Distributed Computation of Heat Kernel Smoothing Using Series Expansion Method
Chien‐Cheng Tseng, Su‐Ling Lee · 2023
Heat kernel smoothing (HKS) is one of important methods to reduce noise corrupted in the irregular data collected from various complex network. In this paper, the distributed computation of HKS method using series expansion is studied. First, the relation between HKS computation and matrix exponential is presented and the centralized computation of HKS method is derived. Then, two series expansion methods are used to implement the HKS operator in a distributed manner. They include Taylor series expansion (TSE) and Laguerre series expansion (LSE). The TSE method corresponds to a maximally-flat graph filter method, and LSE method corresponds to the weighted-least-squares graph filter method. Next, the realization structures of two series expansion methods are described by choosing the Laplacian matrix as graph shift operator. Finally, the denoising experiments of data collected from sensor network and social network are used to demonstrate the effectiveness of HKS methods in terms of the improvement of signal to noise ratio.