Multiple Kernel Clustering with Pure Graph Learning Scheme

Abstract Existing graph-based multiple kernel clustering (GMKC) methods usually adopt a hybridization scheme, termed HGMKC for short, which binds multiple kernel learning (MKL) and graph-based clustering (GBC) together, the former aims to construct a consensus kernel and the latter is used to learn an affinity graph based on the consensus kernel. Obviously, HGMKC performs graph learning and spectral clustering separately. Additionally, the performance of this hybridization is largely determined by MKL, which is empirically contrary to the fact that graph learning is the key of graph-based methods, rather than kernel learning. In this paper, we propose a pure GMKC method, dubbed PGMKC, which contains two parts, including candidate kernel graphs learning (CKGL) and kernel graph fusion (KGF). Specially, CKGL concentrates on constructing multiple candidate kernel graphs in Hilbert kernel space relying on kernel self-expressiveness; KGF leverages a flexibly auto-weighted graph fusion strategy and a connectivity regularizer to yield a consensus kernel graph directly. Compared to HGMKC, PGMKC avoids paying too much attention to consensus kernel construction, thus can focus more on affinity graph learning. Moreover, an efficient and effective optimization algorithm is developed to solve the proposed model. Experimental results on ten benchmark datasets demonstrate that the proposed PGMKC performs better than the state-of-the-art HGMKC competitors.