Goyal et al., 2010, Learning Influence Probabilities In Social Networks
Contents
Online version
An online version of this paper is available at the [ACM digital library].
Summary
Influence propagation in social networks has interesting applications, especially for viral marketing. Most past studies assume as input a graph with nodes for each person, and weighted edges between the nodes if there is influence between the two persons. However, less attention has been put on how to build this graph using social media data. This paper introduces a model of influence built using social graph data on one hand, and a log of action (e.g., joining a community) on the other hand. The model is validated on the Flick dataset, which consists in a social graph with 1.3M nodes/40M edges and action log of 300K distinct actions. They propose and evaluate both static and dynamic models for this problem, and show that the influence of users on others (e.g., influence another user to join a group) can be modeled with a high accuracy.
Key Contributions
The biggest contribution claimed by the authors in this paper is the empirical evidence of influence in social networks using a discrete time model.
Models
Static Model
Everytime a user tries to activate (i.e. influence) his neighbor, he has a probability Pi of succeeding. This can be modeled using a Bernouilli distribution.
Continuous Time
The previous model neglect the variation over time of the influence users have on each others. For this reason, Goyal et al, present a continuous time model where the probability of a user influencing a neighbor depends on a time t variable (e.g., similar to an exponential decay model).
Discrete Time
The above continuous model isn't truly continuous has it has to be simulated using increment on the variable t. This process requires long run time for testing. For this reason, the authors present a discrete time model which assumes that the probability of a user influencing his neighbors his constant over a certain window of time after an action.
Experiments and Evaluation
The different models are evaluated with a ROC curve with true positive rate and false positive rate varying for different threshold values. The threshold value controls how much influence a user need to have from his neighbors in order to do the action (e.g., join a group). The result show that the static model fail to perform as well as the two temporally aware models, which probably indicates that influence does vary over time in social networks. Also, although discrete and continuous time models show similar performance, the discrete model has a faster run time.
Source: the original paper
