Knowing who follows whom and what patterns they are following are crucial steps to understand collective behaviors (e.g. a group of human, a school of fish, or a stock market). Time series is one of resources that can be used to get insight regarding following relations. However, the concept of following patterns or motifs and the solution to find them in time series are not obvious. In this work, we formalize a concept of following motifs between two time series and present a framework to infer following patterns between two time series. The framework utilizes one of efficient and scalable methods to retrieve motifs from time series called the Matrix Profile Method. We compare our proposed framework with several baselines. The framework performs better than baselines in the simulation datasets. In the dataset of sound recording, the framework is able to retrieve the following motifs within a pair of time series that two singers sing following each other. In the cryptocurrency dataset, the framework is capable of capturing the following motifs within a pair of time series from two digital currencies, which implies that the values of one currency follow the values of another currency patterns. Our framework can be utilized in any field of time series to get insight regarding following patterns between time series.

翻译：理解谁跟随谁以及跟随何种模式是理解集体行为（例如人类群体、鱼群或股票市场）的关键步骤。时间序列是获取跟随关系洞察的资源之一，但跟随模式或基序的概念及其在时间序列中的发现方法尚不明确。本研究形式化了两个时间序列之间跟随基序的概念，并提出了一个推断两个时间序列之间跟随模式的框架。该框架利用名为矩阵轮廓法的高效可扩展方法来提取时间序列中的基序。我们将所提出的框架与多个基线方法进行比较，结果表明该框架在模拟数据集上优于基线方法。在录音数据集中，该框架能够从两名歌手交替演唱的时间序列对中提取跟随基序。在加密货币数据集中，该框架成功捕捉到两种数字货币时间序列对之间的跟随基序，表明一种货币的价值遵循另一种货币的价值模式。本框架可应用于任何领域的时间序列分析，以揭示时间序列间的跟随模式。