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To cluster data that are not linearly separable in the original featurespace, $k$-means clustering was extended to the kernel version. However, theperformance of kernel $k$-means clustering largely depends on the choice ofkernel function. To mitigate this problem, multiple kernel learning has beenintroduced into the $k$-means clustering to obtain an optimal kernelcombination for clustering. Despite the success of multiple kernel $k$-meansclustering in various scenarios, few of the existing work update thecombination coefficients based on the diversity of kernels, which leads to theresult that the selected kernels contain high redundancy and would degrade theclustering performance and efficiency. In this paper, we propose a simple butefficient strategy that selects a diverse subset from the pre-specified kernelsas the representative kernels, and then incorporate the subset selectionprocess into the framework of multiple $k$-means clustering. The representativekernels can be indicated as the significant combination weights. Due to thenon-convexity of the obtained objective function, we develop an alternatingminimization method to optimize the combination coefficients of the selectedkernels and the cluster membership alternatively. We evaluate the proposedapproach on several benchmark and real-world datasets. The experimental resultsdemonstrate the competitiveness of our approach in comparison with thestate-of-the-art methods.

Multiple Kernel $k$-Means Clustering by Selecting Representative Kernels