Asymptotic Performance Analysis of Majority Sentiment Detection in Online Social Networks

TL;DR

This paper studies how the structure of online social networks affects the accuracy of detecting the majority sentiment, revealing phase transition phenomena similar to physics models.

Contribution

It models social networks as Ising Markov random fields and analyzes asymptotic detection error based on network topology and connection strength.

Findings

Detection always inaccurate for empty and chain graphs.

Detection accuracy improves for complete graphs above a critical connection strength.

Phase transition phenomenon observed in detection performance.

Abstract

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.