In the following, we present how we extract team coordination indicators from automatically sensed team networks. First, we describe how moving subgroups are detected to derive the sub-group network. Second, we describe how temporal activity alignment is quantified to extract the activity alignment network. Third, we detail how team coordination indicators are extracted from the team networks.
Detection and visualization of moving sub-groups
In our previous work [34], we have shown how moving sub-groups within teams can be detected from radio-based proximity data obtained with smartphones. The detected sub-groups can be visualized in the form of narrative charts to display which team members were in sub-groups at each point in time and show how sub-groups merge and split over time. The narrative chart presented in Figure 4a illustrates the moving sub-groups of firefighters during the described training scenario. The chart allows for example to identify the points in time when the first (1) and second troop (3) reached the top of the turntable ladder and when the first troop entered the building (2). As can be seen in the narrative chart the lines representing the members of the first troop (T1a, T1b, T1c) split from the other lines (other team members) at time point (1) when the first troop forms a sub-group and uses the turntable ladder to reach the roof window. At time point (2) two members (T1a, T1b) of the first troop enter the building and team member T1c remains outside on the top of the ladder. In the narrative chart this is shown by the splitting of the yellow line from the orange and purple lines. At time point (3) members of the second troop (T2a, T2b) climb the turntable ladder and join team member T1c which is shown in the chart by the merging of the red and brown lines with the yellow line.
Having detected moving sub-groups, we are able to calculate a sub-group network that summarizes which team member was for how long in a sub-group with another team member. Thus, the sub-group network captures the overall spatial structure of the team during a mission. In Figure 4a the corresponding sub-group network is presented on the right of the narrative chart. The network graphs highlights three sub-groups that belong to the first and second troop that enter the building via the turntable ladder as well as the ground support team that includes the incident commander, turntable ladder operator and the engineer. In the graph darker links between nodes correspond to team members that were longer than 60% of the mission together in a sub-group.
In the following we briefly describe our method to detect moving sub-groups using radio-based proximity data. Please refer to [34] for more details. We follow a two stage approach to detect moving sub-groups: We first calculate the proximity matrix Dt for consecutive time intervals t of length L=5 s. Each binary element indicates whether device i received any ANT message of device j during time interval t. Considering proximity to be undirected, we further symmetrize the proximity matrix to obtain .
In the second stage, moving sub-groups are clustered from the proximity data. Clusters are first identified independently from the symmetrized proximity matrices of each time interval and secondly, the clustering output is smoothed by applying a temporal filter, so that clusters last for at least 10 s. We cluster each symmetrized proximity matrix using the single-link criterion. As a result, if group member A is connected with B and B with C, but not with A, all three devices are still clustered into one group.
Using only radio based proximity information might lead to individuals on different height levels to be clustered into one group. To address this problem, we added height information derived from the atmospheric pressure sensor. If the absolute atmospheric pressure difference between two devices is greater than a predefined threshold, the two devices are considered to be on different height levels and are thus not clustered to the same sub-group. To obtain the sub-group network, we average the clustering results over all time intervals.
As the ANT-radio protocol operates in the 2.4 GHz band, radio signals are particularly influenced by the surrounding environment. In our experiments, we observed that depending on the relative orientation and environment of the individuals, the maximal transmit distance varied in the range of 1 m to 20 m. In [34] we evaluated our algorithm to detect moving sub-groups of firefighters during the described training scenario by comparing the results to a manually annotated ground truth. On average, team members were assigned to the correct sub-group with 95% accuracy.
Temporal alignment of activity level
In order to capture the temporal aspect of coordination in teams, we measure and compare activity levels of individual team members. Thus, we assume that well coordinated team members change their activity level at similar points in time.
We define the activity level to be the fraction of time that an individual is active within a moving window of length L. The activity level increases when individuals become active and decreases as soon as team members stop moving. The window length L determines the slope of the activity level and the minimum time that an individual needs to be active to reach the maximum activity level. The value of L also affects the temporal resolution, a small value requires individuals to change their activity closer in time, whereas a larger value allows for a delay between activity changes, as the activity level is calculated over a longer period.
Figure 5 illustrates the calculation of the motion activity level. In a first step, we detect when a team member is active, by thresholding the moving standard deviation of the linear acceleration magnitude. When a predefined threshold is exceeded, motion activity is detected (top in Figure 5). In a second step, the motion activity level is calculated as the percentage of time that motion activity was detected within a hopping window of length L and step size S (bottom in Figure 5). For further processing, the continuous activity level is linearly quantized into 10 discrete activity levels {0..9}.
In order to compare two motion activity level signals X,Y∈{0..9} of two team members, we use the mutual information as similarity measure. In general, mutual information measures the dependency between two random variables, that is how much information two variables share and is defined as:
(1)
The dependency between X and Y is expressed by the joint distribution p(x,y) and compared to the joint distribution when independence is assumed, in which case p(x,y)=p(x)p(y). Thus, I(X,Y) is zero if and only if X and Y are independent.
Two examples of activity level alignment that occurred during the firefighting training scenario are presented in Figure 4b. The two activity levels presented in the top graph belong two team members from the first troop (T1a, T1b), whereas the activity levels shown in the bottom graph belong to team member T1b and the incident commander. While the activity levels of the troop members change often together in time and are well aligned, the activity levels of the troop member T1b and the incident commander are not well aligned in time. Consequently, the observed mutual information is higher between the activity levels of the troop members as opposed to those of troop member T1b and the incident commander.
In order to summarize the temporal alignment for the whole team, the mutual information between all pairs of activity levels are calculated. This results in the activity alignment network. An example is presented on the right side of Figure 4b. As can be seen, troop member T1b had highest activity alignment with troop member T1a and lowest with the incident commander.
Team coordination indicators
On each of the extracted team networks (sub-group network and activity alignment network), we calculate network density and degree centralization in order to characterize the global network structure. In summary, we extract the following team coordination indicators from the team networks:
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Density of the sub-group network measures how long team members were on average in sub-groups. As the sub-group network captures the spatial distribution of team members, a high density indicates that many team members were together for a long time, whereas a low density indicates that team members were mostly on their own.
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Degree centralization of the sub-group network measures how differently team members were part of a sub-group. A high degree centralization indicates that there was at least one well connected large group and one other small group.
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Density of the activity alignment network measures how well team members aligned their activity level on average. It can thus be seen as an overall measure of how coordinated a team moved.
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Degree centralization of the activity alignment network measures how differently the team members aligned their activity levels with that of others. It can thus be seen as an overall measure of how differently team members’ motions were coordinated.
In the following, we give the definition of network density and centralization. Degree centrality of a node in the network captures how well each node (team member) in the network is connected to other nodes (other team members). Degree centrality of node i is defined by
with a
ij
∈[0..1] being an element of the adjacency matrix defining the network and i,j∈[1..N], with N being the number of nodes in the network. Network density D is the average degree centrality and thus captures how well nodes in the network are connected with each other. Network density is given by
Degree centralization DC measures how central its most central node (highest degree) is in relation to how central all the other nodes are. Thus, it is a measure of degree variation and is zero in a homogeneously connected network where each node has the same degree and one in a star network. Degree centralization is defined by
with d* being the maximum degree observed in the network.