| We extend a classical multivariate technique: Linear Discriminant Analysis (LDA) and apply it in the analysis of PET and fMRI images of human brain function to discover regions of activation driven by the experimental stimuli. We re-examine and specialize some equivalences between LDA and: Canonical Correlation Analysis (CCA) and Multivariate ANOVA (MANOVA). Furthermore, efficient algorithms are derived to facilitate applying these multivariate models to extremely large image data. We deal with the ill-posed nature of the problem using spatial basis expansion and the penalization (with Penalized Discriminant Analysis (PDA) of Hastie et al. (1995)), and utilize efficient measures of predictive performance to optimize hyperparameters and validate the models in a robust fashion. We examine expanding the images into a 3D tensor-product B-spline and Wavelet basis and compare to the results obtained without expansion. Some parallels between our proposal and some of those currently popular in the neuroimage community are discussed. Another extension to PDA is derived and applied that allows one to model time series effects that exist in fMRI images. We conclude with many possible enhancements to the proposed paradigm. |
