Localized Simple Multiple Kernel K-Means Clustering with Matrix-Induced Regularization

Abstract

Multikernel clustering achieves clustering of linearly inseparable data by applying a kernel method to samples in multiple views. A localized SimpleMKKM (LI-SimpleMKKM) algorithm has recently been proposed to perform min-max optimization in multikernel clustering where each instance is only required to be aligned with a certain proportion of the relatively close samples. The method has improved the reliability of clustering by focusing on the more closely paired samples and dropping the more distant ones. Although LI-SimpleMKKM achieves remarkable success in a wide range of applications, the method keeps the sum of the kernel weights unchanged. Thus, it restricts kernel weights and does not consider the correlation between the kernel matrices, especially between paired instances. To overcome such limitations, we propose adding a matrix-induced regularization to localized SimpleMKKM (LI-SimpleMKKM-MR). Our approach addresses the kernel weight restrictions with the regularization term and enhances the complementarity between base kernels. Thus, it does not limit kernel weights and fully considers the correlation between paired instances. Extensive experiments on several publicly available multikernel datasets show that our method performs better than its counterparts.