标题： 通过Wasserstein均值的多层聚类 显示英文标题

标题： Multilevel Clustering via Wasserstein Means

摘要： 我们提出了一种针对多级聚类问题的新方法，该方法旨在同时对每个组内的数据进行划分，并在潜在的大规模具有层次结构的数据集中发现组与组之间的分组模式。 我们的方法涉及在多个离散概率测度空间上的联合优化公式，这些空间配备了 Wasserstein 距离度量。 通过利用与计算 Wasserstein 平均问题的联系，我们提出了该问题的若干变体，这些变体可以采用快速优化算法。 建立了局部和全局聚类估计的一致性性质。 最后，展示了合成数据和真实数据的实验结果，以证明所提出方法的灵活性和可扩展性。 显示英文摘要

摘要： We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our method involves a joint optimization formulation over several spaces of discrete probability measures, which are endowed with Wasserstein distance metrics. We propose a number of variants of this problem, which admit fast optimization algorithms, by exploiting the connection to the problem of finding Wasserstein barycenters. Consistency properties are established for the estimates of both local and global clusters. Finally, experiment results with both synthetic and real data are presented to demonstrate the flexibility and scalability of the proposed approach.