Online High-Dimensional Change-Point Detection using Topological Data Analysis

Xiaojun Zheng, Simon Mak, Yao Xie

Keywords: Topological Data Analysis, Persistent Homology, Change Point Detection, Image Processing, Sublevel Set Filtration, Persistence Diagram.

TL;DR: We propose a new method called Persistence Diagram based Change-Point (PD-CP), which tackles sequentially change detection by integrating the widely-used persistence diagrams in TDA with recent developments in nonparametric change-point detection.

Abstract: Topological Data Analysis (TDA) is a rapidly growing field, which studies methods for learning underlying topological structures present in complex data representations. TDA methods have found recent success in extracting useful geometric structures for a wide range of applications, including protein classification, neuroscience, and time-series analysis. However, in many such applications, one is also interested in sequentially detecting changes in this topological structure. We propose a new method called Persistence Diagram based Change-Point (PD-CP), which tackles this problem by integrating the widely-used persistence diagrams in TDA with recent developments in nonparametric change-point detection. The key novelty in PD-CP is that it leverages the distribution of points on persistence diagrams for online detection of topological changes. We demonstrate the effectiveness of PD-CP in an application to solar flare monitoring.