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

  • Niels Mørch
  • Lars K. Hansen
  • Stephen C. Strother
  • Claus Svarer
  • David A. Rottenberg
  • Benny Lautrup
  • Robert Savoy
  • Olaf B. Paulson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1230)


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.


Multivariate brain modeling ill-posed learning generalization learning curves 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Niels Mørch
    • 1
    • 2
  • Lars K. Hansen
    • 2
  • Stephen C. Strother
    • 3
    • 4
  • Claus Svarer
    • 1
  • David A. Rottenberg
    • 3
    • 4
  • Benny Lautrup
    • 5
  • Robert Savoy
    • 6
  • Olaf B. Paulson
    • 1
  1. 1.Neurobiology Research UnitCopenhagen University Hospital, RigshospitaletCopenhagen ØDenmark
  2. 2.Department for Mathematical ModellingTechnical University of DenmarkLyngbyDenmark
  3. 3.Radiology and Neurology DepartmentsUniversity of MinnesotaUSA
  4. 4.PET Imaging ServiceMinneapolis VA Medical CenterMinnesotaUSA
  5. 5.Niels Bohr InstituteUniversity of CopenhagenCopenhagen Ø
  6. 6.Massachusetts General HospitalBostonUSA

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