Abstract
Representational similarity analysis (RSA) is another multivariate analysis method that enables sophisticated inferences to be made about the cerebral coding of cognitive information. It is based on the concept of second-order isomorphism, coined by Californian psychologist Roger Shepard.
Shepard's argument is based first and foremost on the refutation of the common but false idea that there is a direct correspondence between objects in the external world and their internal representation in the brain (a first-order isomorphism). We sometimes naively think that, when a person imagines a green square, there must be a " image " of this square in his or her brain. But this kind of reasoning quickly leads to absurdities : Who recognizes the image of this square in the brain (regression to infinity) ? How is the color green coded - by green neurons ? How are abstract concepts such as number or freedom coded?
Instead of a first-order isomorphism, Shepard argues that we should look for a second-order isomorphism, i.e. a correspondence between the relations between objects in the external world, and the relations between their internal representations. The idea is that, if the internal representation of a rectangle is in no way the image of a rectangle, this representation must resemble that of a square more than that of, say, a cauliflower. So, we need to measure the subjective similarity between mental representations and compare it with the similarity of brain representations. In each brain region, the analysis consists in (1) extracting the patterns of activity for each stimulus ; (2) assessing their dissimilarity, for example 1-r where r is the correlation coefficient ; (3) comparing this empirical matrix with one or more matrices predicted by different models, or by subjective similarity measured behaviorally. This matrix can also be studied directly, for example using multi-dimensional scaling, a method for visualizing similarity matrices invented by Roger Shepard.
