The Annals of Applied Statistics

Network classification with applications to brain connectomics

Jesús D. Arroyo Relión, Daniel Kessler, Elizaveta Levina, and Stephan F. Taylor

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While statistical analysis of a single network has received a lot of attention in recent years, with a focus on social networks, analysis of a sample of networks presents its own challenges which require a different set of analytic tools. Here we study the problem of classification of networks with labeled nodes, motivated by applications in neuroimaging. Brain networks are constructed from imaging data to represent functional connectivity between regions of the brain, and previous work has shown the potential of such networks to distinguish between various brain disorders, giving rise to a network classification problem. Existing approaches tend to either treat all edge weights as a long vector, ignoring the network structure, or focus on graph topology as represented by summary measures while ignoring the edge weights. Our goal is to design a classification method that uses both the individual edge information and the network structure of the data in a computationally efficient way, and that can produce a parsimonious and interpretable representation of differences in brain connectivity patterns between classes. We propose a graph classification method that uses edge weights as predictors but incorporates the network nature of the data via penalties that promote sparsity in the number of nodes, in addition to the usual sparsity penalties that encourage selection of edges. We implement the method via efficient convex optimization and provide a detailed analysis of data from two fMRI studies of schizophrenia.

Article information

Ann. Appl. Stat., Volume 13, Number 3 (2019), 1648-1677.

Received: January 2017
Revised: January 2019
First available in Project Euclid: 17 October 2019

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Graph classification high-dimensional data variable selection fMRI data


Arroyo Relión, Jesús D.; Kessler, Daniel; Levina, Elizaveta; Taylor, Stephan F. Network classification with applications to brain connectomics. Ann. Appl. Stat. 13 (2019), no. 3, 1648--1677. doi:10.1214/19-AOAS1252.

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Supplemental materials

  • Supplement A: Algorithms, proofs, and data aquisition and preprocessing details. In this supplementary material, we provide the details of the optimization algorithms, proof of the theoretical results and a detailed description of the data aquisition and preprocessing.
  • Supplement B: Code and data. The .zip file contains source code of an R package that implements the methods described in this paper, as well as the post-processed connectomes used in the analysis.