Multiple kernel clustering (MKC) optimally utilizes a group of pre-specified base kernels to improve clustering performance. Among existing MKC algorithms, the recently proposed late fusion MKC methods demonstrate promising clustering performance in various applications and enjoy considerable computational acceleration. However, we observe that the kernel partition learning and late fusion processes are separated from each other in the existing mechanism, which may lead to suboptimal solutions and adversely affect the clustering performance. In this article, we propose a novel late fusion multiple kernel clustering with proxy graph refinement (LFMKC-PGR) framework to address these issues. First, we theoretically revisit the connection between late fusion kernel base partition and traditional spectral embedding. Based on this observation, we construct a proxy self-expressive graph from kernel base partitions. The proxy graph in return refines the individual kernel partitions and also captures partition relations in graph structure rather than simple linear transformation. We also provide theoretical connections and considerations between the proposed framework and the multiple kernel subspace clustering. An alternate algorithm with proved convergence is then developed to solve the resultant optimization problem. After that, extensive experiments are conducted on 12 multi-kernel benchmark datasets, and the results demonstrate the effectiveness of our proposed algorithm. The code of the proposed algorithm is publicly available at https://github.com/wangsiwei2010/graphlatefusion_MKC .

中文翻译：

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具有代理图细化的后期融合多内核集群

多内核聚类（MKC）最佳地利用一组预先指定的基本内核来提高聚类性能。在现有的 MKC 算法中，最近提出的后期融合 MKC 方法在各种应用中展示了有前途的聚类性能，并享有相当大的计算加速。然而，我们观察到，在现有机制中，内核分区学习和后期融合过程是相互分离的，这可能会导致次优解决方案并对聚类性能产生不利影响。在本文中，我们提出了一种新颖的带有代理图细化的后期融合多核聚类（LFMKC-PGR）框架来解决这些问题。首先，我们从理论上重新审视后期融合核基划分和传统谱嵌入之间的联系。基于这一观察，我们从内核基础分区构建了一个代理自我表达图。代理图反过来细化了各个内核分区，并且还捕获了图结构中的分区关系，而不是简单的线性变换。我们还提供了所提出的框架和多内核子空间聚类之间的理论联系和考虑因素。然后开发出一种具有收敛性的替代算法来解决由此产生的优化问题。之后，在 12 个多核基准数据集上进行了广泛的实验，结果证明了我们提出的算法的有效性。所提出算法的代码可在以下位置公开获取：https://github.com/wangsiwei2010/graphlatefusion_MKC 。