Riemannian Geometry Boosts Representational Similarity Analyses of Dense Neural Time Series

Abstract

Representational similarity analysis (RSA) is a popular technique to estimate the structure of mental representations from neuroimaging data. However, RSA can be difficult to estimate for neural time series, where mental representations may be distributed in a highly dimensional space. Here, we show that RSA can be efficiently estimated from dense neural time series using Riemannian geometry. Using a public magneto-encephalography dataset, we decoded 24 classes from the brain evoked responses to 720 visual stimuli. RSA estimated from the confusion matrices of a standard regularized logistic regression achieved an average decoding accuracy of 23% (chance=4%). Our approach based on spatial filtering and Riemannian geometry nearly doubled this score with an average 42% decoding accuracy. Finally, our results revealed how RSA becomes ill-conceived when it derives from confusion matrices of highly accurate multivariate pattern classifications. Instead, we propose to directly estimate RSA from Riemannian metrics without fitting a multivariate pattern classifier. Overall, our approach, based on Riemannian geometry provides a principled and efficient basis to study the structure of mental representations from highly dimensional neural time series.