Framework for Inferring Leadership Dynamics of Complex Movement from Time Series

Abstract

Leadership plays a key role in social animals, including humans, decision-making and coalescence in coordinated activities such as hunting, migration, sport, diplomatic negotiation etc. In these coordinated activities, leadership is a process that organizes interactions among members to make a group achieve collective goals. Understanding initiation of coordinated activities allows scientists to gain more insight into social species behaviors. However, by using only time series of activities data, inferring leadership as manifested by the initiation of coordinated activities faces many challenging issues. First, coordinated activities are dynamic and are changing over time. Second, several different coordinated activities might occur simultaneously among subgroups. Third, there is no fundamental concept to describe these activities computationally. In this paper, we formalize Faction Initiator Inference Problem and propose a leadership inference framework as a solution of this problem. The framework makes no assumption about the characteristics of a leader or the parameters of the coordination process. The framework performs better than our non-trivial baseline in both simulated and biological datasets (schools of fish). Moreover, we demonstrate the application of our framework as a tool to study group merging and splitting dynamics on another biological dataset of trajectories of wild baboons. In addition, our problem formalization and framework enable opportunities for scientists to analyze coordinated activities and generate scientific hypotheses about collective behaviors that can be tested statistically and in the field.

Mining and modeling complex leadership–followership dynamics of movement data

“…To address these computational questions, in the previous paper in Amornbunchornvej and Berger-Wolf (2018b), we formalize the problem of Mining Patterns of Leadership Dynamics, as well as propose a framework, which is the extension of mFLICA Amornbunchornvej and Berger-Wolf (2018a), as a solution to this problem. We adapt the traditional framework of frequent pattern mining Aggarwal and Han (2014);Agrawal et al (1993); Han et al (2007) and the Hidden Markov Model (HMM) approach Rabiner (1989) to model the dynamics of frequent patterns of leadership.…”

“…In this paper, we use leadership definitions from the work in Amornbunchornvej and Berger-Wolf (2018a). Given a D-dimensional time series Q, we use Q(t) to refer to an element of the time series Q at time t and, for a given ∆ ∈ Z, Q ∆ as a time-shifted version of Q where, Q(t) = Q ∆ (t + ∆).…”

“…We can use mFLICA framework Amornbunchornvej and Berger-Wolf (2018a) to extract a time series of leaders from time series of movement. Next, we define the support of a leader set S. Let T be the length of the time series of leaders and 1 x be an indicator function, which is 1 if the statement x is true, and 0 otherwise.…”

“…4.2.1 Type 1 Dynamics: Splitting/Merging coordination event Amornbunchornvej and Berger-Wolf (2018a) In this type of coordination event (Fig. 3 above), ID1 leads the entire group for 200 time steps.…”

“…However, only the state-of-the-art approach, mFLICA Amornbunchornvej and Berger-Wolf (2018a), is capable of inferring dynamics of leadership -i.e. emergence, convergence, or a change of leaders -during coordinated movement.…”