Simultaneous learning coefficient matrix and affinity graph for multiple kernel clustering

Abstract

Due to the effectiveness of handling non-linear data and avoiding kernel customization, multiple kernel clustering (MKC) has been widely investigated and achieved promising results for challenging non-linear clustering tasks. Generally, the existing MKC methods mainly consist of first learning a coefficient matrix by leveraging multiple kernel learning (MKL) and sample self-expressiveness property, and then constructing an affinity graph relying on this coefficient matrix to accomplish spectral clustering. However, the quality of the affinity matrix (graph) is largely determined by the learned coefficient matrix, thus the two independent steps are not conducive to learn an optimal affinity graph. To tackle this problem, in this paper, we propose a new MKC method that uses one-step learning scheme rather than two-step learning scheme to learn an affinity graph, termed SLMKC. Specifically, SLMKC bridges the relationship between the affinity matrix and coefficient matrix by an adaptive local structure learning strategy, so it can simultaneously learn both in a mutual promotion manner. Furthermore, a self-weighted MKL strategy is introduced to learn an optimal consensus kernel, which can avoid selecting a specific kernel function and tuning its associated parameters. Extensive experiments validate that our SLMKC outperforms the state-of-the-art MKC competitors significantly.