arXiv:2509.07766quant-phcs.LG2025-09

用量子算法直接聚类金融资产相关性,自动确定最佳分组数。

Toward Quantum Utility in Finance: A Robust Data-Driven Algorithm for Asset Clustering

  • 基于图的联盟结构生成,直接处理带符号权重的相关性图。
  • 在真实和合成数据上优于传统方法,调整兰德指数提升12%以上。
  • 适合量化金融、投资组合优化等需要动态聚类的场景。

基于收益相关性的金融资产聚类是投资组合优化与统计套利的基础任务。然而,经典聚类方法在处理带符号相关性结构时表现不足,通常需经过有损变换并依赖固定聚类数等启发式假设。本文将基于图的联盟结构生成算法(GCS-Q)应用于直接聚类带符号加权图,无需上述变换。GCS-Q将每次划分建模为QUBO问题,可利用量子退火高效探索指数级大的解空间。我们在合成数据和真实金融市场数据上验证该方法,与SPONGE和k-Medoids等先进经典算法对比。实验表明,GCS-Q在调整兰德指数和结构平衡惩罚指标上均持续表现更优,且能动态确定聚类数量。结果证明近中期量子计算在金融图学习中的实际应用潜力。

原文摘要 · Abstract (English)

Clustering financial assets based on return correlations is a fundamental task in portfolio optimization and statistical arbitrage. However, classical clustering methods often fall short when dealing with signed correlation structures, typically requiring lossy transformations and heuristic assumptions such as a fixed number of clusters. In this work, we apply the Graph-based Coalition Structure Generation algorithm (GCS-Q) to directly cluster signed, weighted graphs without relying on such transformations. GCS-Q formulates each partitioning step as a QUBO problem, enabling it to leverage quantum annealing for efficient exploration of exponentially large solution spaces. We validate our approach on both synthetic and real-world financial data, benchmarking against state-of-the-art classical algorithms such as SPONGE and k-Medoids. Our experiments demonstrate that GCS-Q consistently achieves higher clustering quality, as measured by Adjusted Rand Index and structural balance penalties, while dynamically determining the number of clusters. These results highlight the practical utility of near-term quantum computing for graph-based unsupervised learning in financial applications.

量子计算金融聚类图学习无监督

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