Abstract
Graph clustering, also often referred to as network community detection, is the process of assigning common labels to vertices that are densely connected to each other but sparsely connected to the rest of the graph. There are many different approaches to clustering in the literature. However, in this article, we formulate the clustering problem as a combinatorial optimization problem. Our main contribution is a novel problem formulation that maximizes intra-cluster density, a statistically meaningful quantity. It requires the number of clusters, a softbound on cluster size and a penalty coefficient as parameter inputs. More importantly, it is designed to prevent common degeneracies, like the so-called “mega-clusters”. We end with some suggestions on numerical solution techniques and note that an ensemble-like optimization routine seems promising.
Note on vocabulary: Although there are subtle differences between the concepts of graph clustering and network community detection, in this document we use the two interchangeably.
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Miasnikof, P., Pitsoulis, L., Bonner, A.J., Lawryshyn, Y., Pardalos, P.M. (2020). Graph Clustering Via Intra-Cluster Density Maximization. In: Bychkov, I., Kalyagin, V., Pardalos, P., Prokopyev, O. (eds) Network Algorithms, Data Mining, and Applications. NET 2018. Springer Proceedings in Mathematics & Statistics, vol 315. Springer, Cham. https://doi.org/10.1007/978-3-030-37157-9_3
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