Localized incomplete multiple kernel $k$ -means (LI-MKKM) is recently put forward to boost the clustering accuracy via optimally utilizing a quantity of prespecified incomplete base kernel matrices. Despite achieving significant achievement in a variety of applications, we find out that LI-MKKM does not sufficiently consider the diversity and the complementary of the base kernels. This could make the imputation of incomplete kernels less effective, and vice versa degrades on the subsequent clustering. To tackle these problems, an improved LI-MKKM, called LI-MKKM with matrix-induced regularization (LI-MKKM-MR), is proposed by incorporating a matrix-induced regularization term to handle the correlation among base kernels. The incorporated regularization term is beneficial to decrease the probability of simultaneously selecting two similar kernels and increase the probability of selecting two kernels with moderate differences. After that, we establish a three-step iterative algorithm to solve the corresponding optimization objective and analyze its convergence. Moreover, we theoretically show that the local kernel alignment is a special case of its global one with normalizing each base kernel matrices. Based on the above observation, the generalization error bound of the proposed algorithm is derived to theoretically justify its effectiveness. Finally, extensive experiments on several public datasets have been conducted to evaluate the clustering performance of the LI-MKKM-MR. As indicated, the experimental results have demonstrated that our algorithm consistently outperforms the state-of-the-art ones, verifying the superior performance of the proposed algorithm.

中文翻译：

---

具有矩阵诱导正则化的局部不完全多核 k-均值

局部不完全多核 $k$ -均值 (LI-MKKM) 最近提出通过优化利用大量预先指定的不完整基核矩阵来提高聚类精度。尽管在各种应用中取得了显着的成就，但我们发现 LI-MKKM 没有充分考虑基核的多样性和互补性。这可能会使不完整内核的归因效率降低，反之亦然会降低后续聚类的效果。为了解决这些问题，提出了一种改进的 LI-MKKM，称为具有矩阵诱导正则化的 LI-MKKM (LI-MKKM-MR)，通过结合矩阵诱导正则化项来处理基核之间的相关性。合并的正则化项有利于降低同时选择两个相似内核的概率，并增加选择两个具有适度差异的内核的概率。之后，我们建立了一个三步迭代算法来求解相应的优化目标并分析其收敛性。此外，我们从理论上表明，局部内核对齐是其全局内核对齐的一种特殊情况，其中对每个基本内核矩阵进行了归一化。基于上述观察，推导了所提出算法的泛化误差界，从理论上证明了其有效性。最后，对几个公共数据集进行了广泛的实验，以评估 LI-MKKM-MR 的聚类性能。如..所示，