标题： 金融机构的几何结构 -- 金融数据的Wasserstein聚类 显示英文标题

标题： The geometry of financial institutions -- Wasserstein clustering of financial data

摘要： 随着对各种感兴趣对象的细粒度和大数据的日益可用，有必要开发将这些信息压缩成具有代表性和易理解的地图的方法。金融监管是一个体现这一需求的领域，因为监管机构需要从金融机构获取多样且往往非常细粒度的数据来监控和评估其活动。然而，处理和分析此类数据可能是一项艰巨的任务，尤其是在处理缺失值和基于特定特征识别聚类的挑战方面。为了解决这些挑战，我们提出了一种适用于概率分布的Lloyd算法变体，并使用广义Wasserstein质心构建一个度量空间，以浓缩的形式表示各种对象上的数据。通过将我们的方法应用于金融监管的背景，我们展示了它在处理该领域监管机构所面临的具体挑战方面的有用性。我们认为，我们的方法还可以更广泛地应用于其他需要以简洁形式表示大型和复杂数据集的领域。 显示英文摘要

摘要： The increasing availability of granular and big data on various objects of interest has made it necessary to develop methods for condensing this information into a representative and intelligible map. Financial regulation is a field that exemplifies this need, as regulators require diverse and often highly granular data from financial institutions to monitor and assess their activities. However, processing and analyzing such data can be a daunting task, especially given the challenges of dealing with missing values and identifying clusters based on specific features. To address these challenges, we propose a variant of Lloyd's algorithm that applies to probability distributions and uses generalized Wasserstein barycenters to construct a metric space which represents given data on various objects in condensed form. By applying our method to the financial regulation context, we demonstrate its usefulness in dealing with the specific challenges faced by regulators in this domain. We believe that our approach can also be applied more generally to other fields where large and complex data sets need to be represented in concise form.