280 research outputs found
Early Warning Analysis for Social Diffusion Events
There is considerable interest in developing predictive capabilities for
social diffusion processes, for instance to permit early identification of
emerging contentious situations, rapid detection of disease outbreaks, or
accurate forecasting of the ultimate reach of potentially viral ideas or
behaviors. This paper proposes a new approach to this predictive analytics
problem, in which analysis of meso-scale network dynamics is leveraged to
generate useful predictions for complex social phenomena. We begin by deriving
a stochastic hybrid dynamical systems (S-HDS) model for diffusion processes
taking place over social networks with realistic topologies; this modeling
approach is inspired by recent work in biology demonstrating that S-HDS offer a
useful mathematical formalism with which to represent complex, multi-scale
biological network dynamics. We then perform formal stochastic reachability
analysis with this S-HDS model and conclude that the outcomes of social
diffusion processes may depend crucially upon the way the early dynamics of the
process interacts with the underlying network's community structure and
core-periphery structure. This theoretical finding provides the foundations for
developing a machine learning algorithm that enables accurate early warning
analysis for social diffusion events. The utility of the warning algorithm, and
the power of network-based predictive metrics, are demonstrated through an
empirical investigation of the propagation of political memes over social media
networks. Additionally, we illustrate the potential of the approach for
security informatics applications through case studies involving early warning
analysis of large-scale protests events and politically-motivated cyber
attacks
Learning heat diffusion graphs
Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or pre-determined sensing arrangements, like in road transportation networks for example. In general though, the data structure is not readily available and becomes pretty difficult to define. In particular, the global smoothness assumptions, that most of the existing works adopt, are often too general and unable to properly capture localized properties of data. In this paper, we go beyond this classical data model and rather propose to represent information as a sparse combination of localized functions that live on a data structure represented by a graph. Based on this model, we focus on the problem of inferring the connectivity that best explains the data samples at different vertices of a graph that is a priori unknown. We concentrate on the case where the observed data is actually the sum of heat diffusion processes, which is a quite common model for data on networks or other irregular structures. We cast a new graph learning problem and solve it with an efficient nonconvex optimization algorithm. Experiments on both synthetic and real world data finally illustrate the benefits of the proposed graph learning framework and confirm that the data structure can be efficiently learned from data observations only. We believe that our algorithm will help solving key questions in diverse application domains such as social and biological network analysis where it is crucial to unveil proper geometry for data understanding and inference
Graph topology inference based on sparsifying transform learning
Graph-based representations play a key role in machine learning. The
fundamental step in these representations is the association of a graph
structure to a dataset. In this paper, we propose a method that aims at finding
a block sparse representation of the graph signal leading to a modular graph
whose Laplacian matrix admits the found dictionary as its eigenvectors. The
role of sparsity here is to induce a band-limited representation or,
equivalently, a modular structure of the graph. The proposed strategy is
composed of two optimization steps: i) learning an orthonormal sparsifying
transform from the data; ii) recovering the Laplacian, and then topology, from
the transform. The first step is achieved through an iterative algorithm whose
alternating intermediate solutions are expressed in closed form. The second
step recovers the Laplacian matrix from the sparsifying transform through a
convex optimization method. Numerical results corroborate the effectiveness of
the proposed methods over both synthetic data and real brain data, used for
inferring the brain functionality network through experiments conducted over
patients affected by epilepsy.Comment: Submitted to IEEE Transactions on Signal Processing, March 201
- …