  Representational similarity analysis (RSA) tests models of brain computation
by investigating how neural activity patterns reflect experimental conditions.
Instead of predicting activity patterns directly, the models predict the
geometry of the representation, as defined by the representational
dissimilarity matrix (RDM), which captures to what extent experimental
conditions are associated with similar or dissimilar activity patterns. RSA
therefore first quantifies the representational geometry by calculating a
dissimilarity measure for each pair of conditions, and then compares the
estimated representational dissimilarities to those predicted by each model.
Here we address two central challenges of RSA: First, dissimilarity measures
such as the Euclidean, Mahalanobis, and correlation distance, are biased by
measurement noise, which can lead to incorrect inferences. Unbiased
dissimilarity estimates can be obtained by crossvalidation, at the price of
increased variance. Second, the pairwise dissimilarity estimates are not
statistically independent, and ignoring this dependency makes model comparison
statistically suboptimal. We present an analytical expression for the mean and
(co)variance of both biased and unbiased estimators of the squared Euclidean
and Mahalanobis distance, allowing us to quantify the bias-variance trade-off.
We also use the analytical expression of the covariance of the dissimilarity
estimates to whiten the RDM estimation errors. This results in a new criterion
for RDM similarity, the whitened unbiased RDM cosine similarity (WUC), which
allows for near-optimal model selection combined with robustness to correlated
measurement noise.
