论文标题
度量测量空间中点之间的相似性
Similarity Between Points in Metric Measure Spaces
论文作者
论文摘要
本文是关于对象之间的相似性，这些对象可以表示为度量度量空间中的点。度量测量空间是一个装备量度的度量空间。例如，在其节点和重量分配给节点之间具有距离的网络是度量测量空间。给定点x和y在不同的度量度量空间或同一空间中，它们有多相似？一种众所周知的方法是考虑x和y的邻居相似。对于度量度量空间，Gromov-Hausdorff-Prokhorov距离很好地捕获了社区之间的相似性，但是即使在非常简单的情况下，也可以计算此距离也是NP。我们提出了一种可拖动的替代方法：X和Y邻域之间的径向分布距离。基于径向分布距离的相似性度量比基于Gromov-Hausdorff-Prokhorov距离的相似性要粗糙，但要容易得多。
This paper is about similarity between objects that can be represented as points in metric measure spaces. A metric measure space is a metric space that is also equipped with a measure. For example, a network with distances between its nodes and weights assigned to its nodes is a metric measure space. Given points x and y in different metric measure spaces or in the same space, how similar are they? A well known approach is to consider x and y similar if their neighborhoods are similar. For metric measure spaces, similarity between neighborhoods is well captured by the Gromov-Hausdorff-Prokhorov distance, but it is NP-hard to compute this distance even in quite simple cases. We propose a tractable alternative: the radial distribution distance between the neighborhoods of x and y. The similarity measure based on the radial distribution distance is coarser than the similarity based on the Gromov-Hausdorff-Prokhorov distance but much easier to compute.
