Mutual structure learning for multiple kernel clustering

Abstract

Multiple kernel clustering (MKC) has garnered considerable attention in recent years, aiming to obtain an optimal partition from multiple base kernels. Existing MKC methods typically focus on either learning the pairwise structure by constructing an optimal kernel from the base kernels or learning the cluster structure by integrating multiple base partitions into a consensus one for clustering. However, these previous approaches overlook the potential for mutual structure learning between the two aspects, i.e., pairwise and cluster structure, of clustering. To address this limitation, we propose a novel multiple kernel clustering method, referred to as MSL-MKC, which simultaneously learns pairwise and cluster structure to achieve an improved consensus partition matrix for clustering. Specifically, MSL-MKC extends the adaptive neighbor graph learning approach into kernel space to construct a discriminative similarity graph from multiple base kernels for pairwise structure learning. The consensus partition is formulated by aligning it with multiple base partitions for cluster structure learning. We utilize a Laplacian regularization term to preserve the pairwise structure in the consensus partition and inject the cluster structure into the discriminative similarity graph. The proposed method integrates similarity graph learning, partition fusion, and Laplacian regularization into a unified framework, optimized using an iterative algorithm. Experimental results on various benchmark datasets demonstrate the efficacy of MSL-MKC. The demo code of this work is publicly available at https://github.com/guanyuezhen/MSL-MKC.