With the rapid development of online payment platforms, it is now possible to record massive transaction data. Clustering on transaction data significantly contributes to analyzing merchants' behavior patterns. This enables payment platforms to provide differentiated services or implement risk management strategies. However, traditional methods exploit transactions by generating low-dimensional features, leading to inevitable information loss. In this study, we use the empirical cumulative distribution of transactions to characterize merchants. We adopt Wasserstein distance to measure the dissimilarity between any two merchants and propose the Wasserstein-distance-based spectral clustering (WSC) approach. Based on the similarities between merchants' transaction distributions, a graph of merchants is generated. Thus, we treat the clustering of merchants as a graph-cut problem and solve it under the framework of spectral clustering. To ensure feasibility of the proposed method on large-scale datasets with limited computational resources, we propose a subsampling method for WSC (SubWSC). The associated theoretical properties are investigated to verify the efficiency of the proposed approach. The simulations and empirical study demonstrate that the proposed method outperforms feature-based methods in finding behavior patterns of merchants.

翻译：随着在线支付平台的快速发展，记录海量交易数据已成为可能。对交易数据进行聚类有助于分析商户的行为模式，从而使支付平台能够提供差异化服务或实施风险管理策略。然而，传统方法通过生成低维特征来利用交易数据，这不可避免地导致信息损失。本研究采用交易的经验累积分布来表征商户，利用Wasserstein距离衡量任意两个商户之间的差异，并提出基于Wasserstein距离的谱聚类方法（WSC）。基于商户交易分布之间的相似性，构建商户图，从而将商户聚类问题视为图割问题，并在谱聚类框架下求解。为确保该方法在有限计算资源下适用于大规模数据集，我们提出了一种用于WSC的子采样方法（SubWSC），并研究了相关的理论性质以验证该方法的效率。模拟实验和实证研究表明，所提方法在发现商户行为模式方面优于基于特征的方法。