Online Change Point Detection for Weighted and Directed Random Dot Product Graphs

@article{Marenco2022OnlineCP,
  title={Online Change Point Detection for Weighted and Directed Random Dot Product Graphs},
  author={Bernardo Marenco and Paola Bermolen and Marcelo Fiori and Federico Larroca and Gonzalo Mateos},
  journal={IEEE Transactions on Signal and Information Processing over Networks},
  year={2022},
  volume={8},
  pages={144-159}
}
Given a sequence of random (directed and weighted) graphs, we address the problem of online monitoring and detection of changes in the underlying data distribution. Our idea is to endow sequential change-point detection (CPD) techniques with a graph representation learning substrate based on the versatile Random Dot Product Graph (RDPG) model. We consider efficient, online updates of a judicious monitoring function, which quantifies the discrepancy between the streaming graph observations and… 

Algorithmic Advances for the Adjacency Spectral Embedding

First-order gradient descent methods are developed to better solve the original optimization problem, and to accommodate broader network embedding applications in an organic way and can track the latent positions over time when the graphs are acquired in a streaming fashion.

Graph Filters for Signal Processing and Machine Learning on Graphs

The aim is that this article serves the dual purpose of providing a unifying framework for both beginner and experienced researchers, as well as a common understanding that promotes collaborations between signal processing, machine learning, and application domains.

References

SHOWING 1-10 OF 43 REFERENCES

Online Change Point Detection for Random Dot Product Graphs

This paper considers the cumulative sum of a judicious monitoring function, which quantifies the discrepancy between the streaming graph observations and the nominal model, and develops a lightweight online CPD algorithm, with a proven capability to flag distribution shifts in the arriving graphs.

Change Point Detection in Weighted and Directed Random Dot Product Graphs

This work first extends the RDPG model to accommodate directed and weighted graphs, a contribution whose interest transcends change-point detection (CPD), and facilitates adoption of scalable geometric CPD techniques.

Statistical Inference on Random Dot Product Graphs: a Survey

This survey paper describes a comprehensive paradigm for statistical inference on random dot product graphs, a paradigm centered on spectral embeddings of adjacency and Laplacian matrices, and investigates several real-world applications, including community detection and classification in large social networks and the determination of functional and biologically relevant network properties from an exploratory data analysis of the Drosophila connectome.

Change point localization in dependent dynamic nonparametric random dot product graphs

This paper proposes a novel change point detection algorithm and constructs a nonparametric version of the CUSUM statistic that allows for temporal dependence and is proved theoretically and supported by extensive numerical experiments, which illustrate state-of-the-art performance.

Sequential Graph Scanning Statistic for Change-point Detection

This work presents two graph scanning statistics that can detect local changes in the distribution of edges in a subset of the graph and demonstrates the efficiency of the detection statistics for ambient noise imaging, using a real dataset that records real-time seismic signals around the Old Faithful Geyser in the Yellowstone National Park.

A Central Limit Theorem for an Omnibus Embedding of Multiple Random Dot Product Graphs

A central limit theorem is proved for this omnibus embedding and it is shown that simultaneous embedding into a common space allows comparison of graphs without the need to perform pairwise alignments of graph embeddings.

A statistical interpretation of spectral embedding: The generalised random dot product graph

A generalisation of the latent position network model known as the random dot product graph is proposed, to allow interpretation of those vector representations as latent position estimates, and the potential to uncover richer latent structure is uncovered.

Detecting Change Points in the Large-Scale Structure of Evolving Networks

This paper formalizes for the first time the network change-point detection problem within an online probabilistic learning framework and introduces a method that can reliably solve it and analyzes the detectability of this method using synthetic data with known change points of different types and magnitudes.

A Random Dot Product Model for Weighted Networks

This paper presents a generalization of the random dot product model for networks whose edge weights are drawn from a parametrized probability distribution and determines a dimension--reducing embedding process that gives geometric interpretations of community structure and centrality.

Consistent Latent Position Estimation and Vertex Classification for Random Dot Product Graphs

If class labels are observed for a number of vertices tending to infinity, then it is shown that the remaining vertices can be classified with error converging to Bayes optimal using the $(k)$-nearest-neighbors classification rule.