On spectral algorithms for community detection in stochastic blockmodel graphs with vertex covariates

  title={On spectral algorithms for community detection in stochastic blockmodel graphs with vertex covariates},
  author={Cong Mu and Angelo Mele and Lingxin Hao and Joshua Cape and Avanti Athreya and Carey E. Priebe},
  journal={IEEE Transactions on Network Science and Engineering},
  • Cong Mu, A. Mele, C. Priebe
  • Published 4 July 2020
  • Computer Science
  • IEEE Transactions on Network Science and Engineering
In network inference applications, it is often desirable to detect community structure. Beyond mere adjacency matrices, many real-world networks also involve vertex covariates that carry key information about underlying block structure in graphs. To assess the effects of such covariates on block recovery, we present a comparative analysis of two model-based spectral algorithms for clustering vertices in stochastic blockmodel graphs with vertex covariates. The first algorithm uses only the… 

Figures and Tables from this paper

Perfect Spectral Clustering with Discrete Covariates
This paper proposes a spectral algorithm that it is claimed achieves perfect clustering with high probability on a class of large, sparse networks with discrete covariates, effectively separating latent network structure from homophily on observed covariates.
A Time-Varying Network for Cryptocurrencies
It is shown that return inter-predictability and crypto characteristics, including hashing algorithms and proof types, jointly determine the crypto market segmentation and it is natural to employ eigenvector centrality to identify a cryptocurrency’s idiosyncratic risk.


On spectral embedding performance and elucidating network structure in stochastic blockmodel graphs
Abstract Statistical inference on graphs often proceeds via spectral methods involving low-dimensional embeddings of matrix-valued graph representations such as the graph Laplacian or adjacency
Spectral Inference for Large Stochastic Blockmodels With Nodal Covariates
The results in this paper provide a foundation to estimate the effect of observed covariates as well as unobserved latent community structure on the probability of link formation in networks.
Pairwise Covariates-adjusted Block Model for Community Detection
It is shown that both the coefficient estimates of the covariates and the community assignments are consistent under suitable sparsity conditions and PCABM compares favorably with the SBM or degree-corrected stochastic block model (DCBM) under a wide range of simulated and real networks when covariate information is accessible.
Community Detection and Classification in Hierarchical Stochastic Blockmodels
This work proposes a robust, scalable, integrated methodology for community detection and community comparison in graphs, and addresses the problem of locating similar sub-communities in a partially reconstructed Drosophila connectome and in the social network Friendster.
Covariate-assisted spectral clustering
This work applies the clustering method to large brain graphs derived from diffusion MRI data, using the node locations or neurological region membership as covariates, and yields results superior both to regularized spectral clustering without node covariates and to an adaptation of canonical correlation analysis.
A Consistent Adjacency Spectral Embedding for Stochastic Blockmodel Graphs
It is proved that this method to estimate block membership of nodes in a random graph generated by a stochastic blockmodel is consistent for assigning nodes to blocks, as only a negligible number of nodes will be misassigned.
Statistical Inference on Random Dot Product Graphs: a Survey
This survey paper describes a comprehensive paradigm for statistical inference on random dot product graphs, a paradigm centered on spectral embeddings of adjacency and Laplacian matrices, and investigates several real-world applications, including community detection and classification in large social networks and the determination of functional and biologically relevant network properties from an exploratory data analysis of the Drosophila connectome.
Spectral clustering and the high-dimensional stochastic blockmodel
The asymptotic results in th is paper are the first clustering results that allow the number of clusters in the model to grow with theNumber of nodes, hence the name high-dimensional.
Likelihood Inference for Large Scale Stochastic Blockmodels With Covariates Based on a Divide-and-Conquer Parallelizable Algorithm With Communication
  • Sandipan Roy, Y. Atchadé, G. Michailidis
  • Computer Science
    Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
  • 2019
A fast, scalable Monte Carlo EM type algorithm based on case-control approximation of the log-likelihood coupled with a subsampling approach is devised for analyzing social network data equipped with node covariate information.
Community detection and stochastic block models: recent developments
  • E. Abbe
  • Computer Science
    J. Mach. Learn. Res.
  • 2017
The recent developments that establish the fundamental limits for community detection in the stochastic block model are surveyed, both with respect to information-theoretic and computational thresholds, and for various recovery requirements such as exact, partial and weak recovery.