%0 Journal Article
%T Extending Local Canonical Correlation Analysis to Handle General Linear Contrasts for fMRI Data
%A Mingwu Jin
%A Rajesh Nandy
%A Tim Curran
%A Dietmar Cordes
%J International Journal of Biomedical Imaging
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/574971
%X Local canonical correlation analysis (CCA) is a multivariate method that has been proposed to more accurately determine activation patterns in fMRI data. In its conventional formulation, CCA has several drawbacks that limit its usefulness in fMRI. A major drawback is that, unlike the general linear model (GLM), a test of general linear contrasts of the temporal regressors has not been incorporated into the CCA formalism. To overcome this drawback, a novel directional test statistic was derived using the equivalence of multivariate multiple regression (MVMR) and CCA. This extension will allow CCA to be used for inference of general linear contrasts in more complicated fMRI designs without reparameterization of the design matrix and without reestimating the CCA solutions for each particular contrast of interest. With the proper constraints on the spatial coefficients of CCA, this test statistic can yield a more powerful test on the inference of evoked brain regional activations from noisy fMRI data than the conventional t-test in the GLM. The quantitative results from simulated and pseudoreal data and activation maps from fMRI data were used to demonstrate the advantage of this novel test statistic. 1. Introduction The General Linear Model (GLM) is a widely used mass univariate analysis method to determine brain activations in functional magnetic resonance imaging (fMRI) because of its simplicity in both estimation and inference and its greater sensitivity to regional effects than global multivariate analyses [1]. The least-squares (LS) solution of the GLM is the minimum variance unbiased (MVU) estimator when Gaussian white noise assumption is satisfied, otherwise the weighted LS solution (using the inverse of the noise covariance matrix) becomes the best linear unbiased estimator (BLUE) [2]. The estimated parameters and their variances are used to construct various contrast statistics, either or , to test the null hypothesis of effects of interest. Another popular approach to analyze fMRI time series uses the correlation coefficient [3]. The statistical significance of the correlation coefficient is equivalent to a -statistic testing for a regression on one single regressor [4]. The correlation coefficient is more restricted in assessing the significance of regional effects than the -test in fMRI data analysis because the correlation coefficient does not allow more than one regressor to be included for a direct calculation. It is known, however, that the partial correlation coefficient is also equivalent to a -test and thus could potentially be used
%U http://www.hindawi.com/journals/ijbi/2012/574971/