用拓扑速度检测网络异常，预测加密货币价格更准。
Hierarchical Persistence Velocity for Network Anomaly Detection: Theory and Applications to Cryptocurrency Markets
- 基于持久性图的拓扑速度分析，自动降噪。
- 在以太坊网络上实现最高10.4%的AUC提升。
- 适合中长周期金融异常检测场景。
我们提出一种新型拓扑数据分析方法——重叠加权分层归一化持久性速度（OW-HNPV），用于检测时变网络中的异常。与以往测量累积拓扑存在性的方法不同，该方法首次引入基于持久性图的速率视角，衡量特征出现与消失的速度，并通过重叠加权机制自动抑制噪声。我们证明了OW-HNPV在数学上具有稳定性，在比较具有不同特征类型的网络持久性图时仍表现可控、可预测。应用于以太坊交易网络（2017年5月至2018年5月），该方法在7天价格走势预测中相比基线模型最高提升10.4% AUC。相较于向量平均贝蒂数（VAB）、持久性景观和持久性图像等方法，基于速度的摘要在中长周期（4-7天）预测中表现更优，且在不同预测时长下保持最稳定性能。结果表明，建模拓扑速度对识别动态网络中的结构异常至关重要。
原文摘要 · Abstract (English)
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.
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