Analyzing a Perturbation in Actor Alignments

1
Analyzing a Perturbation in Actor
Alignments Political Swarms Before and After the
Bali Bombing Lacey Kitch and Whitman
Richards Massachusetts Institute of Technology,
CSAIL ljkitch, wrichards_at_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)
Differential MDS
MDS
7 Days Before 10/12/02
7 Days Before 10/12/02
Immediately Following
Immediately Following
Actor groupings on Day 1 with arrows indicating
actor transitions by Day 24
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.
10 Days After
10 Days After
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.
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.