Multiple kernel clustering with local kernel reconstruction and global heat diffusion

Abstract

Multiple Kernel Clustering (MKC) is an effective approach for revealing nonlinear cluster structures in candidate kernels. However, existing MKC methods still face two key challenges. Firstly, the pairwise affinity in these methods is primarily determined by kernel similarity, disregarding the correlations among highly similar neighbors and resulting in redundant weight assignments and reduced clustering discriminability. Secondly, the direct utilization of affinity matrices overlooks high-order connections and introduces noise due to independent row-wise solving. To address these issues, we propose a novel local MKC method called LKRGDF. We begin by exploring affinity using the Local Kernel Reconstruction (LKR) model, reducing redundancy and enhancing clustering discriminability. Furthermore, we exploit the affinities with the Global heat kernel Diffusion (GD) procedure to capture long-range connections smoothly. The GD process acts as a low pass filter, focusing on small eigenvalues corresponding to top clusters. Finally, we integrate these smooth affinities within an auto-weighted Multiple Graph Fusion (MGF) framework to obtain a consensus graph. By assembling LKR, GD, and MGF in a sequential pipeline, our approach achieves the exploration and exploitation of local structures, gradually improving clustering performance while ensuring computational efficiency without the need for iterative steps. Extensive experiments on ten datasets demonstrate the superiority of our algorithm in terms of effectiveness and efficiency compared to state-of-the-art methods. The code for our method is publicly available at https://github.com/YanChenSCU/LKRGDF-2023.git.