Abstract
Studying the interaction between a system's components and the temporal evolution of the system are two common ways to uncover and characterize its internal workings. Recently, several maps from a time series to a network have been proposed with the intent of using network metrics to characterize time series. Although these maps demonstrate that different time series result in networks with distinct topological properties, it remains unclear how these topological properties relate to the original time series. Here, we propose a map from a time series to a network with an approximate inverse operation, making it possible to use network statistics to characterize time series and time series statistics to characterize networks. As a proof of concept, we generate an ensemble of time series ranging from periodic to random and confirm that application of the proposed map retains much of the information encoded in the original time series (or networks) after application of the map (or its inverse). Our results suggest that network analysis can be used to distinguish different dynamic regimes in time series and, perhaps more importantly, time series analysis can provide a powerful set of tools that augment the traditional network analysis toolkit to quantify networks in new and useful ways.
Highlights
In the context of dynamical systems, time series analysis is frequently used to identify the underlying nature of a phenomenon of interest from a sequence of observations and to forecast future outcomes
These techniques allow researchers to summarize the characteristics of a time series into compact metrics, which can be used to understand the dynamics or predict how the system will evolve with time
To verify the extent to which the properties of the original time series or network are recovered when MQT and M{ QT1 are applied sequentially, we introduce an ensemble of time series that range from periodic to random: 8 >< modðx(t{1)zdzg,1Þ, with probability p x(t)~>: modðx(t{1)zd,1Þ, otherwise ð2Þ
Summary
In the context of dynamical systems, time series analysis is frequently used to identify the underlying nature of a phenomenon of interest from a sequence of observations and to forecast future outcomes. One of the most interesting advances is mapping a time series into a network, based on different concepts such as correlations [11,12], visibility [13,14], recurrence analysis [15], transition probabilities [16,17,18] and phase-space reconstructions [19,20] (a complete list of all the proposed maps can be found in Donner et al,(2010) [21] and references therein) These studies have demonstrated that distinct features of a time series can be mapped onto networks with distinct topological properties. This finding suggests that it may be possible to differentiate properties of time series using network measures
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