Review Article

Understanding Neural Population Coding: Information Theoretic Insights from the Auditory System

Figure 5

Schematic illustration of the sample-based nonnegative matrix trifactorization algorithm. The algorithm [58] factorizes the full spatiotemporal matrix into three matrices: a temporal module matrix, a spatial module matrix, and a coefficient matrix. The temporal module matrix contains temporal activity patterns that are present in the data. The spatial module matrix contains groups of neurons that fired together in fixed proportions. The coefficient matrix specifies the strength of activation of each temporal activity pattern by each spatial group of neurons during individual trials. Each column of the coefficient matrix corresponds to a spatial module and the values in each column specify the strength of each temporal activity pattern shown by the neurons of that spatial module during a particular trial. Therefore, once sample-based nonnegative matrix trifactorization is applied, the full spatiotemporal matrix can be collapsed into a lower dimensional representation that is contained in the coefficient matrix. To obtain an approximation to the activity of one trial, the coefficients of the respective trial are multiplied with the temporal and spatial module matrices as shown.