Influence maximization, defined by Kempe, Kleinberg, and
Tardos (2003), is the problem of finding a small set of seed
nodes in a social network that maximizes the spread of influence
under certain influence cascade models. In this paper,
we propose an extension to the independent cascade model
that incorporates the emergence and propagation of negative
opinions. The new model has an explicit parameter called
quality factor to model the natural behavior of people turning
negative to a product due to product defects. Our model
incorporates negativity bias (negative opinions usually dominate
over positive opinions) commonly acknowledged in
the social psychology literature. The model maintains some
nice properties such as submodularity, which allows a greedy
approximation algorithm for maximizing positive influence
within a ratio of 1 1=e. We define a quality sensitivity ratio
(qs-ratio) of influence graphs and show a tight bound of
(
p
n=k) on the qs-ratio, where n is the number of nodes
in the network and k is the number of seeds selected, which
indicates that seed selection is sensitive to the quality factor
for general graphs. We design an efficient algorithm to compute influence in tree structures, which is nontrivial due to
the negativity bias in the model. We use this algorithm as the
core to build a heuristic algorithm for influence maximization
for general graphs. Through simulations, we show that
our heuristic algorithm has matching influence with a standard
greedy approximation algorithm while being orders of
magnitude faster.
