Multiple kernel k-means clustering with block diagonal property

Multiple kernel k-means clustering (MKKC) is proposed to efficiently incorporate multiple base kernels to generate an optimal kernel. However, many existing MKKC methods all involve two stages: learning a clustering indicator matrix and performing clustering on it. This cannot ensure the ultimate clustering results are optimal because the optimal values of two steps are not equivalent to those of the original problem. To address this issue, in this paper, we propose a novel method named multiple kernel k-means clustering with block diagonal property (MKKC-BD). It is the first time to find the relationship between an indicator matrix and Laplacian matrix of the graph theory and get a block diagonal (BD) representation of the indicator matrix. By imposing the BD constraint on the indicator matrix, the BD property of the indicator matrix is ensured. Further, the explicit clustering results are generated directly from the unified framework integrating the three processes of learning an optimal kernel, an indicator matrix and clustering results, which shows the clustering task is executed just by one step. In addition, a simple kernel weight strategy is used in this framework to obtain the optimal kernel, where the value of each kernel weight directly reveals the relationship of each base kernel and the optimal kernel. Finally, by extensive experiments on ten data sets and comparison of clustering results with eight state-of-the-art multiple kernel clustering methods, it is concluded that MKKC-BD is effective. Our code is available at https://​github.​com/​mathchen-git/​MKKC-BD.