Local Linear Discriminant Analysis (LLDA) for group and region of interest (ROI)-based fMRI analysis Martin J. McKeown, a,b,c, ⁎ Junning Li, d Xuemei Huang, e Mechelle M. Lewis, e Seungshin Rhee, f K.N. Young Truong, f and Z. Jane Wang c,d a Pacific Parkinson’s Research Centre, University of British Columbia, Vancouver, Canada b Department of Medicine (Neurology), University of British Columbia, Vancouver, Canada c Brain Research Centre, University of British Columbia, Vancouver, Canada d Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, Canada e Department of Neurology, School of Medicine, University of North Carolina, Chapel Hill, NC 27599, USA f Department of Biostatistics, School of Public Health, University of North Carolina, Chapel Hill, NC 27599, USA Received 17 October 2006; revised 18 March 2007; accepted 19 April 2007 Available online 26 May 2007 A post-processing method for group discriminant analysis of fMRI is proposed. It assumes that the fMRI data have been pre-processed and analyzed so that each voxel is given a statistic specifying task-related activation(s), and that individually specific regions of interest (ROIs) have been drawn for each subject. The method then utilizes Local Linear Discriminant Analysis (LLDA) to jointly optimize the individually-specific and group linear combinations of ROIs that maximally discriminates between groups (or between tasks, if using the same subjects). LLDA tries to linearly transform each subject’s voxel- based activation statistics within ROIs to a common vector space of ROI combinations, enabling the relative similarity of different subjects’ activation to be assessed. We applied the method to data recorded from 10 normal subjects during a motor task expected to activate both cortical and subcortical structures. The proposed method detected activation in multiple cortical and subcortical structures that were not present when the data were analyzed by warping the data to a common space. We suggest that the method be applied to group fMRI data when warping to a common space may be ill-advised, such as examining activation in small subcortical structures susceptible to mis- registration, or examining older or neurological patient populations. © 2007 Elsevier Inc. All rights reserved. Keywords: Discriminant analysis; fMRI; Group analysis; Regions of interest Introduction Group analysis in fMRI is typically done in several consecutive steps. First, fMRI data are corrected for motion, despite the fact that most methods cannot easily distinguish changes in fMRI signal from that induced by motion (Liao et al., 2005, 2006). Data are then spatially transformed to a common space such as the atlas by Talaraich (Talairach and Tournoux, 1988) or the probabilistic space suggested by the Montreal Neurological Institute (Collins et al., 1998) to minimize intersubject differences. However, because of the variability in human brain anatomy, the inter-subject registration is typically imperfect, so spatial low-pass filtering (“smoothing”) is performed to de-emphasize anatomical differ- ences (Friston, 1996). Once data have been motion corrected, warped to a common space, and spatially smoothed, the task- related activation of a voxel of a subject k is estimated with linear regression techniques: Y k ¼ X k b k þ e k ; and Covðe k Þ¼ r 2 k V k ð1Þ where Y k is the T k × 1 time course of the voxel, X k is the T k × D design matrix containing the hypothesized activation (often incorporating estimates of the hemodynamic response function) as well as other covariates, ε k is the T k × 1 vector of residuals, σ k 2 is the homogeneous variance of the residuals, and V k is the correlation matrix. The subscript k indicates that all the variables are related to subject k. As fMRI data are typically not temporally white, data are often pre-whitened using a whitening matrix W k such that: W k V k W T k ¼ I ð2Þ (for an excellent summary the reader is referred to: Mumford and Nichols, 2006). If each term in Eq. (1) is pre-multiplied by W k , we have: Y k * ¼ X k *b k þ e k * ð3Þ www.elsevier.com/locate/ynimg NeuroImage 37 (2007) 855 – 865 ⁎ Corresponding author. Pacific Parkinson’s Research Centre, University of British Columbia (UBC) M31, Purdy Pavilion, University Hospital, UBC Site, 2221 Wesbrook Mall, Vancouver, British Columbia, Canada V6T 2B5. Fax: +1 604 822 7866. E-mail address: mmckeown@interchange.ubc.ca (M.J. McKeown). Available online on ScienceDirect (www.sciencedirect.com). 1053-8119/$ - see front matter © 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.neuroimage.2007.04.072