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什么模式是理解集体行为（例如人群、鱼群或股票市场）的关键步骤。时序数据是揭示跟随关系的资源之一，但跟随模式或跟随基序的概念及其在时序中的发现方法尚不明确。本文形式化了两条时序间跟随基序的概念，并提出了一个推断两条时序间跟随模式的框架。该框架采用高效且可扩展的时序基序提取方法——矩阵概貌法。我们将所提框架与多个基线进行对比，在仿真数据集中框架性能优于基线。在录音数据集中，该框架能够从两位歌手交替演唱的成对时序中提取跟随基序。在加密货币数据集中，框架成功捕捉两种数字货币成对时序间的跟随基序，表明一种货币的价值跟随另一种货币的模式。本框架可应用于任意时序领域，以揭示时序间的跟随模式。