通过子采样相似性查询更快的DBSCAN
Faster DBSCAN via subsampled similarity queries
摘要：
DBSCAN是一种流行的基于密度的聚类算法。它计算数据集的$ε$ -邻域图，并使用高度节点的连通分量来确定聚类。然而，全邻域图可能太昂贵而无法以$O(n^2)$的最坏情况复杂度来计算。在本文中，我们提出了一个简单的变种称为SNG-DBSCAN，它集群的基础上的一个子采样$ε$ -邻域图，只需要访问相似性查询对点，特别是避免了任何复杂的数据结构，需要嵌入的数据点本身。程序的运行时间为$O(sn^2)$，其中$s$为采样率。我们表明，在一些自然的理论假设下，$s \approx \log n/n$是足够的统计集群恢复保证导致$O(n\log n)$的复杂性。我们提供了一个广泛的实验分析，表明在大型数据集上，可以对邻域图的$0.1\%$进行子采样，与scikit-learn的DBSCAN实现相比，可以实现超过200倍的加速和250倍的RAM消耗减少，同时仍然保持有竞争力的聚类性能。
英文摘要：
DBSCAN is a popular density-based clustering algorithm. It computes the $ε$-neighborhood graph of a dataset and uses the connected components of the high-degree nodes to decide the clusters. However, the full neighborhood graph may be too costly to compute with a worst-case complexity of $O(n^2)$. In this paper, we propose a simple variant called SNG-DBSCAN, which clusters based on a subsampled $ε$-neighborhood graph, only requires access to similarity queries for pairs of points and in particular avoids any complex data structures which need the embeddings of the data points themselves. The runtime of the procedure is $O(sn^2)$, where $s$ is the sampling rate. We show under some natural theoretical assumptions that $s \approx \log n/n$ is sufficient for statistical cluster recovery guarantees leading to an $O(n\log n)$ complexity. We provide an extensive experimental analysis showing that on large datasets, one can subsample as little as $0.1\%$ of the neighborhood graph, leading to as much as over 200x speedup and 250x reduction in RAM consumption compared to scikit-learn's implementation of DBSCAN, while still maintaining competitive clustering performance.
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