How does activity in the brain relate to things in the world? How does the brain represent stimuli, actions, and concepts? The brain processes information in a distributed manner, so models of neuronal representations need to take into account the full activity pattern in a brain region, not just the level of average activity. In the fMRI field there are many analysis methods that attempt to build and evaluate such models, coming under a variety of names, including multi-voxel pattern, decoding, classification, representational similarity analysis, population receptive field models, and encoding models. Our lab is working on improving the statistical methods in this new field. We have provided a general framework, showning that nearly all representational techniques can be understood as testing specific aspects of the distribution of neurons or voxels in the space of experimental conditions (Diedrichsen & Kriegeskorte, 2017).

Multivariate brain activity data visualized by plotting the activity of each neuron or voxel (measurement channel) in the space of experimental conditions, or by plotting the multivariate activity pattern in the space of channels. Encoding models describe the distribution of activity profiles in terms of features (red errors), PCM models the full co-variance matrix of the distribution, while RSA analyzes distances between patterns, which again capture the co-variance matrix of the distribution.

Representational similarity analysis (RSA)

In collaboration with Niko Kriegeskorte's lab, we are developing tools and methods for representational similarity analysis, openly available as a Matlab toolbox and the newest version as a Python package. We have focussed on the crossnobis distance estimate, a bias free, reliable, and easily interpretable measure of dissimilarity (Walther et al., 2015). We have in detail described the distributional properties of this measure (Diedrichsen et al., 2020), and ways to use these to make optimal inferences in subsequent analyses.

Pattern component modelling (PCM)

Because we often want to fit and compare more complex representational models, RSA or encoding models often do not provide an optimal approach (Diedrichsen & Kriegeskorte, 2017). We have therefore developed a hierarchical Bayesian approach that allows the decomposition of activity patterns into different representational components or feature sets (Diedrichsen et al., 2011, 2013, 2017, 2018). PCM can efficiently estimate the weights of these proportions and also fit nonlinear representational models. It allows for both RSA-style or Encoding-style representational models, and extends both approaches by providing advanced techniques of model fitting and evaluation. On Github, we are maintaining a fully optimized PCM toolbox for Matlab, as well as the PCM package for Python.