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Perfect Clustering in Very Sparse Diverse Multiplex Networks

arXiv 2507.19423 ↗First posted 25 Jul 2025stat.ML cs.LG math.STcited by 0

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Abstract (arXiv)

The paper studies the DIverse MultiPLEx Signed Generalized Random Dot Product Graph (DIMPLE-SGRDPG) network model (Pensky (2024)), where all layers of the network have the same collection of nodes. In addition, all layers can be partitioned into groups such that the layers in the same group are embedded in the same ambient subspace but otherwise matrices of connection probabilities can be all different. This setting includes majority of multilayer network models as its particular cases. The key task in this model is to recover the groups of layers with unique subspace structures, since the case where all layers of the network are embedded in the same subspace has been fairly well studied. Until now, clustering of layers in such networks was based on the layer-per-layer analysis, which required the multilayer network to be sufficiently dense. Nevertheless, in this paper we succeeded in pooling information in all layers together and providing a tensor-based methodology that ensures perfect clustering for a much sparser network. Our theoretical results, established under intuitive non-restrictive assumptions, assert that the new technique achieves perfect clustering under sparsity conditions that, up to logarithmic factors, coincide with the computational lower bound derived for a much simpler model.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 18 of its 28 references that are in the map. First posted on arXiv 25 Jul 2025.

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18 of 28 references.

References · 18

  1. 2017Statistical inference on random dot product graphs: a surveycited by 70
  2. 2017A statistical interpretation of spectral embedding: the generalised random dot product graphcited by 55
  3. 2017Tensor SVD: Statistical and Computational Limitscited by 53
  4. 2016Rate-Optimal Perturbation Bounds for Singular Subspaces with Applications to High-Dimensional Statisticscited by 45
  5. 2019Inference for multiple heterogeneous networks with a common invariant subspacecited by 39
  6. 2020Community Detection on Mixture Multi-layer Networks via Regularized Tensor Decompositioncited by 30
  7. 2019Community Detection for Hypergraph Networks via Regularized Tensor Power Iterationcited by 27
  8. 2020The multilayer random dot product graphcited by 19
  9. 2021Latent Space Model for Higher-order Networks and Generalized Tensor Decompositioncited by 13
  10. 2020Inference for Low-rank Tensors -- No Need to Debiascited by 12
  11. 2021ALMA: Alternating Minimization Algorithm for Clustering Mixture Multilayer Networkcited by 8
  12. 2021Clustering of Diverse Multiplex Networkscited by 8
6 more
  1. 2022Estimating Higher-Order Mixed Memberships via the ℓ2,∞ Tensor Perturbation Boundcited by 8
  2. 2020A Sharp Blockwise Tensor Perturbation Bound for Orthogonal Iterationcited by 5
  3. 2024Davis-Kahan Theorem in the two-to-infinity norm and its application to perfect clusteringcited by 4
  4. 2023Optimal Clustering of Discrete Mixtures: Binomial, Poisson, Block Models, and Multi-layer Networkscited by 3
  5. 2024Statistical Inference for Low-Rank Tensors: Heteroskedasticity, Subgaussianity, and Applicationscited by 3
  6. 2024Signed Diverse Multiplex Networks: Clustering and Inferencecited by 1

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