Characterizing nonlinear relationships in functional imaging data using eigenspace maximal information canonical correlation analysis (emiCCA)

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Many important problems in the analysis of neuroimages can be formulated as discovering the relationship between two sets of variables, a task for which linear techniques such as canonical correlation analysis (CCA) have been commonly used. However, to further explore potential nonlinear processes that might co-exist with linear ones in brain function, a more flexible method is required. Here, we propose a new unsupervised and data-driven method, termed the eigenspace maximal information canonical correlation analysis (emiCCA), which is capable of automatically capturing the linear and/or nonlinear relationships between various data sets. A simulation confirmed the superior performance of emiCCA in comparison with linear CCA and kernel CCA (a nonlinear version of CCA). An emiCCA framework for functional magnetic resonance imaging (fMRI) data processing was designed and applied to data from a real motor execution fMRI experiment.

This analysis uncovered one linear (in primary motor cortex) and a few nonlinear networks (e.g., in the supplementary motor area, bilateral insula, and cerebellum). This suggests that these various task-related brain areas are part of networks that also contribute to the execution of movements of the hand. These results suggest that emiCCA is a promising technique for exploring various data.

Graphical abstract

A novel unsupervised and data-driven method termed eigenspace maximal information canonical correlation analysis (emiCCA) and a framework of fMRI data analysis using emiCCA are proposed. The crucial point of our work was to utilize the eigenvectors and eigenvalues from the eigenspaces of the maximal information coefficient (MIC) matrix as a new measure for assessing the relationships between two data sets.

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