Multiple kernel alignment (MKA) maximization criterion has been widely applied into multiple kernel clustering (MKC) and many variants have been recently developed. Though demonstrating superior clustering performance in various applications, it is observed that none of them can effectively handle incomplete MKC, where parts or all of the pre-specified base kernel matrices are incomplete. To address this issue, we propose to integrate the imputation of incomplete kernel matrices and MKA maximization for clustering into a unified learning framework. The clustering of MKA maximization guides the imputation of incomplete kernel elements, and the completed kernel matrices are in turn combined to conduct the subsequent MKC. These two procedures are alternately performed until convergence. By this way, the imputation and MKC processes are seamlessly connected, with the aim to achieve better clustering performance. Besides theoretically analyzing the clustering generalization error bound, we empirically evaluate the clustering performance on five multiple kernel learning (MKL) benchmark datasets, and the results indicate the superiority of our algorithm over existing state-of-the-art counterparts. Our codes and data are publicly available at \url{https://xinwangliu.github.io/}.

中文翻译：

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用于聚类的不完整的多核对齐最大化。

多核对齐 (MKA) 最大化准则已广泛应用于多核聚类 (MKC)，并且最近开发了许多变体。尽管在各种应用中展示了卓越的聚类性能，但观察到它们都不能有效处理不完整的 MKC，其中部分或全部预先指定的基本核矩阵是不完整的。为了解决这个问题，我们建议将不完整核矩阵的插补和用于聚类的 MKA 最大化集成到一个统一的学习框架中。MKA最大化的聚类指导不完整内核元素的插补，完整的内核矩阵依次组合起来进行后续的MKC。这两个过程交替执行直到收敛。通过这种方式，插补和MKC过程无缝连接，旨在实现更好的聚类性能。除了从理论上分析聚类泛化误差界限外，我们还根据经验评估了五个多核学习 (MKL) 基准数据集的聚类性能，结果表明我们的算法优于现有的最先进算法。我们的代码和数据可在 \url{https://xinwangliu.github.io/} 上公开获得。