Multiple Kernel Clustering with Shifted Laplacian on Grassmann Manifold
Abstract: 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 focuse 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 partition 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.
Primary Subject Area: [Experience] Multimedia Applications
Secondary Subject Area: [Content] Multimodal Fusion
Relevance To Conference: In the domain of multimodal processing, it is widely acknowledged that data often encapsulates diverse information emanating from various sources or sensors. Our work endeavors to integrate these multimodal data and effectively deal with such complex and possibly nonlinear multimodal data. Specifically, our work first constructs the graph shifted Laplacian, which can explore clustering-related information, energy-related information and effectively circumvent noise effects during multimodal processing. In addition, our work introduces a Grassmann manifold, which can help explore topological structures within high-dimensional feature space in multimodal processing. Notably, our work boasts a low time complexity, rendering it highly advantageous for medium- and large-scale multimodal processing tasks. Taken together, this work provides the important theoretical basis and practical tools for the comprehensive analysis and application of multimodal processing, effectively promoting the progress in this field.
Submission Number: 3225
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