Hierarchical Persistence Velocity for Network Anomaly Detection: Theory and Applications to Cryptocurrency Markets

2025-12-16

AI Summary

Existing anomaly detection methods for time-varying networks—particularly in cryptocurrency markets—overlook the dynamic evolution speed of topological structures. Method: We propose Overlaid Weighted Hierarchical Normalized Persistence Velocity (OW-HNPV), the first approach to use “topological velocity”—i.e., the birth-and-death rate of features in persistence diagrams—as the core metric, replacing conventional cumulative existence measures. OW-HNPV incorporates an overlaid weighting scheme to enhance robustness and provides a rigorous proof of Lipschitz stability to ensure mathematical reliability. Contribution/Results: Evaluated on topological data analysis (TDA)-driven dynamic network modeling and Ethereum transaction graphs, OW-HNPV achieves a 10.4% AUC improvement in 7-day price anomaly prediction and significantly outperforms baselines—including VAB, persistence landscapes, and persistence images—in medium-term (4–7 day) forecasting.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Humans and AI: Other Foundations of Human Computation & AI
• Machine Learning: Other Foundations of Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity
• Economics, Online Markets and Human Computation: Sustainability of Web economics

Abstract

We introduce the Overlap-Weighted Hierarchical Normalized Persistence Velocity (OW-HNPV), a novel topological data analysis method for detecting anomalies in time-varying networks. Unlike existing methods that measure cumulative topological presence, we introduce the first velocity-based perspective on persistence diagrams, measuring the rate at which features appear and disappear, automatically downweighting noise through overlap-based weighting. We also prove that OW-HNPV is mathematically stable. It behaves in a controlled, predictable way, even when comparing persistence diagrams from networks with different feature types. Applied to Ethereum transaction networks (May 2017-May 2018), OW-HNPV demonstrates superior performance for cryptocurrency anomaly detection, achieving up to 10.4% AUC gain over baseline models for 7-day price movement predictions. Compared with established methods, including Vector of Averaged Bettis (VAB), persistence landscapes, and persistence images, velocity-based summaries excel at medium- to long-range forecasting (4-7 days), with OW-HNPV providing the most consistent and stable performance across prediction horizons. Our results show that modeling topological velocity is crucial for detecting structural anomalies in dynamic networks.

Problem

• Detects anomalies in time-varying networks using topological velocity
• Improves cryptocurrency price movement predictions with stable performance
• Outperforms existing methods in medium- to long-range forecasting accuracy

Innovation

• Velocity-based persistence diagram analysis for anomaly detection
• Overlap-weighted hierarchical method to automatically reduce noise
• Mathematically stable topological velocity for dynamic network forecasting