A Spectral Method for Activity Shaping in Continuous-Time Information Cascades

Information Cascades Model captures dynamical properties of user activity in a social network. In this work, we develop a novel framework for activity shaping under the Continuous-Time Information Cascades Model which allows the administrator for local control actions by allocating targeted resources that can alter the spread of the process. Our framework employs the optimization of the spectral radius of the Hazard matrix, a quantity that has been shown to drive the maximum influence in a network, while enjoying a simple convex relaxation when used to minimize the influence of the cascade. In addition, use-cases such as quarantine and node immunization are discussed to highlight the generality of the proposed activity shaping framework. Finally, we present the NetShape influence minimization method which is compared favorably to baseline and state-of-the-art approaches through simulations on real social networks.

[1]  Jure Leskovec,et al.  {SNAP Datasets}: {Stanford} Large Network Dataset Collection , 2014 .

[2]  Christos Faloutsos,et al.  On the Vulnerability of Large Graphs , 2010, 2010 IEEE International Conference on Data Mining.

[3]  Christos Faloutsos,et al.  Epidemic spreading in real networks: an eigenvalue viewpoint , 2003, 22nd International Symposium on Reliable Distributed Systems, 2003. Proceedings..

[4]  W. O. Kermack,et al.  Contributions to the Mathematical Theory of Epidemics. II. The Problem of Endemicity , 1932 .

[5]  Nicolas Vayatis,et al.  Tight Bounds for Influence in Diffusion Networks and Application to Bond Percolation and Epidemiology , 2014, NIPS.

[6]  Laks V. S. Lakshmanan,et al.  Information and Influence Propagation in Social Networks , 2013, Synthesis Lectures on Data Management.

[7]  Nicolas Vayatis,et al.  Anytime Influence Bounds and the Explosive Behavior of Continuous-Time Diffusion Networks , 2015, NIPS.

[8]  W. O. Kermack,et al.  Contributions to the mathematical theory of epidemics—II. The problem of endemicity , 1991, Bulletin of mathematical biology.

[9]  D. Stevanović,et al.  Decreasing the spectral radius of a graph by link removals. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Éva Tardos,et al.  Maximizing the Spread of Influence through a Social Network , 2015, Theory Comput..

[11]  Wei Chen,et al.  Scalable influence maximization for independent cascade model in large-scale social networks , 2012, Data Mining and Knowledge Discovery.

[12]  Christos Faloutsos,et al.  Node Immunization on Large Graphs: Theory and Algorithms , 2016, IEEE Transactions on Knowledge and Data Engineering.

[13]  Yoram Singer,et al.  Efficient projections onto the l1-ball for learning in high dimensions , 2008, ICML '08.

[14]  Michalis Faloutsos,et al.  Gelling, and melting, large graphs by edge manipulation , 2012, CIKM.

[15]  Jure Leskovec,et al.  Meme-tracking and the dynamics of the news cycle , 2009, KDD.

[16]  Bernhard Schölkopf,et al.  Uncovering the Temporal Dynamics of Diffusion Networks , 2011, ICML.

[17]  Takuya Akiba,et al.  Fast and Accurate Influence Maximization on Large Networks with Pruned Monte-Carlo Simulations , 2014, AAAI.

[18]  Varun Jog,et al.  Computing and maximizing influence in linear threshold and triggering models , 2016, NIPS.

[19]  Sébastien Bubeck,et al.  Convex Optimization: Algorithms and Complexity , 2014, Found. Trends Mach. Learn..

[20]  Andreas Krause,et al.  Cost-effective outbreak detection in networks , 2007, KDD '07.

[21]  W. O. Kermack,et al.  Contributions to the mathematical theory of epidemics—I , 1991, Bulletin of mathematical biology.

[22]  Michalis Faloutsos,et al.  Threshold conditions for arbitrary cascade models on arbitrary networks , 2011, 2011 IEEE 11th International Conference on Data Mining.