  To cluster data that are not linearly separable in the original feature
space, $k$-means clustering was extended to the kernel version. However, the
performance of kernel $k$-means clustering largely depends on the choice of
kernel function. To mitigate this problem, multiple kernel learning has been
introduced into the $k$-means clustering to obtain an optimal kernel
combination for clustering. Despite the success of multiple kernel $k$-means
clustering in various scenarios, few of the existing work update the
combination coefficients based on the diversity of kernels, which leads to the
result that the selected kernels contain high redundancy and would degrade the
clustering performance and efficiency. In this paper, we propose a simple but
efficient strategy that selects a diverse subset from the pre-specified kernels
as the representative kernels, and then incorporate the subset selection
process into the framework of multiple $k$-means clustering. The representative
kernels can be indicated as the significant combination weights. Due to the
non-convexity of the obtained objective function, we develop an alternating
minimization method to optimize the combination coefficients of the selected
kernels and the cluster membership alternatively. We evaluate the proposed
approach on several benchmark and real-world datasets. The experimental results
demonstrate the competitiveness of our approach in comparison with the
state-of-the-art methods.
