This study proposes a strategy based on the Mapper algorithm, which utilizes topological data analysis to identify symptomatic agents in contagions by leveraging expert knowledge. The context of our paper is financial markets, where insiders may share private information through social links, and other agents may exhibit positive symptoms by opportunistically trading on this information. We verify and demonstrate our methods using both synthetic and empirical data on insider networks and stock market transactions. Recognizing the sensitive nature of insider trading cases, we design a conservative approach to minimize false positives, ensuring that innocent agents are not wrongfully implicated. The mapper-based method systematically outperforms other methods on synthetic data with ground truth. We also apply the method to empirical data and verify the results using a statistical validation method based on persistence homology. Our findings highlight that the proposed mapper-based technique successfully identifies a subpopulation of opportunistic agents within the information cascades. The adaptability of this method to diverse data types and sizes is demonstrated, with potential for tailoring for specific applications.

翻译：本研究提出了一种基于Mapper算法的策略，该方法利用拓扑数据分析，通过专家知识识别传染过程中的症状性代理。本文的研究背景为金融市场，其中内幕信息可能通过社交网络传播，而其他代理可能通过机会主义地利用该信息进行交易而表现出阳性症状。我们使用内幕网络和股票市场交易的合成数据与实证数据验证并展示了我们的方法。考虑到内幕交易案件的敏感性，我们设计了一种保守方法以最小化误报，确保无辜代理不会被错误牵连。基于Mapper的方法在具有真实标签的合成数据上系统性地优于其他方法。我们还将该方法应用于实证数据，并使用基于持续同调的统计验证方法对结果进行验证。我们的研究结果表明，所提出的基于Mapper的技术成功识别了信息级联中的机会主义代理子群体。该方法对不同数据类型和规模的适应性得到了验证，并具备针对特定应用进行定制的潜力。