OMT: Decoding the Cross-Impact of Multiple Topics in Social Influence

TL;DR

The Operator-based Multi-Topic (OMT) model bridges the gap between mathematical diffusion dynamics and the messy reality of multi-topic social interactions. By treating influence as a "heat" that flows through interconnected topic layers, this research provides a high-fidelity simulation tool and a superior seed selection algorithm (MGTS-greedy) for maximizing influence in real-world networks.

The Multi-Topic Blind Spot

Most influence models assume a "one size fits all" propagation probability. However, in reality:

1. Context Matters: A user might be an authority in "Jazz" but ignored in "Electronic Music."
2. Topics Collide: A viral post about "Politics" might inadvertently boost a related "Economics" discussion.
3. Dynamic Status: Hot topics (High Penetration) spread faster than niche ones.

Existing SOTA models often ignore these interdependencies, leading to poor simulation quality when applied to datasets with diverse content.

Methodology: The Synthetic Operator

The core innovation of OMT is the formulation of a Topic-Aware Operator ($H_{OMT}$). This operator defines how influence flows between users ($i$ and $j$) while being moderated by their interests ($\alpha$) and the correlation between topics ($heta$).

1. Topic Correlation ($het{a}^{xy}$)

Instead of assuming topics are independent, the authors use KL-divergence to measure how the distribution of one topic relates to another. If two topics are highly correlated, message exchanges in topic $Y$ can trigger influence adoption in topic $X$.

2. The Diffusion Equation

The model uses a differential equation ${\partial }_{t}m=Hm$ to describe the evolution of the network's influence state. Figure 1: Conceptual framework of topic effects on influence propagation.

The operator $H$ accounts for:

• User Trust ($w_{ji}$): The baseline influence between two individuals.
• Topic Penetration (${\beta }^x$): The current "heat" or momentum of a topic in the network.

Experimental Validation

The authors tested OMT using a massive dataset of musical influence (20 genres/topics).

High-Fidelity Simulation

When compared against the actual Real Diffusion (RD) recorded in the dataset, the OMT model's curves were significantly more accurate than the single-topic OBM model. Figure 2: Simulation results comparing OMT and OBM against real-world data (RD).

Influence Maximization

The MGTS-greedy algorithm uses the OMT operator to find the most influential "seed" users. By accounting for cross-topic support, it outperformed traditional degree-ranking and random selection methods in both 8-topic and 6-topic network samples.

Critical Insights & Conclusion

• Direct vs. Indirect Influence: OMT effectively captures how a user can be influenced by a topic they aren't even discussing, purely through its correlation with their active interests.
• Memory and Context: By inheriting from Agent-Based Modeling, the model respects user capacity and "memory" (context), making the simulation more human-centric.

Limitations: The model currently assumes topic correlations are non-directional ($het{a}^{xy}=het{a}^{yx}$), which may not hold true in cases where one topic is a subset of another (e.g., "Machine Learning" vs "AI").

Future Work: Enhancing the efficiency of the MGTS-greedy algorithm for massive-scale networks and exploring asymmetric topic correlations will be the next frontier for OMT.