mlsanityData to 7 Oct 2026

Directed degree corrected mixed membership model and estimating community memberships in directed networks

arXiv 2109.07826 ↗First posted 16 Sep 2021stat.ML cs.LGcited by 2

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Abstract (arXiv)

This paper considers the problem of modeling and estimating community memberships of nodes in a directed network where every row (column) node is associated with a vector determining its membership in each row (column) community. To model such directed network, we propose directed degree corrected mixed membership (DiDCMM) model by considering degree heterogeneity. DiDCMM is identifiable under popular conditions for mixed membership network when considering degree heterogeneity. Based on the cone structure inherent in the normalized version of the left singular vectors and the simplex structure inherent in the right singular vectors of the population adjacency matrix, we build an efficient algorithm called DiMSC to infer the community membership vectors for both row nodes and column nodes. By taking the advantage of DiMSC's equivalence algorithm which returns same estimations as DiMSC and the recent development on row-wise singular vector deviation, we show that the proposed algorithm is asymptotically consistent under mild conditions by providing error bounds for the inferred membership vectors of each row node and each column node under DiDCMM. The theory is supplemented by a simulation study.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 23 of its 47 references that are in the map. First posted on arXiv 16 Sep 2021.

Builds on

23 of 47 references.

References · 23

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11 more
  1. 2013Hypothesis Testing for Automated Community Detection in Networkscited by 15
  2. 2016On Mixed Memberships and Symmetric Nonnegative Matrix Factorizationscited by 14
  3. 2013Semidefinite Programming Based Preconditioning for More Robust Near-Separable Nonnegative Matrix Factorizationcited by 13
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Cited by year

Citing papers per year: 2021: 2.

2 papers.

  1. 2021A useful criterion on studying consistent estimation in community detectioncited by 3
  2. 2021Overlapping and nonoverlapping modelscited by 0