A Rational Graph Filtering Method for the Implementation of Heat Kernel Smoothing

In this paper, a decentralized implementation of heat kernel smoothing (HKS) is presented by using a rational graph filtering method. First, the basics of graph signal processing (GSP) are briefly described. Then, the centralized implementation of HKS using matrix exponential is studied. Next, the Taylor series expansion of exponential function and Prony method are applied to determine the filter coefficients of a rational graph filter. Because only linear equations need to be solved, the proposed design method is easy to be used. Finally, the performance of the proposed HKS method is evaluated by using the irregular data captured from the sensor network.