Simple multiple kernel k-means with kernel weight regularization

Abstract

Multiple kernel clustering (MKC) aims to determine the optimal kernel from several pre-computed basic kernels. Most of MKC algorithms follow a common assumption that the optimal kernel is linearly combined by basic kernels. Based on a min–max framework, a newly proposed MKC method termed simple multiple kernel k-means can acquire a high-quality unified kernel. Although it has achieved promising clustering performance, we have observed that it cannot benefit from any regularization or prior knowledge, thus the learned kernel weight coefficients may be seriously sparse or over-selected. To tackle this issue, we have developed a new algorithm termed simple multiple kernel k-means with kernel weight regularization (SMKKM-KWR), where we introduce average coefficients to avoid too sparse kernel weights. Specially, we add the average kernel coefficients as a regularization term to prevent the learned weight coefficients being far from the average values. After that, an efficient optimization strategy is proposed to solve the new resultant problem. By this way, the unified partition can learn clustering structure from fusion information of all the kernel views, with the goal to reach better clustering performance. Extensive experiments on nine benchmark datasets and four large-scale datasets have demonstrated the effectiveness and efficiency of the proposed algorithm.