A Robust Clustering Algorithm Based on Aggregated Heat Kernel Mapping

Current spectral clustering algorithms suffer from both sensitivity to scaling parameter selection in similarity matrix construction, and data perturbation. This paper aims to improve robustness in clustering algorithms and combat these two limitations based on heat kernel theory. Heat kernel can statistically depict traces of random walk, so it has an intrinsic connection with diffusion distance, with which we can ensure robustness during any clustering process. By integrating heat distributed along time scale, we propose a novel method called Aggregated Heat Kernel (AHK) to measure the distance between each point pair in their eigen space. Using AHK and Laplace-Beltrami Normalization (LBN) we are able to apply an advanced noise-resisting robust spectral mapping to original dataset. Moreover it offers stability on scaling parameter tuning. Experimental results show that, compared to other popular spectral clustering methods, our algorithm can achieve robust clustering results on both synthetic and UCI real datasets.