Equivalence between representational similarity analysis, centered kernel alignment, and canonical correlations analysis

Abstract

Centered kernel alignment (CKA) and representational similarity analysis (RSA) of dissimilarity matrices are two popular methods for comparing neural systems in terms of representational geometry. Although they follow a conceptually similar approach, typical implementations of CKA and RSA tend to result in numerically different outcomes. Here, I show that these two approaches are largely equivalent once one incorporates a mean-centering step into RSA. This equivalence holds for both linear and nonlinear variants of these methods. These connections are simple to derive, but appear to have been thus far overlooked in the context of comparing neural representations. By unifying these measures, this paper hopes to simplify a complex and fragmented literature on this subject.