Incremental Nyström-based Multiple Kernel Clustering

Yu Feng, Weixuan Liang, Xinhang Wan, Jiyuan Liu, Suyuan Liu, Qian Qu, Renxiang Guan, Huiying Xu, Xinwang Liu

Abstract: Existing Multiple Kernel Clustering (MKC) algorithms commonly utilize the Nyström method to handle large-scale datasets. However, most of them employ uniform sampling for kernel matrix approximation, hence failing to accurately capture the underlying data structure, leading to large approximation errors. Additionally, they often use the same landmark points for all kernel matrix approximations, reducing kernel diversity. Moreover, in scenarios where approximate kernel matrices emerge over time, these methods require storing historical kernel information and recalculating, resulting in inefficient resource utilization. To address these issues, we propose a novel MKC algorithm, termed Incremental Nyström-based Multiple Kernel Clustering (INMKC). Specifically, leverage score sampling is utilized to reduce kernel approximation errors and enhance kernel diversity. Furthermore, we employ a consensus clustering structure that aligns with the newly emerged base kernel matrix for updates, avoiding recalculating previous kernel matrices, thus saving substantial computational resources. Additionally, we tackle the challenge of aligning incremental approximate kernels with different landmark points. Extensive experiments on the proposed INMKC demonstrate its effectiveness and efficiency compared to state-of-the-art methods.