  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.
