Laboratory for Computing and Applied Mathematics, Instituto Nacional de Pesquisas Espaciais, São José dos Campos, São Paulo, Brazil.
PLoS One. 2011;6(8):e23378. doi: 10.1371/journal.pone.0023378. Epub 2011 Aug 11.
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.
研究系统组件之间的相互作用和系统的时间演化是揭示和描述其内部工作机制的两种常见方法。最近，已经提出了几种从时间序列到网络的映射方法，旨在使用网络度量来描述时间序列。尽管这些映射表明不同的时间序列导致具有不同拓扑性质的网络，但仍然不清楚这些拓扑性质如何与原始时间序列相关联。在这里，我们提出了一种从时间序列到网络的映射方法，该方法具有近似逆运算，使得可以使用网络统计数据来描述时间序列，并且可以使用时间序列统计数据来描述网络。作为概念验证，我们生成了一系列从周期性到随机性的时间序列，并证实了所提出的映射的应用保留了在映射（或其逆）应用之后原始时间序列（或网络）中编码的大部分信息。我们的结果表明，网络分析可用于区分时间序列中的不同动态状态，也许更重要的是，时间序列分析可以提供一组强大的工具，这些工具扩展了传统的网络分析工具包，以新的有用方式量化网络。
