TY - JOUR
T1 - Proximal-gradient algorithms for tracking cascades over social networks
AU - Baingana, Brian
AU - Mateos, Gonzalo
AU - Giannakis, Georgios B.
PY - 2014/8
Y1 - 2014/8
N2 - Many real-world processes evolve in cascades over complex networks, whose topologies are often unobservable and change over time. However, the so-termed adoption times when blogs mention popular news items, individuals in a community catch an infectious disease, or consumers adopt a trendy electronics product are typically known, and are implicitly dependent on the underlying network. To infer the network topology, a dynamic structural equation model is adopted to capture the relationship between observed adoption times and the unknown edge weights. Assuming a slowly time-varying topology and leveraging the sparse connectivity inherent to social networks, edge weights are estimated by minimizing a sparsity-regularized exponentially-weighted least-squares criterion. To this end, solvers with complementary strengths are developed by leveraging (pseudo) real-time sparsity-promoting proximal gradient iterations, the improved convergence rate of accelerated variants, or reduced computational complexity of stochastic gradient descent. Numerical tests with both synthetic and real data demonstrate the effectiveness of the novel algorithms in unveiling sparse dynamically-evolving topologies, while accounting for external influences in the adoption times. Key events in the political leadership in North Korea and the initial public offering of LinkedIn explain connectivity changes observed in the associated networks inferred from global cascades of online media.
AB - Many real-world processes evolve in cascades over complex networks, whose topologies are often unobservable and change over time. However, the so-termed adoption times when blogs mention popular news items, individuals in a community catch an infectious disease, or consumers adopt a trendy electronics product are typically known, and are implicitly dependent on the underlying network. To infer the network topology, a dynamic structural equation model is adopted to capture the relationship between observed adoption times and the unknown edge weights. Assuming a slowly time-varying topology and leveraging the sparse connectivity inherent to social networks, edge weights are estimated by minimizing a sparsity-regularized exponentially-weighted least-squares criterion. To this end, solvers with complementary strengths are developed by leveraging (pseudo) real-time sparsity-promoting proximal gradient iterations, the improved convergence rate of accelerated variants, or reduced computational complexity of stochastic gradient descent. Numerical tests with both synthetic and real data demonstrate the effectiveness of the novel algorithms in unveiling sparse dynamically-evolving topologies, while accounting for external influences in the adoption times. Key events in the political leadership in North Korea and the initial public offering of LinkedIn explain connectivity changes observed in the associated networks inferred from global cascades of online media.
KW - Structural equation model
KW - contagion
KW - dynamic network
KW - social network
KW - sparsity
UR - http://www.scopus.com/inward/record.url?scp=84904628437&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84904628437&partnerID=8YFLogxK
U2 - 10.1109/JSTSP.2014.2317284
DO - 10.1109/JSTSP.2014.2317284
M3 - Article
AN - SCOPUS:84904628437
SN - 1932-4553
VL - 8
SP - 563
EP - 575
JO - IEEE Journal on Selected Topics in Signal Processing
JF - IEEE Journal on Selected Topics in Signal Processing
IS - 4
M1 - 6797935
ER -