Parallel Jaccard and Related Graph Clustering Techniques

Alexandre Fender (1, 2, 3) , Nahid Emad (4) , Serge Petiton (5) , Joe Eaton (6) , Maxim Naumov (7)

1 LI-PaRAD - Laboratoire d'Informatique Parallélisme Réseaux Algorithmes Distribués
2 MDLS - Maison de la Simulation
3 NVIDIA - NVIDIA
4 PRISM - Parallélisme, Réseaux, Systèmes, Modélisation
5 LIFL - Laboratoire d'Informatique Fondamentale de Lille
6 NVIDIA Research [Austin]
7 Nvidia Corporation [Santa Clara]

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.

Mots clés: Graph algorithms; Graph theory; Jaccard; Tversky; Laplacian; spectral clustering; community detection; graphs; networks; PageRank; CUDA; GPU

Domaines: Informatique [cs]

Alexandre Fender, Nahid Emad, Serge Petiton, Joe Eaton, Maxim Naumov. Parallel Jaccard and Related Graph Clustering Techniques. 8th Workshop on Latest Advances in Scalable Algo- rithms for Large-Scale Systems (ScalA17), Nov 2017, Denver, United States. ⟨10.1145/3148226.3148231⟩. ⟨hal-01667553⟩