Multiple Kernel k-Means With Low-Rank Neighborhood Kernel

Qiyuan Ou, Long Gao, En Zhu

Abstract: Multiple kernel clustering algorithms achieve promising performances by exploring the complementary information from kernel matrices corresponding to each data view. Most of the existing methods aim to construct a consensus kernel for the afterward clustering. However, they ignore that the desired kernel is supposed to reveal the cluster structure among samples and thus to be low rank. As a consequence, the corresponding clustering performance could decrease. To address this issue, we propose a low-rank kernel learning approach for multiple kernel clustering. Specifically, instead of regularizing the consensus kernel with low-rank constraints, we use a re-parameterize scheme for the kernel matrix. Meanwhile, the consensus kernel is located in the neighborhood area of the linear combination of base kernels. An alternate optimization strategy is designed to solve the resulting optimization problem. We evaluate the proposed method on 13 benchmark datasets with 9 state-of-the-art algorithms. As is demonstrated by experimental results, our proposed algorithm achieves superior clustering scores against the compared algorithms on the reported popular multiple kernel datasets.