  Recently, there has been significant interest in social influence analysis.
One of the central problems in this area is the problem of identifying
influencers, such that by convincing these users to perform a certain action
(like buying a new product), a large number of other users get influenced to
follow the action. The client of such an application is a marketer who would
target these influencers for marketing a given new product, say by providing
free samples or discounts. It is natural that before committing resources for
targeting an influencer the marketer would be interested in validating the
influence (or network value) of influencers returned. This requires digging
deeper into such analytical questions as: who are their followers, on what
actions (or products) they are influential, etc. However, the current
approaches to identifying influencers largely work as a black box in this
respect. The goal of this paper is to open up the black box, address these
questions and provide informative and crisp explanations for validating the
network value of influencers.
  We formulate the problem of providing explanations (called PROXI) as a
discrete optimization problem of feature selection. We show that PROXI is not
only NP-hard to solve exactly, it is NP-hard to approximate within any
reasonable factor. Nevertheless, we show interesting properties of the
objective function and develop an intuitive greedy heuristic. We perform
detailed experimental analysis on two real world datasets - Twitter and
Flixster, and show that our approach is useful in generating concise and
insightful explanations of the influence distribution of users and that our
greedy algorithm is effective and efficient with respect to several baselines.
