Localized Simple Multiple Kernel K-Means

As a representative of multiple kernel clustering (MKC), simple multiple kernel k-means (SimpleMKKM) is recently put forward to boosting the clustering performance by optimally fusing a group of pre-specified kernel matrices. Despite achieving significant improvement in a variety of applications, we find out that SimpleMKKM could indiscriminately force all sample pairs to be equally aligned with the same ideal similarity. As a result, it does not sufficiently take the variation of samples into consideration, leading to unsatisfying clustering performance. To address these issues, this paper proposes a novel MKC algorithm with a "local" kernel alignment, which only requires that the similarity of a sample to its k-nearest neighbours be aligned with the ideal similarity matrix. Such an alignment helps the clustering algorithm to focus on closer sample pairs that shall stay together and avoids involving unreliable similarity evaluation for farther sample pairs. After that, we theoretically show that the objective of SimpleMKKM is a special case of this local kernel alignment criterion with normalizing each base kernel matrix. Based on this observation, the proposed localized SimpleMKKM can be readily implemented by existing SimpleMKKM package. Moreover, we conduct extensive experiments on several widely used benchmark datasets to evaluate the clustering performance of localized SimpleMKKM. The experimental results have demonstrated that our algorithm consistently outperforms the state-of-the-art ones, verifying the effectiveness of the proposed local kernel alignment criterion. The code of Localized SimpleMKKM is publicly available at: https://github.com/xinwangliu/LocalizedSMKKM.