L1 Regularized Regression Modeling of Functional Connectivity

A network is referred to as ‘dense’ when there are a large number of connections between nodes in the network. A sparse network sparse network alternatively has a small number of connected nodes. At times it is beneficial to ‘sparsify’ a dense network to make the data easier to interpret. The brain itself is a very dense network with brain regions representing the nodes of the network, and the neurological pathways between regions representing the connections. We chose to investigate the statistical method known as the Least Absolute Selection and Shrinkage Operator least absolute selection and shrinkage operator (LASSO), as proposed by Tibshirani et. al. (J Roy Stat Soc B 58.1:267–288, 1996), as a feature selection tool to be applied to functional connectivity data. This method is useful in cases when the number of subjects is significantly less than the number of variables. A shrinkage parameter causes a number of variables to be shrunk to zero, creating a sparser network. In this chapter, we analyze data from 86 social regions of the brain of 60 subjects that were identified as either neuro-typical disorder (TD) or autism spectrum disorder (ASD). This created a network with 3656 pairwise correlations as predictor variables. At the same time, LASSO fits the remaining variables to a model which can be used to ‘predict’ whether a subject belongs to the TD or ASD classification.