Balanced Multiple Kernel Clustering with Discrete Partition Entropy Auto Regularization

Clustering, a fundamental task in machine learning and data mining, is essential for uncovering patterns by grouping data points with similar characteristics. Traditional methods struggle with nonlinear data structures, but kernel-based approaches alleviate this issue by mapping data to high dimensional spaces. Multiple Kernel Clustering (MKC) further improves clustering by automating kernel selection and integration. However, MKC faces challenges related to kernel graph quality, information loss during relax-and-discretization, neglect of balanced clustering constraints, and the trade-off between high clustering quality and balance. To address these challenges, we introduce Balanced Multiple Kernel Clustering (BMKC). BMKC utilizes local kernel reconstruction and advanced high-order diffusion techniques for comprehensive kernel graph learning. It directly learns a discrete partition matrix using a robust L1-induced local reconstruction criterion, eliminating the two step process. BMKC incorporates an automatic mechanism for trade-off control between clustering and balance, supported by a versatile optimization algorithm accommodating various balance regularization choices. Experimental validation demonstrates the superior performance of MKC on benchmarks data sets, showcasing its effectiveness. The code for our method is publicly available at https://github.com/ChenYan01TYUT/BMKC-ACM-MM-2025.