mFLICA {mFLICA}

mFLICA: leadership-inference framework for multivariate time series

Description

A leadership-inference framework for multivariate time series. The framework uses a notion of a leader as an individual who initiates collective patterns that everyone in a group follows. Given a set of time series of individual activities, our goal is to identify periods of coordinated activity, find factions of coordination if more than one exist, as well as identify leaders of each faction. For each time step, the framework infers following relations between individual time series, then identifying a leader of each faction whom many individuals follow but it follows no one. A faction is defined as a group of individuals that everyone follows the same leader. mFLICA reports following relations, leaders of factions, and members of each faction for each time step. Please see Chainarong Amornbunchornvej and Tanya Berger-Wolf (2018) <doi:10.1137/1.9781611975321.62> when referring to this package in publications.

Usage

mFLICA(
  TS,
  timeWindow,
  timeShift,
  lagWindow = 0.1,
  sigma = 0.5,
  silentFlag = FALSE
)

Arguments

TS

is a set of time series where TS[i,t,d] is a numeric value of ith time series at time t and dimension d.

timeWindow

is a time window parameter that limits a length of each sliding window. The default is 10 percent of time series length.

timeShift

is a number of time steps a sliding window shifts from a previous window to the next one. The default is 10 percent of timeWindow.

lagWindow

is a maximum possible time delay in the term of percentage of time length of timeWindow supplying to the getDynamicFollNet function.

sigma

is a threshold of following relation. The default is 0.5. Note that if sigma is not one, an individual might be a member of multiple factions.

silentFlag

is a flag that prohibit the function to print the current status of process.

Value

This function returns dynamic following networks, as well as leaders of factions, and members of each faction for each time step.

dyNetOut$dyNetWeightedMat

An adjacency matrix of a dynamic following network s.t. if dyNetWeightedMat[i,j,t]>0, then TS[i,,] follows TS[j,,] at time t with a degree dyNetWeightedMat[i,j,t].

dyNetOut$dyNetBinMat

A binary version of dyNetWeightedMat s.t. dyNetWeightedMat[i,j,t] <- (dyNetWeightedMat[i,j,t] >=sigma) for any i,j,t.

dyNetOut$dyNetWeightedDensityVec

A time series of dynamic network densities of dyNetWeightedMat

dyNetOut$dyNetBinDensityVec

A time series of dynamic network densities of dyNetBinDensityVec

leadersTimeSeries

A time series of leaders of each faction where leadersTimeSeries[[t]] is a set of leaders at time t. A number of factions is the same as a number of leaders.

factionMembersTimeSeries

A time series of sets of faction members where factionMembersTimeSeries[[t]][[k]] is a set of faction-members at time t leading by a leader leadersTimeSeries[[t]][k].

factionSizeRatioTimeSeries

A time series of faction-size ratios of all individuals. A faction size ratio is a number of edges that connect between faction-member nodes divided by a number of total nodes within a following network. If a leader has a higher faction-size ratio, then it has more followers than a leader with a lower faction-size ratio. A faction-size ratio has a value between 0 and 1.

Author(s)

Chainarong Amornbunchornvej, [e-mail]

Examples

# Run the function

obj1<-mFLICA(TS=mFLICA::TS[,60:90,],timeWindow=10,timeShift=10,sigma=0.5)

# Plot time series of faction size ratios of all leaders

plotMultipleTimeSeries(TS=obj1$factionSizeRatioTimeSeries, strTitle="Faction Size Ratios")