Leadership and followership are essential parts of collective decision and organization in social animals, including humans. In nature, relationships of leaders and followers are dynamic and vary with context or temporal factors. Understanding dynamics of leadership and followership, such as how leaders and followers change, emerge, or converge, allows scientists to gain more insight into group decision-making and collective behavior in general. However, given only data of individual activities, it is challenging to infer the dynamics of leaders and followers. In this paper, we focus on mining and modeling frequent patterns of leading and following. We formalize new computational problems and propose a framework that can be used to address several questions regarding group movement. We use the leadership inference framework, mFLICA, to infer the time series of leaders and their factions from movement datasets and then propose an approach to mine and model frequent patterns of both leadership and followership dynamics. We evaluate our framework performance by using several simulated datasets, as well as the real-world dataset of baboon movement to demonstrate the applications of our framework. These are novel computational problems and, to the best of our knowledge, there are no existing comparable methods to address them. Thus, we modify and extend an existing leadership inference framework to provide a non-trivial baseline for comparison. Our framework performs better than this baseline in all datasets. Our framework opens the opportunities for scientists to generate testable scientific hypotheses about the dynamics of leadership in movement data.
Granger causality is a fundamental technique for causal inference in time series data, commonly used in the social and biological sciences. Typical operationalizations of Granger causality make a strong assumption that every time point of the effect time series is influenced by a combination of other time series with a fixed time delay. The assumption of fixed time delay also exists in Transfer Entropy, which is considered to be a non-linear version of Granger causality. However, the assumption of the fixed time delay does not hold in many applications, such as collective behavior, financial markets, and many natural phenomena. To address this issue, we develop Variable-lag Granger causality and Variable-lag Transfer Entropy, generalizations of both Granger causality and Transfer Entropy that relax the assumption of the fixed time delay and allow causes to influence effects with arbitrary time delays. In addition, we propose methods for inferring both variable-lag Granger causality and Transfer Entropy relations. In our approaches, we utilize an optimal warping path of Dynamic Time Warping (DTW) to infer variable-lag causal relations. We demonstrate our approaches on an application for studying coordinated collective behavior and other real-world casual-inference datasets and show that our proposed approaches perform better than several existing methods in both simulated and real-world datasets. Our approaches can be applied in any domain of time series analysis. The software of this work is available in the R-CRAN package: VLTimeCausality.
Granger causality is a fundamental technique for causal inference in time series data, commonly used in the social and biological sciences. Typical operationalizations of Granger causality make a strong assumption that every time point of the effect time series is influenced by a combination of other time series with a fixed time delay. However, the assumption of the fixed time delay does not hold in many applications, such as collective behavior, financial markets, and many natural phenomena. To address this issue, we develop variable-lag Granger causality, a generalization of Granger causality that relaxes the assumption of the fixed time delay and allows causes to influence effects with arbitrary time delays. In addition, we propose a method for inferring variable-lag Granger causality relations. We demonstrate our approach on an application for studying coordinated collective behavior and show that it performs better than several existing methods in both simulated and real-world datasets. Our approach can be applied in any domain of time series analysis.
How do groups of individuals achieve consensus in movement decisions? Do individuals follow their friends, the one predetermined leader, or whomever just happens to be nearby? To address these questions computationally, we formalize "Coordination Strategy Inference Problem". In this setting, a group of multiple individuals moves in a coordinated manner towards a target path. Each individual uses a specific strategy to follow others (e.g. nearest neighbors, pre-defined leaders, preferred friends). Given a set of time series that includes coordinated movement and a set of candidate strategies as inputs, we provide the first methodology (to the best of our knowledge) to infer whether each individual uses local-agreement-system or dictatorship-like strategy to achieve movement coordination at the group level. We evaluate and demonstrate the performance of the proposed framework by predicting the direction of movement of an individual in a group in both simulated datasets as well as two real-world datasets: a school of fish and a troop of baboons. Moreover, since there is no prior methodology for inferring individual-level strategies, we compare our framework with the state-of-the-art approach for the task of classification of group-level-coordination models. The results show that our approach is highly accurate in inferring the correct strategy in simulated datasets even in complicated mixed strategy settings, which no existing method can infer. In the task of classification of group-level-coordination models, our framework performs better than the state-of-the-art approach in all datasets. Animal data experiments show that fish, as expected, follow their neighbors, while baboons have a preference to follow specific individuals. Our methodology generalizes to arbitrary time series data of real numbers, beyond movement data.
Behavior initiation is a form of leadership and is an important aspect of social organization that affects the processes of group formation, dynamics, and decision-making in human societies and other social animal species. In this work, we formalize the "Coordination Initiator Inference Problem" and propose a simple yet powerful framework for extracting periods of coordinated activity and determining individuals who initiated this coordination, based solely on the activity of individuals within a group during those periods. The proposed approach, given arbitrary individual time series, automatically (1) identifies times of coordinated group activity, (2) determines the identities of initiators of those activities, and (3) classifies the likely mechanism by which the group coordination occurred, all of which are novel computational tasks. We demonstrate our framework on both simulated and real-world data: trajectories tracking of animals as well as stock market data. Our method is competitive with existing global leadership inference methods but provides the first approaches for local leadership and coordination mechanism classification. Our results are consistent with ground-truthed biological data and the framework finds many known events in financial data which are not otherwise reflected in the aggregate NASDAQ index. Our method is easily generalizable to any coordinated time-series data from interacting entities.