Detecting change points in the large-scale structure of evolving networks (1403.0989v2)

Abstract: Interactions among people or objects are often dynamic in nature and can be represented as a sequence of networks, each providing a snapshot of the interactions over a brief period of time. An important task in analyzing such evolving networks is change-point detection, in which we both identify the times at which the large-scale pattern of interactions changes fundamentally and quantify how large and what kind of change occurred. Here, we formalize for the first time the network change-point detection problem within an online probabilistic learning framework and introduce a method that can reliably solve it. This method combines a generalized hierarchical random graph model with a Bayesian hypothesis test to quantitatively determine if, when, and precisely how a change point has occurred. We analyze the detectability of our method using synthetic data with known change points of different types and magnitudes, and show that this method is more accurate than several previously used alternatives. Applied to two high-resolution evolving social networks, this method identifies a sequence of change points that align with known external "shocks" to these networks.

• The paper introduces a probabilistic framework that integrates the advanced GHRG model with Bayesian hypothesis testing to detect structural change points in dynamic networks.
• It employs an online learning strategy by modeling change and no-change scenarios over sliding windows to robustly infer evolving network structures.
• The framework demonstrates superior performance on both synthetic and real datasets, accurately capturing significant shifts such as academic schedule changes and organizational events.

An Expert Overview of "Detecting Change Points in the Large-Scale Structure of Evolving Networks"

The paper "Detecting change points in the large-scale structure of evolving networks" by Leto Peel and Aaron Clauset presents a novel approach to identifying change points in dynamic complex networks using a probabilistic framework grounded in generative models of network evolution. This research is motivated by the inherent dynamic nature of interactions among entities across various domains, and the challenge lies in detecting both the occurrence and nature of structural changes within these interactions.

Probabilistic Framework for Change Detection

The authors introduce a method to formalize network change-point detection within an online probabilistic learning framework. They leverage a generative model known as the Generalized Hierarchical Random Graph (GHRG), which is coupled with Bayesian hypothesis testing. This integration provides robust probabilistic assessments of structural changes in the network.

Generalized Hierarchical Random Graph (GHRG)

The GHRG model is an enhancement over traditional stochastic block models and hierarchical random graph models. It captures complex nested community structures while allowing for varying levels of hierarchy and node interactions. Particularly, its flexibility in modeling assortative and disassortative community structures makes it a potent tool for analyzing real-world networks.

Methodology and Statistical Testing

The proposed methodology builds upon three pillars:

1. Selection of an appropriate parametric probability distribution over the network data, accommodating a window size for online detection.
2. Inference of parameter changes over time by modeling both change and no-change scenarios within the defined window.
3. Application of statistical hypothesis testing, using a Bayesian approach, to determine the likelihood of structural change occurrences.

The GHRG model supports Bayesian inference by incorporating connection probability priors, thus offering an analytical solution for marginal likelihood calculations. This enhances the method's sensitivity to network changes by adjusting the posterior distribution as successive networks are evaluated.

Detection in Synthetic and Real Networks

The efficacy of the approach is demonstrated through synthetic networks with predefined change points and two empirical datasets—the MIT Reality Mining dataset and the Enron email corpus. These applications highlight the method's superior performance in identifying known external shocks compared to traditional network metric-based techniques. For example, in the MIT dataset, the method accurately captures academic schedule changes, while in the Enron dataset, it identifies key organizational shifts aligned with significant company events.

Implications and Future Prospects

Peel and Clauset's approach extends beyond passive observation by offering interpretable insights into the processes driving network evolution. Its application can influence network theory, particularly in areas requiring real-time monitoring and analysis, such as cybersecurity, social network analysis, and systems biology. Future work could explore the integration of edge weight dynamics and vertex attributes to enrich the detection framework further.

The research establishes a solid foundation for both theoretical exploration and practical applications in dynamic network analysis, paving the way for further investigation into scalable techniques and hybrid models incorporating additional contextual information.

In summary, this work advances our capabilities in detecting and interpreting structural shifts within evolving networks, offering a statistically sound and computationally feasible method for analyzing complex systems.