Parallel Modularity Clustering

Fender, Alexandre; Emad, Nahid; Petiton, Serge G.; Naumov, Maxim

doi:10.1016/j.procs.2017.05.198

Cited by 8 publications

(7 citation statements)

References 12 publications

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“…We will use the Greedy Modularity algorithm [7] though the Louvain algorithm [3] is known to have a better run-time. A more recent example can be found in [8]. Algorithms based on modularity continue to be used to identify clusterings [4].…”

Section: Modularitymentioning

confidence: 99%

Modularity and Heavy-Tailed Degree Distributions

Wilson

2021

Preprint

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Identifying clusters of vertices in graphs continues to be an important problem, and modularity continues to be used as a tool for solving the problem. Modularity, which measures the quality of a division of the vertices into clusters, explicitly treats vertices of different degrees differently, imposing a larger penalty when high-degree vertices are put in the same cluster. We claim that this unequal treatment negatively impacts the performance of clustering algorithms based on modularity for graphs with heavy-tailed degree distributions. We used the Greedy Modularity hill-climb to find clusters in graphs with power-law degree distributions and observed that it performed poorly clustering low-degree vertices. We propose a simple variant of modularity that we call flat modularity. We found that, using the same algorithm with the modified score instead, we improved the performance of the clustering algorithm on low-degree vertices and the overall performance as well. We believe that the small change-from modularity to flat modularity-could improve the output in the many real-world processes that rely on modularity to measure the quality of a division into clusters with only a small change, which is really a simplification, to the implementation. 2020 Mathematics Subject Classification. 68R10.

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Section: Modularitymentioning

confidence: 99%

Modularity and Heavy-Tailed Degree Distributions

Wilson

2021

Preprint

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“…9. Notice that in spectral clustering it is possible to compute a smaller number of eigenpairs than clusters [8] and in these experiments we have varied them synchronously until 32, after which we have fixed the number of eigenpairs pairs and increased the number of clusters only. The limit of 32 was chosen somewhat arbitrarily based on tradeoffs between computation time, memory usage and quality.…”

Section: Spectral Schemes (Gpu)mentioning

confidence: 99%

Parallel jaccard and related graph clustering techniques

Fender

Emad

Petiton

et al. 2017

Proceedings of the 8th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems

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In this paper we propose to generalize Jaccard and related measures, often used as similarity coefficients between two sets. We define Jaccard, Dice-Sorensen and Tversky edge weights on a graph and generalize them to account for vertex weights. We develop an efficient parallel algorithm for computing Jaccard edge and PageRank vertex weights. We highlight that the weights computation can obtain more than 10× speedup on the GPU versus CPU on large realistic data sets. Also, we show that finding a minimum balanced cut for modified weights can be related to minimizing the sum of ratios of the intersection and union of nodes on the boundary of clusters. Finally, we show that the novel weights can improve the quality of the graph clustering by about 15% and 80% for multi-level and spectral graph partitioning and clustering schemes, respectively.

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“…Fender et al used a parallelized version of the Lanczos iterations to identify the dominant eigenvectors in the adjacency matrix of an input graph. 8 The graph nodes projected onto the eigenvectors are then clustered using the k-means algorithm to approximate the clusters, which would have been obtained by a direct modularity optimization. Empirical evaluation of Fender's algorithm shows that the algorithm can infer a flat set of clusters from an input graph, while achieving a significant speed-up at the same time.…”

Section: Related Workmentioning

confidence: 99%

“…Several seminal distributed and parallel algorithms have been proposed for clustering by leveraging the modularity metric. () Typical modularity maximization algorithms assign ranks to the vertices or edges and based on the ranks assigned determine the vertices to be moved to the neighboring clusters or the edges to be part of the contraction set. Edges in the contraction set are then coalesced to merge two or more related clusters.…”

Section: Related Workmentioning

confidence: 99%

“…Fender et al used a parallelized version of the Lanczos iterations to identify the dominant eigenvectors in the adjacency matrix of an input graph . The graph nodes projected onto the eigenvectors are then clustered using the k‐means algorithm to approximate the clusters, which would have been obtained by a direct modularity optimization.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

A distributed parallel algorithm for inferring hierarchical groups from large‐scale text corpuses

Seshadri¹,

Mercy²,

Manohar³

2017

Concurrency and Computation

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Summary We propose a distributed parallel algorithm for inferring the hierarchical groups present in a large‐scale text corpus. The algorithm is designed to deal with corpuses that typically do not fit into the main memory of a workstation computer. The key contribution of this paper lies in its proposal and verification of a parallel distributed algorithm that exploits the advantages of two complementary techniques based on (i) localized modularity optimization and (ii) spectral clustering. Based on our experimental observations, these are complementary in the sense that the former excels at finding coarse groups in a large‐scale network, while the latter demands a heavy memory footprint but is effective in inferring tightly knit fine‐grained groups. Empirical evaluation of the distributed implementation scheme shows that the algorithm exhibits a significant speed‐up when compared to existing algorithms like Louvain and, at the same time, produces better quality clusters than either Louvain or spectral clustering algorithms in terms of the F‐score and Rand index.

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Parallel Modularity Clustering

Abstract: International audienc

Cited by 8 publications

References 12 publications

Modularity and Heavy-Tailed Degree Distributions

Modularity and Heavy-Tailed Degree Distributions

Parallel jaccard and related graph clustering techniques

A distributed parallel algorithm for inferring hierarchical groups from large‐scale text corpuses

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