A Distance Measure for the Analysis of Polar Opinion Dynamics in Social Networks

Modeling and predicting people's opinions plays an important role in today's life. For viral marketing and political strategy design, it is particularly important to be able to analyze competing opinions, such as pro-Democrat vs. pro-Republican. While observing the evolution of polar opinions in a social network over time, can we tell when the network "behaved"' abnormally? Furthermore, can we predict how the opinions of individual users will change in the future? To answer such questions, it is insufficient to study individual user behavior, since opinions spread beyond users' ego-networks. Instead, we need to consider the opinion dynamics of all users simultaneously. In this work, we introduce the Social Network Distance (SND)—a distance measure that quantifies the likelihood of evolution of one snapshot of a social network into another snapshot under a chosen opinion dynamics model. SND has a rich semantics of a transportation problem, yet, is computable in pseudo-linear time, thereby, being applicable to large-scale social networks analysis. We demonstrate the effectiveness of SND in experiments with Twitter data.

[1]  Robert E. Tarjan,et al.  Improved Algorithms for Bipartite Network Flow , 1994, SIAM J. Comput..

[2]  M. Newman,et al.  Vertex similarity in networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Andrew V. Goldberg,et al.  An efficient implementation of a scaling minimum-cost flow algorithm , 1993, IPCO.

[4]  A. Ozdaglar,et al.  Discrete Opinion Dynamics with Stubborn Agents , 2011 .

[5]  Jure Leskovec,et al.  The bursty dynamics of the Twitter information network , 2014, WWW.

[6]  Donald B. Johnson,et al.  Efficient Algorithms for Shortest Paths in Sparse Networks , 1977, J. ACM.

[7]  Reynold Cheng,et al.  Earth Mover's Distance based Similarity Search at Scale , 2013, Proc. VLDB Endow..

[8]  Michael Werman,et al.  A Linear Time Histogram Metric for Improved SIFT Matching , 2008, ECCV.

[9]  Leonidas J. Guibas,et al.  The Earth Mover's Distance as a Metric for Image Retrieval , 2000, International Journal of Computer Vision.

[10]  Xuelong Li,et al.  A survey of graph edit distance , 2010, Pattern Analysis and Applications.

[11]  Paul Van Dooren,et al.  A MEASURE OF SIMILARITY BETWEEN GRAPH VERTICES . WITH APPLICATIONS TO SYNONYM EXTRACTION AND WEB SEARCHING , 2002 .

[12]  S SawhneyHarpreet,et al.  Efficient Color Histogram Indexing for Quadratic Form Distance Functions , 1995 .

[13]  Andrew V. Goldberg,et al.  Solving minimum-cost flow problems by successive approximation , 1987, STOC.

[14]  James Lee Hafner,et al.  Efficient Color Histogram Indexing for Quadratic Form Distance Functions , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Laks V. S. Lakshmanan,et al.  Learning influence probabilities in social networks , 2010, WSDM '10.

[16]  Trevor Darrell,et al.  Nearest-Neighbor Searching and Metric Space Dimensions , 2006 .

[17]  K SinghAmbuj,et al.  A Distance Measure for the Analysis of Polar Opinion Dynamics in Social Networks , 2019 .

[18]  Ambuj K. Singh,et al.  A Distance Measure for the Analysis of Polar Opinion Dynamics in Social Networks , 2019, ACM Trans. Knowl. Discov. Data.

[19]  Danai Koutra,et al.  NetSimile: A Scalable Approach to Size-Independent Network Similarity , 2012, ArXiv.

[20]  Ambuj K. Singh,et al.  Indexing Spatially Sensitive Distance Measures Using Multi-resolution Lower Bounds , 2006, EDBT.

[21]  Allan Borodin,et al.  Threshold Models for Competitive Influence in Social Networks , 2010, WINE.

[22]  Horst Bunke,et al.  A graph distance metric based on the maximal common subgraph , 1998, Pattern Recognit. Lett..

[23]  Stefan M. Wild,et al.  Maximizing influence in a competitive social network: a follower's perspective , 2007, ICEC.

[24]  Xiaoyun Chen,et al.  A Linear Approximate Algorithm for Earth Mover's Distance with Thresholded Ground Distance , 2014 .

[25]  Edwin R. Hancock,et al.  Pattern Vectors from Algebraic Graph Theory , 2005, IEEE Trans. Pattern Anal. Mach. Intell..

[26]  Ambuj K. Singh,et al.  I act, therefore I judge: Network sentiment dynamics based on user activity change , 2013, 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2013).

[27]  Jacob Ratkiewicz,et al.  Predicting the Political Alignment of Twitter Users , 2011, 2011 IEEE Third Int'l Conference on Privacy, Security, Risk and Trust and 2011 IEEE Third Int'l Conference on Social Computing.

[28]  Ping Zhu,et al.  A Study of Graph Spectra for Comparing Graphs , 2005, BMVC.

[29]  Erhard Rahm,et al.  Similarity flooding: a versatile graph matching algorithm and its application to schema matching , 2002, Proceedings 18th International Conference on Data Engineering.

[30]  K. Clarkson.  Nearest-Neighbor Searching and Metric Space Dimensions , 2005 .

[31]  R. Merris.  Laplacian matrices of graphs: a survey , 1994 .

[32]  Kurt Mehlhorn,et al.  Faster algorithms for the shortest path problem , 1990, JACM.

[33]  Andrew McGregor,et al.  Sketching Earth-Mover Distance on Graph Metrics , 2013, APPROX-RANDOM.