Abstract
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 how similar or dissimilar different activity patterns associated by different experimental conditions are. 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.
Highlights
Systems neuroscience investigates how patterns of brain activity implement the computational processes that support behavior
We focus here on the approach to characterize brain representations at the level of the neural population [2, 3], which abstracts from the roles of individual neurons, and makes it easier to compare representations between brains and models [4]
In the second part of the paper, we propose a simple method to address this issue: Using the analytical expression for the covariance of the different dissimilarity estimates, we can effectively calculate a cosine similarity in a “whitened" space, in which the measurement error is isotropic (Fig. 2b). We show that this whitened representational dissimilarity matrix (RDM) cosine similarity based on biased distance estimates is equivalent to the RV coefficient [11], which is known as the linear Centered Kernel Alignment [12]
Summary
Systems neuroscience investigates how patterns of brain activity implement the computational processes that support behavior. In the second part of the paper, we propose a simple method to address this issue: Using the analytical expression for the covariance of the different dissimilarity estimates, we can effectively calculate a cosine similarity in a “whitened" space, in which the measurement error is isotropic (Fig. 2b). We show that this whitened RDM cosine similarity based on biased distance estimates is equivalent to the RV coefficient [11], which is known as the linear Centered Kernel Alignment [12]. The techniques described in this paper are all implemented in a new Python-toolbox implemented by our group [16]
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