发表机构
University of Evansville（埃文斯维尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究利用拓扑数据分析和图论预测网球比赛结果，第一种方法用低星过滤等提取特征，随机森林模型结合多种特征达66.2%准确率，第二种方法用修正Katz相似性指数，达62.48%准确率，首次应用低星过滤，比较多种方法，证明TDA价值。
AI 中文摘要
我们提出了两种使用拓扑数据分析和图论来预测2000 - 2025年ATP单打比赛网球比赛结果的方法。第一种方法将低星过滤应用于球员竞争网络，通过持久同调结合四种总结方法（VAB、HNAV、HWNAV、OW - HNPV）并结合修正带深度分析提取拓扑特征。算法优化包括自我图近似和三角形消除，能分析约66k场比赛。随机森林模型使用拓扑、图论和排名特征达到66.2%的准确率（AUC = 0.719）。特征重要性分析显示排名贡献36.3%，中心性25.5%，TDA特征24.0%。第二种方法使用带时间边缘加权的修正Katz相似性指数，在留出的测试数据上达到62.48%的准确率。本工作首次将低星过滤应用于网球预测，对四种拓扑总结方法进行了系统比较，证明TDA仅使用网络拓扑就能实现超机遇预测，与传统特征结合时提供附加价值。
英文摘要
We present two approaches for predicting tennis match outcomes using topological data analysis and graph theory on ATP singles matches from 2000-2025. The first method applies lower-star filtration to player competitive networks, extracting topological features through persistent homology using four summary methods (VAB, HNAV, HWNAV, OW-HNPV) combined with Modified Band Depth analysis. Algorithmic optimizations including ego graph approximations and triangle elimination enable analysis of about 66k matches. Our Random Forest model achieves 66.2% accuracy (AUC = 0.719) using topological, graph-theoretic, and ranking features. Feature importance analysis reveals that rankings contribute 36.3%, centralities 25.5%, and TDA features 24.0%, with topological features providing complementary signal. When rankings are unavailable, the topology-only model maintains 63.56% accuracy, demonstrating that network-derived features alone capture meaningful competitive structure. The second method uses a modified Katz similarity index with temporal edge weighting, achieving 62.48% accuracy on held-out test data. This work represents the first application of lower-star filtration to tennis prediction, provides systematic comparison of four topological summary methods in sports analytics, and demonstrates that TDA can achieve above-chance prediction using network topology alone while providing additional value when combined with traditional features.
