Measuring the Impact of Influence on Individuals: Roadmap to Quantifying Attitude

TL;DR

This paper introduces a new model for measuring the degree of influence, called attitude, in social networks, and develops algorithms for maximizing attitude and actionable attitude, with theoretical guarantees and empirical evaluations.

Contribution

It proposes a novel attitude model for influence diffusion, formulates the attitude maximization problem, and provides approximation algorithms with theoretical guarantees.

Findings

Attitude function is monotonic and sub-modular, enabling greedy algorithms.

Attainable actionable attitude is approximately submodular, allowing for approximation algorithms.

Empirical analysis reveals spatial and value distribution patterns of high attitude nodes.

Abstract

Influence diffusion has been central to the study of propagation of information in social networks, where influence is typically modeled as a binary property of entities: influenced or not influenced. We introduce the notion of attitude, which, as described in social psychology, is the degree by which an entity is influenced by the information. We present an information diffusion model that quantifies the degree of influence, i.e., attitude of individuals, in a social network. With this model, we formulate and study attitude maximization problem. We prove that the function for computing attitude is monotonic and sub-modular, and the attitude maximization problem is NP-Hard. We present a greedy algorithm for maximization with an approximation guarantee of $(1-1/e)$. Using the same model, we also introduce the notion of "actionable" attitude with the aim to study the scenarios where attaining individuals with high attitude is objectively more important than maximizing the attitude of the entire network. We show that the function for computing actionable attitude, unlike that for computing attitude, is non-submodular and however is \emph{approximately submodular}. We present approximation algorithm for maximizing actionable attitude in a network. We experimentally evaluated our algorithms and study empirical properties of the attitude of nodes in network such as spatial and value distribution of high attitude nodes.