Optimal Neighborhood Kernel Clustering with Multiple Kernels

Multiple kernel $k$-means (MKKM) aims to improve clustering performance by learning an optimal kernel, which is usually assumed to be a linear combination of a group of pre-specified base kernels. However, we observe that this assumption could: i) cause limited kernel representation capability; and ii) not sufficiently consider the negotiation between the process of learning the optimal kernel and that of clustering, leading to unsatisfying clustering performance. To address these issues, we propose an optimal neighborhood kernel clustering (ONKC) algorithm to enhance the representability of the optimal kernel and strengthen the negotiation between kernel learning and clustering. We theoretically justify this ONKC by revealing its connection with existing MKKM algorithms. Furthermore, this justification shows that existing MKKM algorithms can be viewed as a special case of our approach and indicates the extendability of the proposed ONKC for designing better clustering algorithms. An efficient algorithm with proved convergence is designed to solve the resultant optimization problem. Extensive experiments have been conducted to evaluate the clustering performance of the proposed algorithm. As demonstrated, our algorithm significantly outperforms the state-of-the-art ones in the literature, verifying the effectiveness and advantages of ONKC