Brain kernel: A new spatial covariance function for fMRI data

Anqi Wu, Samuel A. Nastase, Christopher A. Baldassano, Nicholas B. Turk-Browne, Kenneth A. Norman, Barbara E. Engelhardt, Jonathan W. Pillow

Research output: Contribution to journalArticlepeer-review


A key problem in functional magnetic resonance imaging (fMRI) is to estimate spatial activity patterns from noisy high-dimensional signals. Spatial smoothing provides one approach to regularizing such estimates. However, standard smoothing methods ignore the fact that correlations in neural activity may fall off at different rates in different brain areas, or exhibit discontinuities across anatomical or functional boundaries. Moreover, such methods do not exploit the fact that widely separated brain regions may exhibit strong correlations due to bilateral symmetry or the network organization of brain regions. To capture this non-stationary spatial correlation structure, we introduce the brain kernel, a continuous covariance function for whole-brain activity patterns. We define the brain kernel in terms of a continuous nonlinear mapping from 3D brain coordinates to a latent embedding space, parametrized with a Gaussian process (GP). The brain kernel specifies the prior covariance between voxels as a function of the distance between their locations in embedding space. The GP mapping warps the brain nonlinearly so that highly correlated voxels are close together in latent space, and uncorrelated voxels are far apart. We estimate the brain kernel using resting-state fMRI data, and we develop an exact, scalable inference method based on block coordinate descent to overcome the challenges of high dimensionality (10-100K voxels). Finally, we illustrate the brain kernel's usefulness with applications to brain decoding and factor analysis with multiple task-based fMRI datasets.

Original languageEnglish (US)
Article number118580
StatePublished - Dec 15 2021

All Science Journal Classification (ASJC) codes

  • Neurology
  • Cognitive Neuroscience


  • Brain decoding
  • Brain kernel
  • Factor modeling
  • Gaussian process
  • Latent variable model
  • Resting-state fmri
  • Task fmri


Dive into the research topics of 'Brain kernel: A new spatial covariance function for fMRI data'. Together they form a unique fingerprint.

Cite this