PERCEPT: A New Online Change-Point Detection Method using Topological Data Analysis

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 low-dimensional embeddings 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 nonparametric monitoring approach for detecting changes in the resulting point cloud distributions. This yields a nonparametric, topology-aware framework which can efficiently detect online geometric changes. We investigate the effectiveness of PERCEPT over existing methods in a suite of numerical experiments where the data streams have an embedded topological structure. We then demonstrate the usefulness of PERCEPT in two applications on solar flare monitoring and human gesture detection.

KEYWORDS:

• Change-point detection
• Human gesture detection
• Online monitoring
• Persistent homology
• Solar flare monitoring
• Topological data analysis

Data Availability Statement

Code accompanying this article can be found at https://github.com/Xiaojzheng/PERCEPT.

Disclosure Statement

The authors report there are no competing interests to declare.

Acknowledgments

The authors thank Yi Ji and Alessandro Zito for helpful comments on the article.

Notes

1 See https://sdo.gsfc.nasa.gov/assets/docs/SDO_Guide.pdf.

Additional information

Funding

Yao Xie is partially supported by NSF DMS-2134037, CCF-1650913, DMS-1938106, and DMS-1830210. Simon Mak is partially supported by NSF CSSI Frameworks 2004571 and NSF DMS-2210729.