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Overlapping and nonoverlapping models

arXiv 2111.01392 ↗First posted 2 Nov 2021cs.SI cs.LG physics.soc-phcited by 0

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Abstract (arXiv)

Consider a directed network with Kr row communities and Kc column communities. Previous works found that modeling directed networks in which all nodes have overlapping property requires Kr=Kc for identifiability. In this paper, we propose an overlapping and nonoverlapping model to study directed networks in which row nodes have overlapping property while column nodes do not. The proposed model is identifiable when Kr≤ Kc. Meanwhile, we provide one identifiable model as extension of ONM to model directed networks with variation in node degree. Two spectral algorithms with theoretical guarantee on consistent estimations are designed to fit the models. A small scale of numerical studies are used to illustrate the algorithms.

Key facts. No citing papers in the map yet (data through 13 Oct 2026). Builds on 12 of its 23 references that are in the map. First posted on arXiv 2 Nov 2021.

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12 of 23 references.

References · 12

  1. 2013Consistency of spectral clustering in stochastic block modelscited by 128
  2. 2013Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodelcited by 45
  3. 2013Impact of regularization on Spectral Clusteringcited by 25
  4. 2014Detecting Overlapping Communities in Networks Using Spectral Methodscited by 22
  5. 2017Estimating Mixed Memberships with Sharp Eigenvector Deviationscited by 22
  6. 2018Analysis of spectral clustering algorithms for community detection: the general bipartite settingcited by 20
  7. 2020Spectral Algorithms for Community Detection in Directed Networkscited by 17
  8. 2013Semidefinite Programming Based Preconditioning for More Robust Near-Separable Nonnegative Matrix Factorizationcited by 13
  9. 2018Overlapping Clustering Models, and One (class) SVM to Bind Them Allcited by 10
  10. 2021A useful criterion on studying consistent estimation in community detectioncited by 3
  11. 2021Directed mixed membership stochastic blockmodelcited by 2
  12. 2021Directed degree corrected mixed membership model and estimating community memberships in directed networkscited by 2

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