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 C oordination I nitiator I nference P roblem 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.

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.

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 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.

Given a dataset of careers and incomes, how large a difference of incomes between any pair of careers would be? Given a dataset of travel time records, how long do we need to spend more when choosing a public transportation mode A instead of B to travel? In this paper, we propose a framework that is able to infer orders of categories as well as magnitudes of difference of real numbers between each pair of categories using an estimation statistics framework. Our framework not only reports whether an order of categories exists, but it also reports magnitudes of difference of each consecutive pair of categories in the order. In a large dataset, our framework is scalable well compared with existing frameworks. The proposed framework has been applied to two real-world case studies: 1) ordering careers by incomes from 350,000 households living in Khon Kaen province, Thailand, and 2) ordering sectors by closing prices from 1,060 companies in NASDAQ stock market between years 2000 and 2016. The results of careers ordering demonstrate income inequality among different careers. The stock market results illustrate dynamics of sector domination that can change over time. Our approach is able to be applied in any research area that has category-real pairs. Our proposed Dominant-Distribution Network provides a novel approach to gain new insight of analyzing category orders. A software of this framework is available for researchers or practitioners in an R CRAN package: EDOIF.

Understanding genetic differences among populations is one of the most important issues in population genetics. Genetic variations, e.g., single nucleotide polymorphisms, are used to characterize commonality and difference of individuals from various populations. This paper presents an efficient graph-based clustering framework which operates iteratively on the Neighbor-Joining (NJ) tree called the iNJclust algorithm. The framework uses well-known genetic measurements, namely the allele-sharing distance, the neighbor-joining tree, and the fixation index. The behavior of the fixation index is utilized in the algorithm's stopping criterion. The algorithm provides an estimated number of populations, individual assignments, and relationships between populations as outputs. The clustering result is reported in the form of a binary tree, whose terminal nodes represent the final inferred populations and the tree structure preserves the genetic relationships among them. The clustering performance and the robustness of the proposed algorithm are tested extensively using simulated and real data sets from bovine, sheep, and human populations. The result indicates that the number of populations within each data set is reasonably estimated, the individual assignment is robust, and the structure of the inferred population tree corresponds to the intrinsic relationships among populations within the data.