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Given all pairwise weights (distances) among a set of objects, filteredgraphs provide a sparse representation by only keeping an important subset ofweights. Such graphs can be passed to graph clustering algorithms to generatehierarchical clusters. In particular, the directed bubble hierarchical tree(DBHT) algorithm on filtered graphs has been shown to produce good hierarchicalclusters for time series data.  We propose a new parallel algorithm for constructing triangulated maximallyfiltered graphs (TMFG), which produces valid inputs for DBHT, and a scalableparallel algorithm for generating DBHTs that is optimized for TMFG inputs. Inaddition to parallelizing the original TMFG construction, which has limitedparallelism, we also design a new algorithm that inserts multiple vertices oneach round to enable more parallelism. We show that the graphs generated by ournew algorithm have similar quality compared to the original TMFGs, while beingmuch faster to generate. Our new parallel algorithms for TMFGs and DBHTs are136--2483x faster than state-of-the-art implementations, while achieving up to41.56x self-relative speedup on 48 cores with hyper-threading, and achievebetter clustering results compared to the standard average-linkage andcomplete-linkage hierarchical clustering algorithms. We show that on a stockdata set, our algorithms produce clusters that align well with human experts'classification.

Parallel Filtered Graphs for Hierarchical Clustering