Estimation and Clustering in Popularity Adjusted Stochastic Block Model
arXiv:1902.00431
Abstract
The paper considers the Popularity Adjusted Block model (PABM) introduced by Sengupta and Chen (2018). 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 modeling 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 the estimators of the probability matrix and the community structure and provide non-asymptotic upper bounds for the estimation and the clustering errors. We use the Sparse Subspace Clustering (SSC) approach to partition the network into communities, the approach that, to the best of our knowledge, has not been used for clustering network data. The theory is supplemented by a simulation study. In addition, we show advantages of the PABM for modeling a butterfly similarity network and a human brain functional network.
arXiv comment39 pages, 5 figures
References in corpus (7)
- Robust Recovery of Subspace Structures by Low-Rank Representation
- Stochastic blockmodels and community structure in networks
- A geometric analysis of subspace clustering with outliers
- Sharp nonasymptotic bounds on the norm of random matrices with independent entries
- Network Enhancement: a general method to denoise weighted biological networks
- Mixed Membership Estimation for Social Networks
- Spectral radii of sparse random matrices