Improved cross-validated distances for multivariate pattern analysis

Characterizing the dissimilarity of neural representations between experimental conditions, and tracking it across time, is a central goal of multivariate pattern analysis. Guggenmos et al. (2018) assessed the reliability of many of the measures that can be used for that purpose on MEG data and recommended the use of either the cross-validated Euclidean distance or the within-class-corrected Pearson distance. In this commentary, we show that we can improve upon these distances. First, we show that the cross-validated Euclidean distance is equivalent to a sum of between-partition distances and that this equivalence can be leveraged to obtain a generalized variant, with increased reliability and accuracy. Second, we use the relationship between Euclidean distance and Pearson correlation to define a cross-validated correlation distance in a similar way. The resulting distance is more accurate and interpretable than a formulation proposed by Guggenmos and colleagues. Finally, we discuss the relationship between our generalized cross-validation and within-class correction, another strategy often used to increase reliability, and we show that generalized cross-validation results in higher accuracy for the correlation distance.