Localized Simple Multiple Kernel K-Means with Matrix Regularization

Multiple kernel clustering (MKC) enhances clustering performance by integrating diverse data views, yet existing methods often struggle with kernel redundancy and suboptimal optimization. The recently proposed method localized simple multiple kernel k-means (LSMKKM) achieves remarkable achievements by using a novel Min-Max optimization framework. Current methods improve on this by incorporating additional prior knowledge. However, its optimization strategy is incompatible with matrix regularization. By reformulating the Min-Max optimization framework, we introduce a tailored reduced gradient descent algorithm that partitions optimization variables and transforms constraints into a linear programming format, enabling seamless integration of matrix and vector regularizations. We first propose a novel LSMKKM with representative kernels regularization (LSMKKM-RKR) that incorporates representative kernel regularization to address kernel redundancy via subset selection. This approach maximizes kernel diversity while enhancing clustering accuracy. Furthermore, we improve LSMKKM-RKR by proposing LSMKKM with representative kernels regularization and matrix-induced regularization (LSMKKM-RKMR) where kernel correlation and dissimilarity are both integrated. Extensive experiments on several benchmark datasets, including Handwritten Numerals and Coil20, demonstrate that our algorithms significantly outperform state-of-the-art multiple kernel k-means methods.