论文标题
基于密度聚类的几何重建
Geometric reconstructions of density based clusterings
论文作者
论文摘要
DBSCAN*和HDBSCAN*是基于密度良好的聚类算法。但是，获得非常大数据集的簇是不可行的，从而限制了它们在现实世界应用中的使用。 通过利用欧几里得空间的几何形状，我们证明可以系统地构建有限的$ x \ subset \ subset \ mathbb {r}^n $的dbscan*和hdbscan*簇，从$ x $的特定子集中。我们能够控制这些子集的大小，因此我们的结果使得群集非常大的数据集成为可能。 为了说明我们的理论，我们将美国的Microsoft构建足迹数据库聚集，这是不可能使用标准实现的。
DBSCAN* and HDBSCAN* are well established density based clustering algorithms. However, obtaining the clusters of very large datasets is infeasible, limiting their use in real world applications. By exploiting the geometry of Euclidean space, we prove that it is possible to systematically construct the DBSCAN* and HDBSCAN* clusters of a finite $X\subset \mathbb{R}^n$ from specific subsets of $X$. We are able to control the size of these subsets and therefore our results make it possible to cluster very large datasets. To illustrate our theory, we cluster the Microsoft Building Footprint Database of the US, which is not possible using the standard implementations.
