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，大规模交易数据的记录已成为可能。对交易数据进行聚类分析，有助于揭示商户的行为模式，从而为支付平台提供差异化服务或实施风险管理策略提供支持。然而，传统方法通过提取低维特征来处理交易数据，不可避免地导致信息损失。本研究采用交易数据的经验累积分布来表征商户，并引入Wasserstein距离衡量任意两个商户之间的差异，进而提出基于Wasserstein距离的谱聚类方法（WSC）。通过构建基于商户交易分布相似度的商户关联图，我们将商户聚类问题转化为图切割问题，并在谱聚类框架下求解。为保障该方法在有限计算资源下处理大规模数据集的可行性，我们进一步提出适用于WSC的子采样方法（SubWSC），并研究了其相关理论性质以验证方法的有效性。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传统方法。