Heat kernel coupling for multiple graph analysis
This addresses a challenge in graph analysis for researchers in machine learning and pattern recognition, though it appears incremental as it builds on existing spectral methods.
The paper tackles the problem of analyzing multiple graphs of different sizes without requiring vertex-wise correspondence by introducing heat kernel coupling (HKC) as a method for constructing multimodal spectral geometry. It demonstrates that Laplacian averaging is a limit case of HKC and applies it to problems in manifold learning and pattern recognition.
In this paper, we introduce heat kernel coupling (HKC) as a method of constructing multimodal spectral geometry on weighted graphs of different size without vertex-wise bijective correspondence. We show that Laplacian averaging can be derived as a limit case of HKC, and demonstrate its applications on several problems from the manifold learning and pattern recognition domain.