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 the 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 the efficient and scalable methods to retrieve motifs from time series called the Matrix Profile Inference 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 in which 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. The code and datasets can be found at https://github.com/hughnaaek/Following-Motif-Relation .

One shirt size cannot fit everybody, while we cannot make a unique shirt that fits perfectly for everyone because of resource limitations. This analogy is true for policy making as well. Policy makers cannot make a single policy to solve all problems for all regions because each region has its own unique issue. At the other extreme, policy makers also cannot make a policy for each small village due to resource limitations. Would it be better if we can find a set of largest regions such that the population of each region within this set has common issues and we can make a single policy for them? In this work, we propose a framework using regression analysis and Minimum Description Length (MDL) to find a set of largest areas that have common indicators, which can be used to predict household incomes efficiently. Given a set of household features, and a multi-resolution partition that represents administrative divisions, our framework reports a set C * of largest subdivisions that have a common predictive model for population-income prediction. We formalize the problem of finding C * and propose an algorithm that can find C * correctly. We use both simulation datasets as well as a real-world dataset of Thailand’s population household information to demonstrate our framework performance and application. The results show that our framework performance is better than the baseline methods. Moreover, we demonstrate that the results of our method can be used to find indicators of income prediction for many areas in Thailand. By adjusting these indicator values via policies, we expect people in these areas to gain more incomes. Hence, the policy makers will be able to make policies by using these indicators in our results as a guideline to solve low-income issues. Our framework can be used to support policy makers in making policies regarding any other dependent variable beyond income in order to combat poverty and other issues. We provide the R package, MRReg, which is the implementation of our framework in the R language. The MRReg package comes with a documentation for anyone who is interested in analyzing linear regression on multi-resolution population 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 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.

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 C oordination S trategy I nference P roblem . In this setting, a group of multiple individuals moves in a coordinated manner toward a target path. Each individual uses a specific strategy to follow others (e.g., nearest neighbors, pre-defined leaders, and 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 directions of movement of an individual in a group in both simulated datasets as well as in 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. Results show that our approach is highly accurate in inferring correct strategies 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.

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.

Leadership is an essential part of collective decision and organization in social animals, including humans. In nature, leadership is dynamic and varies with context or temporal factors. Understanding dynamics of leadership, such as how leaders 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 these dynamic leadership events. In this paper, we focus on mining and modeling frequent patterns of leadership dynamics. We formalize a new computational problem, Mining Patterns Of Leadership Dynamics, as well as propose a framework as a solution of this problem. Our framework can be used to address several questions regarding leadership dynamics of group movement. We use the leadership inference framework, mFLICA, to infer the time series of leaders from movement datasets, then propose the approach to mine and model frequent patterns of leadership dynamics. We evaluate our framework performance by using several simulated datasets, as well as using the real-world dataset of baboon movement to demonstrate the application of our framework. There are no existing methods to address this problem, thus, we modify and extend the existing leadership inference framework to provide a non-trivial baseline. Our framework performs better than this baseline in all datasets. Moreover, we also propose a method to perform statistical significance tests, comparing inferred frequent patterns of leadership dynamics with our proposed null hypotheses. Our framework opens the opportunities for scientists to generate scientific hypotheses that can be tested statistically regarding dynamics of leadership in movement data.

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.

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.

How do leaders lead? Are individuals with influence always at the front of their group? Do they initiate travel in new directions or are they first to start moving? Which attempts to initiate movement translate to leadership? In this paper we present a computational method to characterize and classify the types of leaders in movement initiation. We adapt a leadership inference framework, FLICA, to extract information about which individuals act as leaders. We then propose a framework for ranking leaders according to their position, velocity, and heading relative to the group and perform hypothesis testing of correlations between target features and leadership ranking. We use a time series of GPS positions of wild olive baboons (Papio anubis) as an application of our approach. Our results demonstrate that there is no correlation between leadership and early movement, there is negative correlation between leadership and new directions, while leadership and new area exploration are positively correlated. Thus, as an example, in baboons, our approach shows that while leaders are not the first to move, they are typically at the front and move in a new area with everybody immediately aligning in the direction of leader. Our simple scheme is flexible to be applied to other data sets and sets of traits to characterize leadership.