Improving CCA based fMRI Analysis by Covariance Pooling - Using the GPU for Statistical Inference

Canonical correlation analysis (CCA) is a statistical method that can be preferable to the general linear model (GLM) for analysis of functional magnetic resonance imaging (fMRI) data. There are, however, two problems with CCA based fMRI analysis. First, it is not feasible to use a parametric approach to calculate an activity threshold for a certain significance level. Second, two covariance matrices need to be estimated in each voxel, from a rather small number of time samples. We recently solved the first problem by doing random permutation tests on the graphics processing unit (GPU), such that the null distribution of any maximum test statistics can be estimated in the order of minutes. In this paper we consider the second problem. We extend the idea of variance pooling, that previously has been used for the GLM, to covariance pooling to improve the estimates of the covariance matrices. Our GPU implementation of random permutation tests is used to calculate significance thresholds, which are needed to compare the different activity maps in an objective way. The covariance pooling results in more robust estimates of the covariance matrices. The number of significantly active voxels that are detected (thresholded at p = 0.05, corrected for multiple comparisons) is increased with 40 120% (if 8 mm smoothing is applied to the covariance estimates). Too much covariance pooling can however result in a loss of small activity clusters, 7-10 mm of smoothing gives the best results. The calculations that were made in order to generate the results in this paper would have taken a total of about 65 days with a Matlab implementation and about 10 days with a multithreaded C implementation, with our multi-GPU implementation they took about 2 hours. By using fast random permutation tests, suggested improvements of existing methods for fMRI analysis can be evaluated in an objective way.