Analyzing a Perturbation in Actor AlignmentsPolitical Swarms Before and After the Bali Bombing

Lacey Kitch and Whitman RichardsMassachusetts Institute of Technology, CSAIL

{ljkitch, wrichards}@mit.edu

How does a terrorist event influence the alignment of “actors” with stakes in the sphere of the event? To answer this question, we look at the frequency of simultaneous news citations of pairs of 19 world leaders (actors) around the time of the Bali Bombings of 2002*. The bombings, which

occurred on October 12, were the deadliest terrorist act in the history of Indonesia, killing both Indonesian citizens and foreign nationals. We investigate the relationships between daily citations of leaders using two methods. The first is classical non-metric multidimensional scaling. The second is a new technique which we have called “differential multidimensional scaling”. This method looks at the ways in which the actors move

relative to each other. The analysis using Classical MDS yields scattered plots that are typically random swarms and are hard to interpret. In contrast, differential MDS yields clear groupings of actors which change over time, and are especially perturbed (mixed) immediately following the

bombing. One week after the bombing, a shift in alignments between the world leaders is found.

Actor Movements from Day 1 to Day 24

(Differential MDS)

Actor groupings on Day 1 with arrows indicating actor transitions by Day 24

Differential MDS

Immediately Following

7+ Days Before 10/12/02

10+ Days After

MDS

7+ Days Before 10/12/02

Immediately Following

10+ Days After

1 - Fundamentalists2 - Faruq3 - Haz4 - US5 - pressure6 - West10 - Hambali12 - CrackDown14 - Jemaah15 - Mahathir17 - Fathur

7 - Ghozi8 - Bashir9 - Megawati11 - Indonesian Govt.13 - United States16 - terror18 - Dwikarna19 - Qaeda

Methods I MDS

We first performed nonmetric multidimensional scaling on the correlation values between the 19 actors. This yielded one plot per day, each showing positions of the 19 actors in a two-dimensional space. Though the plots were cohesive, there was negligible grouping and they gave no obvious insights.

II Differential MDS

A. Actor-Actor comparisons and their change from day to day We are attempting, with this method, to obtain a measure of how the actors were “moving” relative to each other. If we see the correlation values between the actors as a distance value in some multidimensional space, then we can look at whether a pair of actors is moving towards or away from each other in the space. To do this, we compare the correlation value for each pair of actors on two consecutive days. For each such day transition (ie day 1 to day 2, day 2 to day 3, etc.), we note whether the correlation value for that pair increased, decreased, or stayed within a threshold of .01. This gave, for each pair of actors, a string of 23 values: each +, -, or 0, where a + indicated that the actors moved closer together, a – indicated that the actors moved further apart, and a 0 indicated that the actors’ relationship changed little.

For example, the strings for Actor 1 as compared with Actors 2, 3, and 4 are as follows, where each column represents a day transition (starting with day 1 to day 2):Actor #1, paired with Actor #...2: - - + - 0 0 0 0 0 + + + + -3: - - 0 0 + + - - + + + + - -4: - - - + + 0 - - 0 + + + 0 –

B. Comparison of Actor-Actor movement Next, we compare the day to day relative movement of the actors, as captured in the 171 pairwise strings computed previously. Of interest here is whether two actors change relative to given third actors in the same way. To compute a similarity measure of these movements, we take two actors, say 1 and 2, and compute their Hamming distance for each pair of days. This equates to comparing columns in the above strings. Specifically, this is done by comparing the value (for the given day, or column) of 1 vs. X and 2 vs. X, where X represents each other actor. For each position in which they contain the same value (+, -, or 0), the Hamming distance is increased by one. This is shown in Table 1, where H(1, 2) represents the Hamming distance between 1 and 2 between two certain days, and columns “1 & X” and “2 & X” are analogous to a column in the above example. This distance was computed for each pair of actors. Again, these distances represent the similarity between the way two actors are moving relative to other actors.

X 1 & X 2 & X H(1, 2)3 - - 14 - - 15 - 0 06 0 0 17 0 + 08 0 + 09 0 + 0

10 + + 111 + - 012 + - 013 + - 014 + 0 015 - - 116 0 + 017 0 + 018 - - 119 - 0 0

Total H(1, 2): 6

C. Non-metric Scaling

If actors are influenced in the same way, their Hamming distance should be large. Therefore we next perform Non-metric Multidimensional Scaling to look for groups of similar actors. We take the Hamming distances (171 values) as similarity measures and perform Multidimensional Scaling, giving a configuration for all 19 actors on each of the 23 day transitions.

III Results

Using Differential MDS, we found distinct groupings of actors. These groups started out as stable, then underwent turbulence, and then settled down again. Even in the stable regions, there were a few actors which occasionally switched groups. However these small perturbations were small compared to the effect of the Bali Bombing.

Supported by AFOSR contract 6894705 (26 Jan 07)

*Statistical data shaped in the Cultural Simulation Modeler (CSM) by IndaSea Inc.  Raw data feed supplied by Dow Jones, Inc.

The raw data which we are working with is a set of “correlations” between 19 actors. For each day in a 15 day period, each of the 19 actors has a 1x19 vector of correlations with himself and the other actors. When two actors are highly correlated on a particular day, it means that their names were mentioned often together in news articles appearing on that day. The correlations are thus symmetric between actors, and so the aggregated data for each day is a symmetric 19x19 matrix with 171 independent correlations.