Contagions, such as the spread of popular news stories, or infectious diseases, propagate in cascades over dynamic networks with unobservable topologies. However, 'social signals,' such as product purchase time, or blog entry timestamps are measurable, and implicitly depend on the underlying topology, making it possible to track it over time. Interestingly, network topologies often 'jump' between discrete states that may account for sudden changes in the observed signals. The present paper advocates a switched dynamic structural equation model to capture the topology dependent cascade evolution, as well as the discrete states driving the underlying topologies. Conditions under which the proposed switched model is identifiable are established. Leveraging the edge sparsity inherent to social networks, a recursive ℓ1-norm regularized least-squares estimator is put forth to jointly track the states and network topologies. An efficient first-order proximal-gradient algorithm is developed to solve the resulting optimization problem. Numerical experiments on both synthetic data and real cascades measured over the span of one year are conducted, and test results corroborate the efficacy of the advocated approach.
Bibliographical noteFunding Information:
This work was supported in part by the ARO Grant W911NF-15-1-0492; in part by the NSF Grants 1343248, 1442686, and 1514056; in part by the NIH Grant 1R01GM104975-01; in part by the AFOSR-MURI Grant FA9550-10-1-0567; in part by the European Union (European Social Fund-ESF)
© 2016 IEEE.
- Social networks
- network cascade
- structural equation model
- switched linear systems
- topology inference