Network classification with applications to brain connectomics

Abstract

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.

Learning Clique Subgraphs in Structural Brain Network Classification with Application to Crystallized Cognition

“…Their penalty factor pair ( λ , ρ ) is tuned over a 5 × 11 grid, where λ ∈ {10 −4 , 10 −3 , …, 1} × λ max and ρ ∈ {1, 10, 20, …, 100}, with ( λ max , ρ = 100) ensuring that all the coefficients are penalized to zero. As Arroyo Relión et al (2019) suggest, values of ρ < 1 do not result in node selection. This method is fitted with graphclass package in R. Screening method based on multiple testing with false discovery rate control (MT-FDR), where a two-sample t -test is performed on each edge in the network between the two groups.…”

“…This method is fitted with glmnet toolbox in Matlab ( http://www.stanford.edu/~hastie/glmnet_matlab ). Penalized graph classification (GC) approach ( Arroyo Relión et al, 2019 ), which also uses edge weights as predictors, but incorporates L 1 and group lasso penalty to promote sparsity in selection of edges and nodes. Their penalty factor pair ( λ , ρ ) is tuned over a 5 × 11 grid, where λ ∈ {10 −4 , 10 −3 , …, 1} × λ max and ρ ∈ {1, 10, 20, …, 100}, with ( λ max , ρ = 100) ensuring that all the coefficients are penalized to zero.…”

“…Fig. 5 displays the estimated results under optimal penalty pair for the GC approach ( Arroyo Relión et al, 2019 ). Although this approach identifies all the true signal edges under larger sample size, it also selects a larger number of false edges.…”

“… Durante et al (2018) developed a method for testing global and local changes in SC between groups, which gains power by accounting for dependence structure among edges through a Bayesian nonparametric modeling of the networks. Arroyo Relión et al (2019) proposed a graph classification method that uses edge weights as predictors and incorporates L 1 and group lasso penalty to penalize both the number of edges and the number of nodes selected.…”

Averages of unlabeled networks: Geometric characterization and asymptotic behavior

“…Other results of this type include additional work on asymptotics for network empirical means [Tang et al, 2016] and regression modeling with a network response variable, where for the latter there have been both frequentist [Cornea et al, ] and Bayesian [Durante and Dunson, 2014] proposals. Work in this area continues at a quick pace -see, for example, [Arroyo Relión et al, 2017], which proposes a classification model based on network-valued inputs and [Durante, Dunson and Vogelstein, 2017], which proposes a nonparametric Bayes model for distributions on populations of networks. Earlier efforts in this space have focused on the specific case of trees.…”