论文标题
固有的分层聚类行为恢复了更高的维度信息
Intrinsic Hierarchical Clustering Behavior Recovers Higher Dimensional Shape Information
论文作者
论文摘要
我们表明，可以通过观察较低维层次群集动力学来恢复点云数据的特定更高的形状信息。我们从点云中生成多个点样本，并在每个样品中执行分层聚类以产生树状图。从这些树状图中，我们采用群集的演化和合并数据，以构建捕获聚类行为的数据来构建简化的图表，这些图记录了类似于零维持续图在拓扑数据分析中的群集的寿命。我们使用瓶颈度量标准比较了这些图表之间的差异，并检查所得分布。最后，我们表明，从这些瓶颈距离分布中绘制的统计特征检测到伪像的人物，并可以挖掘以恢复更高的尺寸形状特征。
We show that specific higher dimensional shape information of point cloud data can be recovered by observing lower dimensional hierarchical clustering dynamics. We generate multiple point samples from point clouds and perform hierarchical clustering within each sample to produce dendrograms. From these dendrograms, we take cluster evolution and merging data that capture clustering behavior to construct simplified diagrams that record the lifetime of clusters akin to what zero dimensional persistence diagrams do in topological data analysis. We compare differences between these diagrams using the bottleneck metric, and examine the resulting distribution. Finally, we show that statistical features drawn from these bottleneck distance distributions detect artefacts of, and can be tapped to recover higher dimensional shape characteristics.
