01 Mar

Christian Brownlees, “Community Detection in Partial Correlation Networks”

Friday March 11 2016
10:30
Scuola Normale Superiore
Aula Bianchi

Christian Brownlees
Universitat Pompeu Fabra, Barcelona

Abstract

In this work we propose a community detection algorithm for partial correlation networks. We assume that the variables in the network are partitioned into communities. The presence of nonzero partial correlation between two variables is determined by a Bernoulli trial whose probability depends on whether the variables belong to the same community or not. The community partition is assumed to be unobserved and the goal is to recover it from a sample of observations. To tackle this problem we introduce a community detection algorithm called Blockbuster. The algorithm detects communities by applying k-means clustering to the eigenvectors corresponding to the largest eigenvalues of the sample covariance matrix. We study the properties of the procedure and show that Blockbuster consistently detects communities when the network dimension and the sample size are large. The methodology is used to study real activity clustering in the United States.