Asymptotic Performance Analysis of Majority Sentiment Detection in Online Social Networks

We analyze the problem of majority sentiment detection in Online Social Networks (OSN), and relate the detection error probability to the underlying graph of the OSN. Modeling the underlying social network as an Ising Markov random field prior based on a given graph, we show that in the case of the empty graph (independent sentiments) and the chain graph, the detection is always inaccurate, even when the number of users grow to infinity. In the case of the complete graph, the detection is inaccurate if the connection strength is below a certain critical value, while it is asymptotically accurate if the strength is above that critical value, which is analogous to the phase transition phenomenon in statistical physics.