用于层次聚类的并行过滤图
Parallel Filtered Graphs for Hierarchical Clustering
摘要：
给定一组对象之间的所有成对权重（距离），过滤图通过仅保留权重的重要子集来提供稀疏表示。这样的图可以被传递到图聚类算法以生成分层聚类。特别是，定向气泡层次树（DBHT）算法过滤图已被证明产生良好的层次聚类的时间序列数据。我们提出了一个新的并行算法，用于构建三角最大过滤图（TMFG），它产生有效的输入DBHT，和一个可扩展的并行算法生成DBHTs是优化TMFG输入。除了并行化原始的TMFG结构，这具有有限的并行性，我们还设计了一个新的算法，插入多个顶点上的每一轮，以实现更多的并行性。我们表明，我们的新算法生成的图形具有类似的质量相比，原来的TMFG，而更快地生成。我们的新的并行算法的TMFG和DBHT是136- 2483倍的速度比国家的最先进的实现，同时实现高达41.56倍的自相对加速48核与超线程，并实现更好的聚类结果相比，标准的平均链接和完全链接层次聚类算法。我们表明，在股票数据集上，我们的算法产生的聚类与人类专家的分类非常一致。
英文摘要：
Given all pairwise weights (distances) among a set of objects, filtered graphs provide a sparse representation by only keeping an important subset of weights. Such graphs can be passed to graph clustering algorithms to generate hierarchical clusters. In particular, the directed bubble hierarchical tree (DBHT) algorithm on filtered graphs has been shown to produce good hierarchical clusters for time series data. We propose a new parallel algorithm for constructing triangulated maximally filtered graphs (TMFG), which produces valid inputs for DBHT, and a scalable parallel algorithm for generating DBHTs that is optimized for TMFG inputs. In addition to parallelizing the original TMFG construction, which has limited parallelism, we also design a new algorithm that inserts multiple vertices on each round to enable more parallelism. We show that the graphs generated by our new algorithm have similar quality compared to the original TMFGs, while being much faster to generate. Our new parallel algorithms for TMFGs and DBHTs are 136--2483x faster than state-of-the-art implementations, while achieving up to 41.56x self-relative speedup on 48 cores with hyper-threading, and achieve better clustering results compared to the standard average-linkage and complete-linkage hierarchical clustering algorithms. We show that on a stock data set, our algorithms produce clusters that align well with human experts' classification.
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