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

TL;DR

This paper introduces a new topological data analysis method, OW-HNPV, that measures the rate of change in network features to detect anomalies, demonstrating improved cryptocurrency market prediction performance.

Contribution

The paper presents the first velocity-based approach to persistence diagrams, with a novel overlap-weighted method that is mathematically stable and effective for dynamic network anomaly detection.

Findings

OW-HNPV outperforms baseline models with up to 10.4% AUC gain.

Velocity-based summaries excel in medium- to long-range forecasting.

OW-HNPV provides stable and consistent anomaly detection across prediction horizons.

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.