Journal Article10.1093/BIOMET/ASZ068
Consistent community detection in multi-layer network data
Jing Lei,Kehui Chen,Brian Lynch +2 more
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TL;DR: The theorems show that, as compared to single-layer community detection, a multi-layer network provides much richer information that allows for consistent community detection from a much sparser network, with required edge density reduced by a factor of the square root of the number of layers.
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Abstract: SummaryWe consider multi-layer network data where the relationships between pairs of elements are reflected in multiple modalities, and may be described by multivariate or even high-dimensional vectors. Under the multi-layer stochastic block model framework we derive consistency results for a least squares estimation of memberships. Our theorems show that, as compared to single-layer community detection, a multi-layer network provides much richer information that allows for consistent community detection from a much sparser network, with required edge density reduced by a factor of the square root of the number of layers. Moreover, the multi-layer framework can detect cohesive community structure across layers, which might be hard to detect by any single-layer or simple aggregation. Simulations and a data example are provided to support the theoretical results.
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Citations
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Community Detection in General Hypergraph via Graph Embedding
Yaoming Zhen,Junhui Wang +1 more
TL;DR: In this paper, a null vertex is introduced to augment a non-uniform hypergraph into a uniform multi-hypergraph, and then embeds the multihop in a low-dimensional vector space such that vertices within the same community are close to each other.
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