{"ID":2828613,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.14615","arxiv_id":"2512.14615","title":"Hierarchical Persistence Velocity for Network Anomaly Detection: Theory and Applications to Cryptocurrency Markets","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.","short_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 diag...","url_abs":"https://arxiv.org/abs/2512.14615","url_pdf":"https://arxiv.org/pdf/2512.14615v2","authors":"[\"Omid Khormali\"]","published":"2025-12-16T17:23:07Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}