A generalized visibility graph algorithm for analyzing biological time series having rotation in polar plane

Abstract

Time series analysis is exploited when temporal measurements about a phenomenon exist. Visibility graphs are a method for representing and analyzing time series. One of the challenges biological time series introduce is rotation in polar plane. Rotation in polar plane is a change in the angle of the time series in polar plane. Rotation in the polar plane exists in any time series that has positive and negative observations together. In this research, a visibility graph algorithm is proposed which could efficiently handle biological time series which have rotation in polar plane. In the proposed algorithm, two observation in the time series are visible to each other in the graph, if the line connecting the points doesn't cross any other point placed between them. The proposed visibility graph algorithm has been evaluated with synthetic and real world time series. The generated visibility graphs are used to evaluate the proposed visibility graph algorithm with different metrics such as pearson autocorrelation and classification accuracy. The synthetic time series are generated by a bipolar feedback process. In one of the synthetic bios series with g = 10, the pearson autocorrelation of the graph is 0.9815 whereas the baseline is 0.9211. In the main experiment with real world time series, the proposed visibility graph algorithm is compared with the state of the art algorithm. The ANOVA test is performed on the results of 60 experiments. The p-value is smaller than 0.05, which states GVG has improved CLPVG significantly.