Analysing the Dynamics of Interbeat Interval Time Series Using Grouped Horizontal Visibility Graph

Abstract

Horizontal visibility graph (HVG) motifs have been recently introduced to analyze the dynamical information encoded by biological signals. However, the result of the analysis strongly depends on the selected window size of the motifs. Different sizes ranging from 3 to 5 have been previously used, but such small window sizes are insufficient to cope with the complexity of biological systems and often fail to extract salient features of the encoded information. It is known that larger window size increases the total number of possible motifs, and it leads to the distribution of the statistics into too many motifs, which causes each individual motif to contain too little information and make it even more difficult to reliably detect system dynamics. To resolve this problem, we group the motifs based on the number of edges. Using the grouped motifs, we propose grouped horizontal visibility entropy (GHVE) to quantify the complexity based on the probability distribution of the observations within these groups. We apply GHVE to quantify the complexity of simulated white and 1/f noise. The results reveal that the 1/f noise time series exhibits a higher complexity than white noise time series, which indicates that the 1/f noise is structurally more complex than white Gaussian noise. We apply the method for analyzing interbeat intervals time series. The results show that the proposed GHVE measure is more accurate in distinguishing healthy and pathological subjects than its non-grouped counterpart HVG. It is, therefore, better suited to detect changes in aging, disease severity, and activity levels (sleep and wake period). INDEX TERMS Complex network, HVG motifs, HRV analysis, time series data.

Classification of Interbeat Interval Time-Series Using Attention Entropy

“…[33] Sample [34] Bub. [35] HVE [36] GHVE [22] SVDE [38] EPE [32] Spe. [27] Ave. [28] MSE [21] Attention 100 <1 <1 <1 59 68 50 78 85 91 206 1 41 <1 <1 <1 1000 3 5 5 60 74 53 7714 8763 253 206 5 42 5 2 2 10000 36 77 75 67 254 237 795821 885471 1935 223 523 43 44 160 16 100000 636 1328 1374 133 7599 8236 >1h >1h 19019 229 5001 106 448 16404 166…”

“…Bubble entropy [35] and GHVE [22] are not sensitive to the parameter settings. However, they have high computational costs, and therefore, they are not practical for largescale data [35], [36].…”

“…Grouped horizontal visibility [22] Grouped visibility graph SVDE [38] Delay vector Singular values Edge permutation [32] Permutation Spectral [27] YES Single value Single value Average [28] Multiscale [21] Template vector [30], spectral entropy [27], and average entropy [28] use the values directly. Permutation entropy [31] and edge permutation entropy (EPE) [32] use the permutations of the rankings of each value in the template vectors as the patterns.…”

“…Bubble entropy [35] uses the swaps of sorting sub-series with bubble sort algorithm as the patterns. Horizontal visibility entropy (HVE) [36] uses visibility graphs [37] and GHVE [22] uses grouped visibility graphs as the patterns. The singular value decomposition entropy (SVDE) [38] uses the singular values obtained by performing singular value decomposition on the embedding space spanned by the delay vectors as the patterns.…”

“…There also has been considerable interest in quantifying the complexity of HRV to uncover hidden information, such as heart failures [17], [18], [19] and coronary artery disease [20]. Typical methods such as multiscale entropy (MSE) [21] and grouped horizontal visibility graph entropy (GHVE) [22] analyze complexity by segmenting the signals into equal-length sub-series and calculating the entropy based on how frequently the artificial patterns occur extracted from the sub-series. The process of a typical method is illustrated in Fig.…”