Representational models: A common framework for understanding encoding, pattern-component, and representational-similarity analysis

Representational models specify how activity patterns in populations of neurons (or, more generally, in multivariate brain-activity measurements) relate to sensory stimuli, motor responses, or cognitive processes. In an experimental context, representational models can be defined as hypotheses about the distribution of activity profiles across experimental conditions. Currently, three different methods are being used to test such hypotheses: encoding analysis, pattern component modeling (PCM), and representational similarity analysis (RSA). Here we develop a common mathematical framework for understanding the relationship of these three methods, which share one core commonality: all three evaluate the second moment of the distribution of activity profiles, which determines the representational geometry, and thus how well any feature can be decoded from population activity. Using simulated data for three different experimental designs, we compare the power of the methods to adjudicate between competing representational models. PCM implements a likelihood-ratio test and therefore provides the most powerful test if its assumptions hold. However, the other two approaches—when conducted appropriately—can perform similarly. In encoding analysis, the linear model needs to be appropriately regularized, which effectively imposes a prior on the activity profiles. With such a prior, an encoding model specifies a well-defined distribution of activity profiles. In RSA, the unequal variances and statistical dependencies of the dissimilarity estimates need to be taken into account to reach near-optimal power in inference. The three methods render different aspects of the information explicit (e.g. single-response tuning in encoding analysis and population-response representational dissimilarity in RSA) and have specific advantages in terms of computational demands, ease of use, and extensibility. The three methods are properly construed as complementary components of a single data-analytical toolkit for understanding neural representations on the basis of multivariate brain-activity data.Author summary: Modern neuroscience can measure activity of many neurons or the local blood oxygenation of many brain locations simultaneously. As the number of simultaneous measurements grows, we can better investigate how the brain represents and transforms information, to enable perception, cognition, and behavior. Recent studies go beyond showing that a brain region is involved in some function. They use representational models that specify how different perceptions, cognitions, and actions are encoded in brain-activity patterns. In this paper, we provide a general mathematical framework for such representational models, which clarifies the relationships between three different methods that are currently used in the neuroscience community. All three methods evaluate the same core feature of the data, but each has distinct advantages and disadvantages. Pattern component modelling (PCM) implements the most powerful test between models, and is analytically tractable and expandable. Representational similarity analysis (RSA) provides a highly useful summary statistic (the dissimilarity) and enables model comparison with weaker distributional assumptions. Finally, encoding models characterize individual responses and enable the study of their layout across cortex. We argue that these methods should be considered components of a larger toolkit for testing hypotheses about the way the brain represents information.