Simultaneous Global and Local Graph Structure Preserving for Multiple Kernel Clustering

Multiple kernel learning (MKL) is generally recognized to perform better than single kernel learning (SKL) in handling nonlinear clustering problem, largely thanks to MKL avoids selecting and tuning predefined kernel. By integrating the self-expression learning framework, the graph-based MKL subspace clustering has recently attracted considerable attention. However, the graph structure of data in kernel space is largely ignored by previous MKL methods, which is a key concept of affinity graph construction for spectral clustering purposes. In order to address this problem, a novel MKL method is proposed in this article, namely, structure-preserving multiple kernel clustering (SPMKC). Specifically, SPMKC proposes a new kernel affine weight strategy to learn an optimal consensus kernel from a predefined kernel pool, which can assign a suitable weight for each base kernel automatically. Furthermore, SPMKC proposes a kernel group self-expressiveness term and a kernel adaptive local structure learning term to preserve the global and local structure of the input data in kernel space, respectively, rather than the original space. In addition, an efficient algorithm is proposed to solve the resulting unified objective function, which iteratively updates the consensus kernel and the affinity graph so that collaboratively promoting each of them to reach the optimum condition. Experiments on both image and text clustering demonstrate that SPMKC outperforms the state-of-the-art MKL clustering methods in terms of clustering performance and computational cost.