CLPVG: Circular limited penetrable visibility graph as a new network model for time series

Abstract

A visibility graph transforms time series into graphs, facilitating signal processing by advanced graph data mining algorithms. In this paper, based on the classic limited penetrable visibility graph method, we propose a novel mapping method named circular limited penetrable visibility graph, which replaces the linear visibility line in limited penetrable visibility graph with nonlinear visibility arc for pursuing more flexible and reasonable mapping of time series. Tests on degree distribution and some common network features of the generated graphs from typical time series demonstrate that our circular limited penetrable visibility graph can effectively capture the important features of time series and show higher robust classification performance than the traditional limited penetrable visibility graph in the presence of noise. The experiments on real-world time-series datasets of radio and electroencephalogram signals also suggest that the structural features provided by a circular limited penetrable visibility graph, rather than a limited penetrable visibility graph, are more useful for time-series classification, leading to higher accuracy. This classification performance can be further enhanced through structural feature expansion by adopting subgraph networks. All of these results demonstrate the effectiveness of our circular limited penetrable visibility graph model.

A Review of Visibility Graph Analysis

“…This category has been extensively explored by articles that employed visibility graph analysis to improve diverse time series in order to generate optimal outputs. For instance, visibility graph analysis has been employed to analyze the complexity of multivariate time series [54], classify time series [55], provide novel solutions for time series prediction [56], estimating the time interval between a pair of time series in practical applications [57], presenting a new solution for building a weighted complex network from time series [58], data ensuring safe use and more optimal than the memory space without reducing the speed [59], providing a new version of the limited penetrable visibility graph to better depict the important features of time series and its high anti-noise capability [60], measuring the action and nonlinear reactions have been used in non-stationary time series [61], multi-scale network analysis [62] etc., which are part of all the applications that we examined .…”

A symmetric adaptive visibility graph classification method of orthogonal signals for automatic modulation classification

“…Currently, Xuan et al [36,37] explore two visibility graph classification methods suitable for modulated I/Q signal graph analysis. The circle system was first introduced in [36]; the circular limited penetration visibility graph (CLPVG) was proposed, and the graph embedding technique was used to obtain higher recognition accuracy than the LPVG method on the radio modulation classification benchmark dataset.…”

“…Currently, Xuan et al [36,37] explore two visibility graph classification methods suitable for modulated I/Q signal graph analysis. The circle system was first introduced in [36]; the circular limited penetration visibility graph (CLPVG) was proposed, and the graph embedding technique was used to obtain higher recognition accuracy than the LPVG method on the radio modulation classification benchmark dataset. An adaptive visibility graph (AVG) method was proposed in [37], where AVG reconstructs the weighted adjacency matrix of the signal features using convolution as the sequential feature extractor and uses the GNN model DiffPool as the classifier to identify the modulation type.…”

Generalized limited penetrable vector visibility graph

“…Markov binary visibility graph is introduced for the binary data [34]. Our group proposed the limited penetrable visibility graph, renowned for its robustness against noise [35][36][37]. Based on this premise, a circular limited penetrable visibility graph has been developed [36].…”

“…Our group proposed the limited penetrable visibility graph, renowned for its robustness against noise [35][36][37]. Based on this premise, a circular limited penetrable visibility graph has been developed [36]. This graph replaces the linear visibility line with a nonlinear visibility arc to achieve a more flexible and reasonable mapping of time series.…”