A multivariate method to determine the dimensionality of neural representation from population activity

How do populations of neurons represent a variable of interest? The notion of feature spaces is a useful concept to approach this question: According to this model, the activation patterns across a neuronal population are composed of different pattern components. The strength of each of these components varies with one latent feature, which together are the dimensions along which the population represents the variable. Here we propose a new method to determine the number of feature dimensions that best describes the activation patterns. The method is based on Gaussian linear classifiers that use only the first d most important pattern dimensions. Using cross-validation, we can identify the classifier that best matches the dimensionality of the neuronal representation. We test this method on two datasets of motor cortical activation patterns measured with functional magnetic resonance imaging (fMRI), during (i) simultaneous presses of all fingers of a hand at different force levels and (ii) presses of different individual fingers at a single force level. As expected, the new method shows that the representation of force is low-dimensional; the neural activation for different force levels is scaled versions of each other. In comparison, individual finger presses are represented in a full, four-dimensional feature space. The approach can be used to determine an important characteristic of neuronal population codes without knowing the form of the underlying features. It therefore provides a novel tool in the building of quantitative models of neuronal population activity as measured with fMRI or other approaches.