Grouped Horizontal Visibility Graph Entropy (GHVE)

Horizontal visibility graph belongs to the family of visibility network that are utilized in robotics, network communication and fluid dynamics. We used the horizontal visibility graph based approach to develop a predictive models, and apply information theoretic measures to predict disease onset in cardiovascular patients. It computes the probability of each motif type from horizontal visibility graph, and the probability of occurrence of each group of motifs (have the same number of edges) and Shannon entrop as a measure of the uncertanity among these groups. This approach is useful to apply physiological signals (e.g. RR-intervals extracted from electrocardiogram) higher entropy value represents the healthy people and lower entropy value shows the higher level of stress(sick, multimorbid and irregularities in autonomic nervouse system activity).

Example 1: Calculate Grouped Horizontal Visibility Graph Entropy

//Sample RR-intervals
List<Double> list =  Arrays.asList(0.695,0.711,0.711,0.703,0.711,0.68,0.695,0.664,0.688,0.656,0.672,0.68,0.711,0.703,0.727);
int window = 5;
//Horizontal visibility graph class
HVG hvg = new HVG(window);

//Visibility information
hvg.HorrVisibility(list);

//count motifs by their edges
Hashtable<String, Integer> motif = hvg.countMotif();

//Motifs found are
System.out.println("Motifs found in data : ");
System.out.println(motif.toString());
		
//Grouped horizontal visibility graph entropy
double ghe = hvg.shannonEntropy(motif, list.size()-window+1);

//print the hvg graph source to destination list
System.out.println("Entropy value is : "+ghe);

//degree distribution statistics
System.out.println(hvg.countDegree());

Output

Motifs found in data : 
{[]=1, [14, 15]=1, [14]=3, [26]=2, [1, 2, 3]=1, [1, 26]=3}
Entropy value is : 2.413088436425758
{8=1, 7=1, 6=3, 5=2, 4=3, 3=1}

Reference

If you are using this code then site the following paper.
Choudhary, G. I., Aziz, W., Khan, I. R., Rahardja, S., & Fränti, P. (2019). Analysing the Dynamics of Interbeat Interval Time Series Using Grouped Horizontal Visibility Graph. IEEE Access, 7, 9926–9934.

License

MIT