Multiple Kernel Clustering with Shifted Laplacian on Grassmann Manifold

Multiple kernel clustering (MKC) has garnered considerable attention, as their efficacy in handling nonlinear data in high-dimensional space. However, current MKC methods have three primary issues: (1) Solely focuses on clustering information while neglecting energy information and potential noise interference within the kernel; (2) The inherent manifold structure in the high-dimensional space is complex, and they lack the insufficient exploration of topological structure; (3) Most encounter cubic computational complexity, posing a formidable resource consumption challenge. To tackle the above issues, we propose a novel MKC method with shifted Laplacian on Grassmann manifold (sLGm). Firstly, sLGm constructs r-rank shifted Laplacian and subsequently reconstructs it, retaining the clustering-related and energy-related information while reducing the influence of noise. Additionally, sLGm introduces a Grassmann manifold for information fusion, which can preserve topological information in the high-dimensional space. Notably, an optimal consensus partition can be concurrently learnt from above two procedures, thereby yielding the clustering assignments, and the computational complexity of the whole procedure drops to the quadratic. Conclusively, a comprehensive suite of experiments is executed to roundly prove the effectiveness of sLGm.