Detecting Stubborn Behaviors in Influence Networks: A Model-Based Approach for Resilient Analysis

The wide spread of on-line social networks poses new challenges in information environment and cybersecurity. A key issue is detecting stubborn behaviors to identify leaders and influencers for marketing purposes, or extremists and automatic bots as potential threats. Existing literature typically relies on known network topology and extensive centrality measures computation. However, the size of social networks and their often unknown structure could make social influence computation impractical. We propose a new approach based on opinion dynamics to estimate stubborn agents from data. We consider a DeGroot model in which regular agents adjust their opinions as a linear combination of their neighbors' opinions, whereas stubborn agents keep their opinions constant over time. We formulate the stubborn nodes identification and their influence estimation problems as a low-rank approximation problem. We then propose an interpolative decomposition algorithm for their solution. We determine sufficient conditions on the model parameters to ensure the algorithm's resilience to noisy observations. Finally, we corroborate our theoretical analysis through numerical results.