[Paper Review] Using Linear Dynamical Topic Model for Inferring Temporal Social Correlation in Latent Space

Freddy Chong Tat Chua, Richard J. Oentaryo+1 more|arXiv (Cornell University)|Jan 6, 2015

Complex Network Analysis Techniques41 references3 citations

TL;DR

This paper proposes a Linear Dynamical Topic Model (LDTM) to infer temporal social correlation (TSC) in latent topic space from users' item adoption sequences. By modeling topic dynamics over time and applying Granger causality tests on time series of topic distributions, the method reveals that authors whose names appear first in co-authorship tend to influence those listed later, with influence decreasing over time.

ABSTRACT

The abundance of online user data has led to a surge of interests in understanding the dynamics of social relationships using computational methods. Utilizing users' items adoption data, we develop a new method to compute the Granger-causal (GC) relationships among users. In order to handle the high dimensional and sparse nature of the adoption data, we propose to model the relationships among users in latent space instead of the original data space. We devise a Linear Dynamical Topic Model (LDTM) that can capture the dynamics of the users' items adoption behaviors in latent (topic) space. Using the time series of temporal topic distributions learned by LDTM, we conduct Granger causality tests to measure the social correlation relationships between pairs of users. We call the combination of our LDTM and Granger causality tests as Temporal Social Correlation. By conducting extensive experiments on bibliographic data, where authors are analogous to users, we show that the ordering of authors' name on their publications plays a statistically significant role in the interaction of research topics among the authors. We also present a case study to illustrate the correlational relationships between pairs of authors.

Motivation & Objective

• To model temporal dynamics in users' item adoption behavior using a probabilistic latent space representation.
• To infer social influence relationships between users based on temporal correlations in their adoption patterns.
• To address the limitations of existing methods that ignore temporal and causal structure in social influence analysis.
• To validate the hypothesis that author name ordering in publications reflects information transfer dynamics.
• To quantify how influence evolves over time in co-authorship networks using time series of topic distributions.

Proposed method

• Proposes a Linear Dynamical Topic Model (LDTM) that combines probabilistic topic modeling with linear dynamical systems to model topic evolution over time.
• Uses an EM algorithm with Gibbs sampling and Kalman filtering in the E-step to infer latent topic distributions across time points.
• Applies Kullback-Leibler divergence minimization in the M-step to estimate the dynamics matrix governing topic transitions.
• Imposes stability and non-negativity constraints on the dynamics matrix to ensure interpretable and meaningful topic decay patterns.
• Constructs time series of topic distributions per user from LDTM outputs to enable Granger causality testing.
• Performs pairwise Granger causality tests between co-authors to compute Temporal Social Correlation (TSC) values.

Experimental results

Research questions

• RQ1 Does the temporal sequence of topic adoption among co-authors reflect information transfer patterns?
• RQ2 Is there a statistically significant relationship between author name ordering and direction of influence in co-authorship?
• RQ3 How does the strength of influence between co-authors evolve over time?
• RQ4 Do authors listed earlier in a publication have greater influence on their co-authors than those listed later?
• RQ5 To what extent does the TSC measure reflect actual information transfer rather than random correlation?

Key findings

• The Ratio metric, measuring the probability that TSC from author i to j exceeds TSC from j to i, is consistently below 0.5, indicating that authors listed later are more influenced by those listed earlier.
• The Ratio decreases over time, showing that the influence of later-listed authors on earlier-listed authors diminishes as co-authorship duration increases.
• Second authors (i) exert more influence on first authors (j) than generic later authors, suggesting a role for author position in influence dynamics.
• Last authors (i) influence first authors (j) more than second authors do, indicating that seniority or contribution level affects influence patterns.
• The results reject the hypotheses AB, AZ, and Bf_Af, confirming that author name ordering correlates with directional influence in topic adoption.
• The study demonstrates that temporal social correlation derived from latent topic dynamics can reveal meaningful, statistically significant patterns of information transfer in academic collaboration.