Subspace segmentation-based robust multiple kernel clustering

摘要

Multiple kernel clustering (MKC) is an important research topic during the last few decades. It optimally combines a group of pre-specified base kernels to improve clustering performance. Though demonstrating promising performance in various applications, this task is still challenging due to lack of reliable discriminative guidance for the base kernel combination. Moreover, noise from either corrupted data or inappropriately selected base kernel parameters would undermine the intrinsic manifold and makes the problem even harder. In this paper, we integrate subspace segmentation into MKC and propose a robust subspace segmentation-based multiple kernel clustering (SS-MKC) algorithm to address these issues. In our formulation, we unify the constrained kernel polarization and subspace segmentation into a single procedure, where the resultant affinity matrix embedded with robust subspace structural information is utilized to guide the linear combination of base kernels. In addition, we carefully design the noise representation matrix as well as two sparse constraints, i.e., the l(1)-norm and the probability constraints, to eliminate the adverse effect of noise among base kernels. We then propose a novel Alternative Direction Method of Multiplier (ADMM)-based algorithm to solve the resulting optimization problem. Extensive experiments have been conducted on both synthetic and public benchmark datasets, and the results well demonstrate the superiority of the proposed algorithm when compared with the state-of-the-art MKC methods.