Fig. 5: Demixed PCA unmixes attention and behavioral outcome-related variance.

A Pie chart shows how the total signal variance is split among parameters: Attention (red), behavioral outcome (blue), Interaction between attention and behavior (dark gray), and the condition independent variance (light gray). (B, Left) Cumulative variance explained by PCA (gray) and dPCA (black). Demixed PCA explains almost the same amount of variance as PCA. (B, Right) Cumulative demixed variance specific for each marginalization. C−E Demixed principal component. In each plot, the full firing rates from −300ms to 0 ms from target onset are projected onto the respective dPCA decoder axis (attention, behavioral outcome and interaction), as a function of trial type categories (based on TA distance and behavioral outcome) so that there are six lines corresponding with six conditions (see legend). Thick black lines show time intervals during which the respective task parameters can be reliably extracted from single-trial activity (as assessed against a 95% C.I., permutation test). F For each neuron, we use the first attention- and behavioral outcome-related demixed PCs to plot its location on the plane defined by these two components. These components present a weight distribution that tends to be centered and equally distributed around zero (cf. respective histograms, N = 848 neurons). The scatter plot shows the relationship between the neurons’ weights in the attention and behavioral outcome demixed component. This correlation is significant (N = 848 electrodes, Spearman correlation, ρ = 0.16, p = 3e-4). The dot product between these components indicates that these components were non-orthogonal (77 degrees).