Change-Point Methods on a Sequence of Graphs

Abstract

Given a finite sequence of graphs, e.g., coming from technological, biological, and social networks, the paper proposes a methodology to identify possible changes in stationarity in the stochastic process generating the graphs. In order to cover a large class of applications, we consider the general family of attributed graphs where both topology (number of vertexes and edge configuration) and related attributes are allowed to change also in the stationary case. Novel Change Point Methods (CPMs) are proposed, that (i) map graphs into a vector domain; (ii) apply a suitable statistical test in the vector space; (iii) detect the change -if any-according to a confidence level and provide an estimate for its time occurrence. Two specific multivariate CPMs have been designed: one that detects shifts in the distribution mean, the other addressing generic changes affecting the distribution. We ground our proposal with theoretical results showing how to relate the inference attained in the numerical vector space to the graph domain, and vice versa. We also show how to extend the methodology for handling multiple change points in the same sequence. Finally, the proposed CPMs have been validated on real data sets coming from epileptic-seizure detection problems and on labeled data sets for graph classification. Results show the effectiveness of what proposed in relevant application scenarios.

Modeling and detecting change in temporal networks via the degree corrected stochastic block model

“…The authors then generate a sample of “null” networks by bootstrapping a sample of t networks where no change is introduced. There are a number of sequential change point methodologies that have been developed for networks recently (see, for example, Zambon et al). Chen introduced a nonparametric method for detecting change via a k nearest neighbor approach.…”

RING-CPD: Asymptotic Distribution-free Change-point Detection for Multivariate and Non-Euclidean Data

“…For each subject, both the normal brain activity and the seizure activity are recorded multiple times, which are one-second clips with various channels (from 16 to 72), reducing to a multivariate stream of iEEGs. Following the procedure of Zambon, Alippi and Livi (2019), we represent the iEEG data as functional connectivity networks using Pearson correlation in the high-gamma band (70-100Hz) (Bastos and Schoffelen, 2016). Functional connectivity networks are weighted graphs, where the vertexes are the electrodes, and the weights of edges correspond to the coupling strength of the vertexes.…”

“…Change-point detection (CPD) has attracted a lot of interests since the seminal work of Page (1954). In this big data era, it has diverse applications in many fields, including functional magnetic resonance recordings (Barnett and Onnela, 2016;Zambon, Alippi and Livi, 2019), healthcare (Staudacher et al, 2005;Malladi, Kalamangalam and Aazhang, 2013), communication network evolution (Kossinets and Watts, 2006;Eagle, Pentland and Lazer, 2009;Peel and Clauset, 2015), and financial modeling (Bai and Perron, 1998;Talih and Hengartner, 2005). Parametric approaches (see for example Srivastava and Worsley, 1986;Zhang et al, 2010;Siegmund, Yakir and Zhang, 2011;Chen and Gupta, 2012;Wang, Zou and Yin, 2018) are useful to address the problem for univariate and low-dimensional data, however, they are limited for high-dimensional or non-Euclidean data due to a large number of parameters to be estimated unless very strong assumptions are imposed.…”