Nonlinear versus linear models in functional neuroimaging: Learning curves and generalization crossover

We introduce the concept of generalization for models of functional neuroactivation, and show how it is affected by the number, N, of neuroimaging scans available. By plotting generalization as a function of N (i.e. a “learning curve”) we demonstrate that while simple, linear models may generalize better for small N's, more flexible, low-biased nonlinear models, based on artificial neural networks (ANN's), generalize better for larger N's. We demonstrate that for sets of scans of two simple motor tasks—one set acquired with [O15]water using PET, and the other using fMRI—practical N's exist for which “generalization crossover” occurs. This observation supports the application of highly flexible, ANN models to sufficiently large functional activation datasets.