Elham Shaabani

Diffusion in Social Networks

This book presents the leading models of social network diffusion that are used to demonstrate the spread of disease, ideas, and behavior. It introduces diffusion models from the fields of computer science (independent cascade and linear threshold), sociology (tipping models), physics (voter models), biology (evolutionary models), and epidemiology (SIR/SIS and related models). A variety of properties and problems related to these models are discussed including identifying seeds sets to initiate diffusion, game theoretic problems, predicting diffusion events, and more. The book explores numerous connections between social network diffusion research and artificial intelligence through topics such as agent-based modeling, logic programming, game theory, learning, and data mining. The book also surveys key empirical results in social network diffusion, and reviews the classic and cutting-edge research with a focus on open problems.

Evolutionary Graph Theory

Evolutionary graph theory (EGT), studies the ability of a mutant gene to overtake a finite structured population. In this chapter, we describe the original framework for EGT and the major work that has followed it. Here, we will study the calculation of the “fixation probability”—the probability of a mutant taking over a population and focuses on game-theoretic applications. We look at varying topics such as alternate evolutionary dynamics, time to fixation, special topological cases, and game theoretic results.

The Independent Cascade and Linear Threshold Models

In this chapter, we focus on perhaps the two most prevalent diffusion models in computer science—the independent cascade and linear threshold models. We describe different properties of these models and how these properties affect solving problems such as influence maximization and influence spread. We describe approaches to address influence maximization problem in independent cascade model and linear threshold model that rely on the maximization of submodular functions—as well as extensions to these approaches for larger datasets.

Early Identification of Violent Criminal Gang Members

Gang violence is a major problem in the United States accounting for a large fraction of homicides and other violent crime. In this paper, we study the problem of early identification of violent gang members. Our approach relies on modified centrality measures that take into account additional data of the individuals in the social network of co-arrestees which together with other arrest metadata provide a rich set of features for a classification algorithm. We show our approach obtains high precision and recall (0.89 and 0.78 respectively) in the case where the entire network is known and out-performs current approaches used by law-enforcement to the problem in the case where the network is discovered overtime by virtue of new arrests - mimicking real-world law-enforcement operations. Operational issues are also discussed as we are preparing to leverage this method in an operational environment.

MIST: Missing Person Intelligence Synthesis Toolkit

Each day, approximately 500 missing persons cases occur that go unsolved/unresolved in the United States. The non-profit organization known as the Find Me Group (FMG), led by former law enforcement professionals, is dedicated to solving or resolving these cases. This paper introduces the Missing Person Intelligence Synthesis Toolkit (MIST) which leverages a data-driven variant of geospatial abductive inference. This system takes search locations provided by a group of experts and rank-orders them based on the probability assigned to areas based on the prior performance of the experts taken as a group. We evaluate our approach compared to the current practices employed by the Find Me Group and found it significantly reduces the search area - leading to a reduction of 31 square miles over 24 cases we examined in our experiments. Currently, we are using MIST to aid the Find Me Group in an active missing person case.

Examining Diffusion in the Real World

Throughout this book, we studied a variety of diffusion models that are commonly seen in the literature of computer science, physics, and biology. In this chapter, we study diffusion processes from a data-driven perspective—specifiably reviewing the early identification of information cascades that will diffuse through a large portion of the network.

The SIR Model and Identification of Spreaders

In this chapter, we review the classic susceptible-infected-recovered (SIR) model for disease spread as applied to a social network. In particular, we look at the problem of identifying nodes that are “spreaders” which cause a large part of the population to become infected under this model. To do so, we survey a variety of nodal measures based on centrality (degree, betweenness, etc.) and other methods (shell decomposition, nearest neighbor analysis, etc.). We then present a set of experiments that illustrate the relation of these nodal measures to spreading under the SIR model.

Logic Programming Based Diffusion Models

In this chapter, we first show that the well-known generalized annotated program (GAP) paradigm can be used to express many existing diffusion models that can consider not only the topology of the social network, but attributes of the nodes and edges as well. We then define a class of problems called Social Network Diffusion Optimization Problems (SNDOPs). In this chapter, we show how various diffusion processes can be embedded as GAP’s and then study the algorithmic and complexity issues associated with SDNOP’s. Experimental results are also included.

The Tipping Model and the Minimum Seed Problem

In a “tipping” model, each node in a social network, representing an individual, adopts a property or behavior if a certain number of his incoming neighbors currently exhibit the same. A key problem, with respect to this model, is to select an initial “seed” set from the network such that the entire network adopts any behavior given to the seed. In this chapter, we investigate the problem of identifying a seed set of minimum size—which is NP-hard. We provide exact and heuristic methods for solving this problem as well as a suite of results to not only demonstrate the utility of these methods, but provide insight into the dynamics of the tipping model also.