Optimal neighborhood kernel clustering with adaptive local kernels and block diagonal property

The purpose of multiple kernel clustering (MKC) is usually to generate an optimal kernel by fusing the information of multiple base kernels. Among the methods of generating the optimal kernel, a neighborhood kernel is usually used to enlarge the search range of the optimal kernel, or local base kernels are selected to avoid the redundancy of base kernels. However, few studies combine both methods simultaneously; then, the quality of the optimal kernel cannot be improved very well. Furthermore, most MKC methods require two-step strategy to cluster, that is, first generate clustering indicator matrix, and then execute clustering. This does not guarantee that the final clustering results are optimal. In order to overcome the above drawbacks, an optimal neighborhood kernel clustering with adaptive local kernel and block diagonal property (ONKC-ALK-BD) is proposed in this paper. In our proposed method, a simple weight strategy of selecting local base kernels is used to produce a consensus kernel, a neighborhood kernel of which is chosen as the optimal kernel. And a block diagonal (BD) regularizer imposed on the clustering indicator matrix encourages the matrix to be BD. On one hand, our proposed method avoids the redundancy of base kernels and ensures the diversity of selected base kernels. On the other hand, it expands the search range of the optimal kernel and improves its representation ability. Thus, the quality of the optimal kernel is enhanced. In addition, the BD property of the indicator matrix is helpful to obtain explicit clustering indicators and achieve one-step clustering, which ensures that the final results of our method are optimal for the original problem. Finally, extensive experiments on twelve data sets and comparisons with seven clustering methods show that ONKC-ALK-BD is effective.