Localized Incomplete Multiple Kernel k-Means With Matrix-Induced Regularization
针对局部不完整多核k均值聚类未充分利用基核多样性与互补性的问题，引入矩阵诱导正则化项来建模基核间的相关性，从而提升聚类精度，并在多个公开数据集上验证了其优于现有方法。
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.