用拓扑分析和图论预测网球比赛结果，不依赖排名也能达到63.56%准确率。
Topological Data Analysis and Graph-Theoretic Approaches for Tennis Match Prediction
- 通过下星滤波提取球员竞争网络的拓扑特征，结合图中心性与排名数据。
- 融合特征后模型准确率达66.2%（AUC=0.719），拓扑特征贡献24%重要性。
- 首次在网球预测中应用下星滤波，证明仅用网络结构也可实现超随机预测。
我们提出两种方法，利用拓扑数据分析与图论对2000-2025年ATP单打比赛进行赛果预测。第一种方法对球员竞争网络应用下星滤波，通过持久同调提取拓扑特征，结合四种汇总方法（VAB、HNAV、HWNAV、OW-HNPV）与改进的带宽深度分析。算法优化如自环图近似与三角形剔除使约66,000场比赛可分析。随机森林模型使用拓扑、图论与排名特征，准确率达66.2%（AUC=0.719）。特征重要性分析显示：排名贡献36.3%，中心性25.5%，拓扑特征24.0%，表明拓扑特征提供互补信号。当无排名时，仅拓扑模型仍达63.56%准确率，证明网络衍生特征可捕捉有效竞争结构。第二种方法采用带时间边权重的改进卡茨相似度，测试集准确率达62.48%。本工作首次将下星滤波应用于网球预测，系统比较四类拓扑汇总方法在体育分析中的表现，并证实TDA在仅使用网络拓扑时即可实现高于随机水平的预测效果，且与传统特征结合更具价值。
原文摘要 · Abstract (English)
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.
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