Graph-Based Change-Point Detection

TL;DR

This paper introduces a graph-based, non-parametric method for change-point detection in data sequences, offering improved power in moderate to high dimensions and applicable to various data types.

Contribution

A novel graph-based scan statistic approach for change-point detection that is non-parametric and adaptable to any data with a definable similarity measure.

Findings

Better power than existing methods in moderate to high dimensions

Provides accurate analytic significance approximations

Successfully applied to authorship attribution and network change detection

Abstract

We consider the testing and estimation of change-points -- locations where the distribution abruptly changes -- in a data sequence. A new approach, based on scan statistics utilizing graphs representing the similarity between observations, is proposed. The graph-based approach is non-parametric, and can be applied to any data set as long as an informative similarity measure on the sample space can be defined. Accurate analytic approximations to the significance of graph-based scan statistics for both the single change-point and the changed interval alternatives are provided. Simulations reveal that the new approach has better power than existing approaches when the dimension of the data is moderate to high. The new approach is illustrated on two applications: The determination of authorship of a classic novel, and the detection of change in a network over time.