Investigating the relation between functional connectivity in the brain and cognition by applying sparse canonical correlation analysis on fMRI data

Abstract

Canonical Correlation Analysis (CCA) is a multivariate correlation method pioneered by H. Hotelling at the beginning of the twentieth century, that is used to classify and measure the correlation patterns between two sets of variables. With time, both the number of observations and the number of variables in data sets became larger. In fact, data collections in fields like neuroscience appear to have a vast number of variables that often outnumber the number of observations. Due to the high dimensionality of such data sets, estimation methods such as the Classical CCA perform poorly, and the outcomes are either ill-conditioned or ambiguous. As a result, this opens the door to regularization techniques. The Sparse CCA (SCCA) model, which uses the Least Absolute Shrinkage and Selection Operator (LASSO) penalty to account for high-dimensional, is one of several regularisation methods available in the literature. In this dissertation, we will explain the procedure of applying the SCCA model on a high-dimensional fMRI data set, in a step wise procedure, to investigate the relation between the neural organisation of the brain, de fined by functional connectivity, and mind-wandering, which is measured through cognition. We will also provide a statistical explanation using this approach, indicating that a person in a resting state performing mind-wandering, has several functionally linked brain regions.