Sun Xiaoran, Small Michael, Zhao Yi, Xue Xiaoping
Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, People's Republic of China.
School of Mathematics and Statistics, The University of Western Australia, Crawley WA 6009, Australia.
Chaos. 2014 Jun;24(2):024402. doi: 10.1063/1.4868261.
In this work, we propose a novel method to transform a time series into a weighted and directed network. For a given time series, we first generate a set of segments via a sliding window, and then use a doubly symbolic scheme to characterize every windowed segment by combining absolute amplitude information with an ordinal pattern characterization. Based on this construction, a network can be directly constructed from the given time series: segments corresponding to different symbol-pairs are mapped to network nodes and the temporal succession between nodes is represented by directed links. With this conversion, dynamics underlying the time series has been encoded into the network structure. We illustrate the potential of our networks with a well-studied dynamical model as a benchmark example. Results show that network measures for characterizing global properties can detect the dynamical transitions in the underlying system. Moreover, we employ a random walk algorithm to sample loops in our networks, and find that time series with different dynamics exhibits distinct cycle structure. That is, the relative prevalence of loops with different lengths can be used to identify the underlying dynamics.
在这项工作中，我们提出了一种将时间序列转换为加权有向网络的新方法。对于给定的时间序列，我们首先通过滑动窗口生成一组片段，然后使用双重符号方案，通过将绝对幅度信息与顺序模式特征相结合来表征每个加窗片段。基于此构建，可以直接从给定的时间序列构建网络：对应于不同符号对的片段被映射到网络节点，节点之间的时间顺序由有向链接表示。通过这种转换，时间序列背后的动态特性已被编码到网络结构中。我们以一个经过充分研究的动态模型作为基准示例来说明我们网络的潜力。结果表明，用于表征全局特性的网络度量可以检测基础系统中的动态转变。此外，我们采用随机游走算法在我们的网络中对环进行采样，发现具有不同动态特性的时间序列表现出不同的循环结构。也就是说，不同长度环的相对发生率可用于识别基础动态特性。
