141 research outputs found
Stability of Influence Maximization
The present article serves as an erratum to our paper of the same title,
which was presented and published in the KDD 2014 conference. In that article,
we claimed falsely that the objective function defined in Section 1.4 is
non-monotone submodular. We are deeply indebted to Debmalya Mandal, Jean
Pouget-Abadie and Yaron Singer for bringing to our attention a counter-example
to that claim.
Subsequent to becoming aware of the counter-example, we have shown that the
objective function is in fact NP-hard to approximate to within a factor of
for any .
In an attempt to fix the record, the present article combines the problem
motivation, models, and experimental results sections from the original
incorrect article with the new hardness result. We would like readers to only
cite and use this version (which will remain an unpublished note) instead of
the incorrect conference version.Comment: Erratum of Paper "Stability of Influence Maximization" which was
presented and published in the KDD1
Theories for influencer identification in complex networks
In social and biological systems, the structural heterogeneity of interaction
networks gives rise to the emergence of a small set of influential nodes, or
influencers, in a series of dynamical processes. Although much smaller than the
entire network, these influencers were observed to be able to shape the
collective dynamics of large populations in different contexts. As such, the
successful identification of influencers should have profound implications in
various real-world spreading dynamics such as viral marketing, epidemic
outbreaks and cascading failure. In this chapter, we first summarize the
centrality-based approach in finding single influencers in complex networks,
and then discuss the more complicated problem of locating multiple influencers
from a collective point of view. Progress rooted in collective influence
theory, belief-propagation and computer science will be presented. Finally, we
present some applications of influencer identification in diverse real-world
systems, including online social platforms, scientific publication, brain
networks and socioeconomic systems.Comment: 24 pages, 6 figure
Think Globally, Act Locally: On the Optimal Seeding for Nonsubmodular Influence Maximization
We study the r-complex contagion influence maximization problem. In the influence maximization problem, one chooses a fixed number of initial seeds in a social network to maximize the spread of their influence. In the r-complex contagion model, each uninfected vertex in the network becomes infected if it has at least r infected neighbors.
In this paper, we focus on a random graph model named the stochastic hierarchical blockmodel, which is a special case of the well-studied stochastic blockmodel. When the graph is not exceptionally sparse, in particular, when each edge appears with probability omega (n^{-(1+1/r)}), under certain mild assumptions, we prove that the optimal seeding strategy is to put all the seeds in a single community. This matches the intuition that in a nonsubmodular cascade model placing seeds near each other creates synergy. However, it sharply contrasts with the intuition for submodular cascade models (e.g., the independent cascade model and the linear threshold model) in which nearby seeds tend to erode each others\u27 effects.
Finally, we show that this observation yields a polynomial time dynamic programming algorithm which outputs optimal seeds if each edge appears with a probability either in omega (n^{-(1+1/r)}) or in o (n^{-2})
Learning Reputation in an Authorship Network
The problem of searching for experts in a given academic field is hugely
important in both industry and academia. We study exactly this issue with
respect to a database of authors and their publications. The idea is to use
Latent Semantic Indexing (LSI) and Latent Dirichlet Allocation (LDA) to perform
topic modelling in order to find authors who have worked in a query field. We
then construct a coauthorship graph and motivate the use of influence
maximisation and a variety of graph centrality measures to obtain a ranked list
of experts. The ranked lists are further improved using a Markov Chain-based
rank aggregation approach. The complete method is readily scalable to large
datasets. To demonstrate the efficacy of the approach we report on an extensive
set of computational simulations using the Arnetminer dataset. An improvement
in mean average precision is demonstrated over the baseline case of simply
using the order of authors found by the topic models
Optimizing spread dynamics on graphs by message passing
Cascade processes are responsible for many important phenomena in natural and
social sciences. Simple models of irreversible dynamics on graphs, in which
nodes activate depending on the state of their neighbors, have been
successfully applied to describe cascades in a large variety of contexts. Over
the last decades, many efforts have been devoted to understand the typical
behaviour of the cascades arising from initial conditions extracted at random
from some given ensemble. However, the problem of optimizing the trajectory of
the system, i.e. of identifying appropriate initial conditions to maximize (or
minimize) the final number of active nodes, is still considered to be
practically intractable, with the only exception of models that satisfy a sort
of diminishing returns property called submodularity. Submodular models can be
approximately solved by means of greedy strategies, but by definition they lack
cooperative characteristics which are fundamental in many real systems. Here we
introduce an efficient algorithm based on statistical physics for the
optimization of trajectories in cascade processes on graphs. We show that for a
wide class of irreversible dynamics, even in the absence of submodularity, the
spread optimization problem can be solved efficiently on large networks.
Analytic and algorithmic results on random graphs are complemented by the
solution of the spread maximization problem on a real-world network (the
Epinions consumer reviews network).Comment: Replacement for "The Spread Optimization Problem
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