PERCEPT: a new online change-point detection method using topological data analysis
Xiaojun Zheng, Simon Mak, Liyan Xie, Yao Xie

TL;DR
PERCEPT is a novel online change-point detection method that uses topological data analysis to identify structural changes in high-dimensional data streams, demonstrated in applications like solar flare monitoring and gesture detection.
Contribution
It introduces a topology-aware, non-parametric framework for online change detection using persistence diagrams, advancing the application of TDA in real-time data analysis.
Findings
PERCEPT outperforms existing change detection methods in numerical experiments.
It effectively detects changes in high-dimensional data with embedded topological structures.
Demonstrated success in solar flare and human gesture monitoring applications.
Abstract
Topological data analysis (TDA) provides a set of data analysis tools for extracting embedded topological structures from complex high-dimensional datasets. In recent years, TDA has been a rapidly growing field which has found success in a wide range of applications, including signal processing, neuroscience and network analysis. In these applications, the online detection of changes is of crucial importance, but this can be highly challenging since such changes often occur in a low-dimensional embedding within high-dimensional data streams. We thus propose a new method, called PERsistence diagram-based ChangE-PoinT detection (PERCEPT), which leverages the learned topological structure from TDA to sequentially detect changes. PERCEPT follows two key steps: it first learns the embedded topology as a point cloud via persistence diagrams, then applies a non-parametric monitoring approach…
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Taxonomy
TopicsTopological and Geometric Data Analysis
