论文标题
用于几何聚类的变异瓦斯坦堡垒
Variational Wasserstein Barycenters for Geometric Clustering
论文作者
论文摘要
我们建议通过求解具有变化原理的Monge图来计算Wasserstein Barycenters（WBS）。我们讨论了WBS的度量属性，并探讨了它们的连接，尤其是Monge WBS与K-Means聚类和共聚类的连接。我们还讨论了Monge WBS在不平衡度量和球形领域的可行性。我们提出了两个新问题 - 正规化K-均值和Wasserstein Barycenter压缩。我们证明了VWB在解决这些与聚类有关的问题时的使用。
We propose to compute Wasserstein barycenters (WBs) by solving for Monge maps with variational principle. We discuss the metric properties of WBs and explore their connections, especially the connections of Monge WBs, to K-means clustering and co-clustering. We also discuss the feasibility of Monge WBs on unbalanced measures and spherical domains. We propose two new problems -- regularized K-means and Wasserstein barycenter compression. We demonstrate the use of VWBs in solving these clustering-related problems.
