Noise resistance ability analysis of the visibility graph and the limited penetrable visibility graph

Noises exist in many measured systems inevitably. Therefore, noise resistance ability analysis is of great importance to accurately evaluate the performance of information analysis methods. In this paper, we systematically test the noise resistance ability of visibility graph (VG) and its generalization, i.e., limited penetrable visibility graph (LPVG). Taking the Lorenz system as the example, we first generate two groups of chaotic time series using different parameter settings. One group signals contain slight mutation components and another group contains severe mutation components. Then, noises of different intensity levels are added into the original signals. Next, we calculate the network characteristics (i.e., clustering coefficient (CC) and network information entropy (NIE)) of original signals and noised signals using the VG and LPVG (visibility distances N=1, 2) respectively. The network characteristics for noised signals are compared with those of original signals. We find that for the analysis of signals that contain slight mutation components, the LPVG significantly outperforms the traditional VG method, while for the analysis of signals with severe mutation components, minor differences of noise resistance ability are observed for VG and LPVG. Moreover, visibility distance only affects the noise resistance performance of the LPVG when analyzing the signals with slight mutation components. This work provides a valuable guide to use the VG and LPVG.