Working with high-dimensional feature spaces: The example of voxel-wise encoding models

Mohammad Babakmehr, Ghislain St-Yves, Thomas Naselaris

Research output: Chapter in Book/Report/Conference proceedingChapter


This chapter discusses the issue of high-dimensional data in the context of machine learning studies of brain disorders, using the voxel-wise modeling of functional neuroimaging data as exemplar framework. First, we contrast voxel-wise modeling to other approaches such as multivariate pattern analysis. Second, we lay out the critical components in developing a voxel-wise encoding model: these include a feature space encapsulating a set of hypotheses about what the brain activity represents and a (near-linear) regression of that feature space in brain activity. Third, we discuss two complementary approaches to perform the regularization of the regression that is necessary to tackle very high-dimensional feature spaces: these include training regularization and structural regularization, i.e., constraints on the parameter space of the model. Finally, we point out how the quantitative aspect of voxel-wise modeling can lead to better hypothesis testing and improve multisubject comparison in the context of brain disorders.

Original languageEnglish (US)
Title of host publicationMachine Learning
Subtitle of host publicationMethods and Applications to Brain Disorders
Number of pages16
ISBN (Electronic)9780128157398
StatePublished - Jan 1 2019
Externally publishedYes


  • Deep learning networks
  • Feature maps
  • Gabor wavelets
  • High-dimensional data
  • Linear models
  • Machine learning
  • Voxel-wise encoding models


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