Online change-point detection: a weighted sum approach with constraint and application to dynamic network observation

Abstract

This article considers the change detection problem for one-dimensional observation sequences and dynamic network observation sequences. Since for network data, especially for large-scale network data, it is unrealistic to obtain the underlying distribution or underlying probabilistic structure. In this view, we consider a weighted sum approach with constraint for change detection. The purpose of the constraint is to highlight the changes, thus the method proposed has better performance for small shift. Meanwhile, different metrics for network data are suitable for different types of changes, the detection ability of L 1-norm is better for dense change, and the detection ability of max-norm is better for sparse change. A parallel multi-chart is proposed as a guidance for improving the performance of change detection for different types of changes. Furthermore, the theoretical results are illustrated numerically on one-dimensional observation sequences and dynamic network observation sequences.