Wasserstein Distance-based Spectral Clustering with Application to Transaction Data
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With the rapid development of online payment platforms, it is now possible to record massive transaction data. The economic behaviors are embedded in the transaction data for merchants using these platforms. Therefore, clustering on transaction data significantly contributes to analyzing merchants' behavior patterns. This may help the platforms provide differentiated services or implement risk management strategies. However, traditional methods exploit transactions by generating low-dimensional features, leading to inevitable information loss. To fully use the transaction data, we utilize the empirical cumulative distribution of transaction amount to characterize merchants. Then, we adopt Wasserstein distance to measure the dissimilarity between any two merchants and propose the Wasserstein-distance-based spectral clustering (WSC) approach. Considering the sample imbalance in real datasets, we incorporate indices based on local outlier factors to improve the clustering performance. Furthermore, to ensure feasibility if the proposed method on large-scale datasets with limited computational resources, we propose a subsampling version of WSC. 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.
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