Spectral Clustering for Discrete Distributions
Zixiao Wang Dong Qiao Jicong Fan
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.