Premium
Estimation and clustering in popularity adjusted block model
Author(s) -
Noroozi Majid,
Rimal Ramchandra,
Pensky Marianna
Publication year - 2021
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12410
Subject(s) - cluster analysis , estimator , chen , popularity , computer science , spectral clustering , stochastic block model , adjacency matrix , theoretical computer science , graph , data mining , artificial intelligence , mathematics , statistics , biology , psychology , paleontology , social psychology
Abstract The paper considers the Popularity Adjusted Block model (PABM) introduced by Sengupta and Chen (Journal of the Royal Statistical Society Series B, 2018, 80 , 365–386). We argue that the main appeal of the PABM is the flexibility of the spectral properties of the graph which makes the PABM an attractive choice for modelling networks that appear in biological sciences. We expand the theory of PABM to the case of an arbitrary number of communities which possibly grows with a number of nodes in the network and is not assumed to be known. We produce estimators of the probability matrix and of the community structure and, in addition, provide non‐asymptotic upper bounds for the estimation and the clustering errors. We use the Sparse Subspace Clustering (SSC) approach for partitioning the network into communities, the approach that, to the best of our knowledge, has not been used for the clustering network data. The theory is supplemented by a simulation study. In addition, we show advantages of the PABM for modelling a butterfly similarity network and a human brain functional network.