Spectral Clustering for Discrete Distributions

Discrete distribution clustering (D2C) was often solved by Wasserstein barycenter methods. These methods are under a common assumption that clusters can be well represented by barycenters, which may not hold in many real applications. In this work, we propose a simple yet effective framework based on spectral clustering and distribution affinity measures (e.g., maximum mean discrepancy and Wasserstein distance) for D2C. To improve the scalability, we propose to use linear optimal transport to construct affinity matrices efficiently on large datasets. We provide theoretical guarantees for the success of the proposed methods in clustering distributions. Experiments on synthetic and real data show that our methods outperform the baselines largely in terms of both clustering accuracy and computational efficiency.