Estimation and Clustering in Popularity Adjusted Block Model

Noroozi, Majid; Rimal, Ramchandra; Pensky, Marianna

doi:10.1111/rssb.12410

Cited by 11 publications

(9 citation statements)

References 39 publications

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“…The estimation procedure is formulated through theoretical means; it remains to be seen how the procedure compares to the practical estimation approach taken in Sections 4 and 6. The proof of the result adapts ideas from Noroozi et al (2021).…”

Section: A Concentration Inequality For Normal Lsmmentioning

confidence: 79%

“…With these preliminaries in place, we follow the proof of Theorem 1 in Noroozi et al (2021). By assumption, , Ẑ( k) , Ẑ( l) ) to be-tween estimated community subnetworks yields for the trace term in (A.10):…”

Section: A Concentration Inequality For Normal Lsmmentioning

confidence: 99%

“…(1.4) Specifications of the form (1.4) are common for connection probabilities in unweighted degree corrected or SC models. See degree corrected stochastic block models (DCBMs) in Karrer and Newman (2011), Gao et al (2018), or their extensions, popularity adjusted stochastic block models (PABMs) in Sengupta and Chen (2017), Noroozi et al (2021). While in the DCBM, "sociability" parameters are global, in the PABM, each node has a possibly different sociability parameter for each community in the network.…”

Section: Introductionmentioning

confidence: 99%

“…While in the DCBM, "sociability" parameters are global, in the PABM, each node has a possibly different sociability parameter for each community in the network. The models considered here are close in spirit to PABMs and we draw from the techniques in Noroozi et al (2021) to analyze them. However, our focus is on weighted networks where information may be encoded in the patterns of the edge weights rather than the existence of particular edges in a given network.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Block Dense Weighted Networks with Augmented Degree Correction

Leinwand¹,

Pipiras²

2021

Preprint

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Dense networks with weighted connections often exhibit a community like structure, where although most nodes are connected to each other, different patterns of edge weights may emerge depending on each node's community membership. We propose a new framework for generating and estimating dense weighted networks with potentially different connectivity patterns across different communities. The proposed model relies on a particular class of functions which map individual node characteristics to the edges connecting those nodes, allowing for flexibility while requiring a small number of parameters relative to the number of edges. By leveraging the estimation techniques, we also develop a bootstrap methodology for generating new networks on the same set of vertices, which may be useful in circumstances where multiple data sets cannot be collected. Performance of these methods are analyzed in theory, simulations, and real data.

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Section: A Concentration Inequality For Normal Lsmmentioning

confidence: 79%

Section: A Concentration Inequality For Normal Lsmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Block Dense Weighted Networks with Augmented Degree Correction

Leinwand¹,

Pipiras²

2021

Preprint

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“…Noroozi, Rimal, and Pensky, 2021+) relies on Sparse Subspace Clustering. The latent structure of the PABM provides a natural justification for SSC for the PABM and leads to an improvement over the previous implementation.…”

mentioning

confidence: 99%

Popularity Adjusted Block Models are Generalized Random Dot Product Graphs

Koo,

Tang,

Trosset

2021

Preprint

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We connect two random graph models, the Popularity Adjusted Block Model (PABM) and the Generalized Random Dot Product Graph (GRDPG), by demonstrating that the PABM is a special case of the GRDPG in which communities correspond to mutually orthogonal subspaces of latent vectors. This insight allows us to construct new algorithms for community detection and parameter estimation for the PABM, as well as improve an existing algorithm that relies on Sparse Subspace Clustering. Using established asymptotic properties of Adjacency Spectral Embedding for the GRDPG, we derive asymptotic properties of these algorithms. In particular, we demonstrate that the absolute number of community detection errors tends to zero as the number of graph vertices tends to infinity. Simulation experiments illustrate these properties.

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Special invited paper: The SCORE normalization, especially for heterogeneous network and text data

Jin

2023

Stat

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SCORE was introduced as a spectral approach to network community detection. Since many networks have severe degree heterogeneity, the ordinary spectral clustering (OSC) approach to community detection may perform unsatisfactorily. SCORE alleviates the effect of degree heterogeneity by introducing a new normalization idea in the spectral domain and makes OSC more effective. SCORE is easy to use and computationally fast. It adapts easily to new directions and sees an increasing interest in practice. In this paper, we review the basics of SCORE, the adaption of SCORE to network mixed membership estimation and topic modeling, and the application of SCORE in real data, including two datasets on the publications of statisticians. We also review the theoretical “ideology” underlying SCORE. We show that in the spectral domain, SCORE converts a simplicial cone to a simplex and provides a simple and direct link between the simplex and network memberships. SCORE attains an exponential rate and a sharp phase transition in community detection, and achieves optimal rates in mixed membership estimation and topic modeling.

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Estimation and Clustering in Popularity Adjusted Block Model

Cited by 11 publications

References 39 publications

Block Dense Weighted Networks with Augmented Degree Correction

Block Dense Weighted Networks with Augmented Degree Correction

Popularity Adjusted Block Models are Generalized Random Dot Product Graphs

Special invited paper: The SCORE normalization, especially for heterogeneous network and text data

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