Frequency - Degree Mapping Algorithm And Its Application In ECG Time Series Analysis

Recently, a bridge between time series analysis and complex networks study has emerged by defining the nodes and edges of complex networks based on the intrinsic information of a give time series. On the one hand, the methods provide traditional time series analysis with a novel network viewpoint and various network measurements; on the other hand, they also offer another choice for constructing complex network directly from time series thus expanding the application of complex networks theory.At present, the transformation algorithms from time series to complex networks are still in their infancy in both theory and application. These approaches can be roughly divided into three classes:proximity networks, transition networks and visibility graphs. In general, these methods have advantages and disadvantages in different aspects due to their different focuses. For example, the ideas of constructing networks are natural and explicit in both proximity networks and transition networks including various types of transformation algorithms. At the same time, visibility graph has been applied in more fields due to its simplicity.We proposed a frequency-degree mapping algorithm based on the previous works, which not only possesses the reasonable explanation of proximity networks in theory but also reserves the simplicity of visibility graph in practice. The basic idea is mapping the recurrence frequency of time series into the degree value of the nodes in the corresponding networks by defining recurrence edges, while characterizing the temporal properties of time series through the definition of temporal edges. The results of random time series and periodic time series demonstrate that the frequency-degree mapping algorithm is able to reserve both temporal and amplitude information at the same time.Then we also investigate the application of the frequency-degree mapping algorithm in electrocardiogram time series analysis. We find that the method can distinguish normal sinus rhythms, ventricular fibrillation and monomorphic ventricular tachycardia by using both the measurements of average degree and average path length of the corresponding networks. In a more general condition, the average degree can serve as an effective indicator in distinguishing malignant ventricular arrhythmias from normal sinus rhythms and other arrhythmias. Meanwhile, the average path length is shown to be capable of characterizing the heart rate, which is helpful in the detection of low rate ventricular tachycardia.