark, which redefines the incomplete multi-view clustering as a joint optimization problem where the imputation and clustering are alternatively performed until convergence. However, the comparatively intensive computational and storage complexities preclude it from practical applications. To address these issues, we propose Late Fusion Incomplete Multi-view Clustering (LF-IMVC) which effectively and efficiently integrates the incomplete clustering matrices generated by incomplete views. Specifically, our algorithm jointly learns a consensus clustering matrix, imputes each incomplete base matrix, and optimizes the corresponding permutation matrices. We develop a three-step iterative algorithm to solve the resultant optimization problem with linear computational complexity and theoretically prove its convergence. Further, we conduct comprehensive experiments to study the proposed LF-IMVC in terms of clustering accuracy, running time, advantages of late fusion multi-view clustering, evolution of the learned consensus clustering matrix, parameter sensitivity and convergence. As indicated, our algorithm significantly and consistently outperforms some state-of-the-art algorithms with much less running time and memory.

中文翻译：

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后期融合不完整多视图聚类

不完整的多视图聚类可以最佳地集成一组预先指定的不完整视图，以提高聚类性能。在各种优秀的解决方案中，具有不完整内核的多个内核$ k $ k-means构成了一个基准，它将不完整多视图聚类重新定义为联合优化问题，在该联合优化问题中，插补和聚类被交替执行直到收敛。但是，相对较密集的计算和存储复杂性使其无法在实际应用中使用。为了解决这些问题，我们提出了后期融合不完整多视图聚类（LF-IMVC），它可以有效地集成不完整视图生成的不完整聚类矩阵。具体来说，我们的算法共同学习了共识聚类矩阵，估算了每个不完整的基本矩阵，并优化相应的置换矩阵。我们开发了一个三步迭代算法来解决线性优化的结果优化问题，并从理论上证明了其收敛性。此外，我们进行了全面的实验，从聚类精度，运行时间，后期融合多视图聚类的优势，学习到的共识聚类矩阵的演化，参数敏感性和收敛性等方面研究了拟议的LF-IMVC。如前所述，我们的算法在运行时间和内存方面要少得多，并且在性能上始终优于某些最新算法。我们进行了全面的实验，从聚类精度，运行时间，后期融合多视图聚类的优势，学习到的共识聚类矩阵的演化，参数敏感性和收敛性等方面研究拟议的LF-IMVC。如前所述，我们的算法在运行时间和内存方面要少得多，并且在性能上始终优于某些最新算法。我们进行了全面的实验，从聚类精度，运行时间，后期融合多视图聚类的优势，学习到的共识聚类矩阵的演化，参数敏感性和收敛性等方面研究拟议的LF-IMVC。如前所述，我们的算法在运行时间和内存方面要少得多，并且在性能上始终优于某些最新算法。