Smooth Multiple Kernel <i>k</i> -Means via Underlying Graph Filtering

Clustering has attracted more and more attention as one of the most fundamental techniques in the field of unsupervised learning. To deal with nonlinear problems, clustering methods have been extended to the kernel version. As a traditional kernel clustering algorithm, multiple kernel k-means (MKKM) aims to learn clustering results from a consensus kernel obtained by combining a set of predefined kernels optimally. However, we observe that the existing MKKM algorithm and its variants insufficiently consider the noise that existed in kernel space and the underlying structure of kernelized data points. To this end, we propose a novel smooth MKKM via underlying graph filtering (SMKKM-UGF) to learn the smooth representations of kernelized data points through their nearby nodes in the underlying graph. In particular, different from the common graph filter, we jointly update the graph filter while learning the smooth kernel, so that the graph filter can be guaranteed to adapt to the updating kernel space constantly. Besides, an iterative algorithm with proven convergence is designed to solve the resultant optimization problem. Extensive experiments have been performed on numerous benchmark datasets, whose results prove the superiority of the proposed SMKKM-UGF compared to the other state-of-the-art clustering methods. The demo code of this work is publicly available at https://github.com/wqyang23/SMKKM-UGF.git.