The Topology of Representational Geometry

Abstract

Representational similarity analysis (RSA) is a powerful tool for abstracting and then comparing neural representations across brains, regions, models and modalities. However, typical RSA analyses compares pairs of representational dissimilarities to judge similarity of two neural systems, and we argue that such methods can not capture the shape of representational spaces. By leveraging tools from computational topology, which can probe the shape of high-dimensional data, we augment RSA to be able to detect more subtle yet real differences and similarities of representational geometries. This new method could be used in conjunction with regular RSA in order to make new inferences about neural function.Significance StatementBig data in high-dimensional spaces, like neuroimaging datasets, contain important shape structures. These shape structures can be analyzed to identify the underlying features and dynamics which drive the system. We showed that such analyses, applied to neural activity patterns elicited by viewing various objects, can identify real but subtle and complex features of those objects which are encoded in the brain.