  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.
