Demixed principal component analysis (dPCA)

Demixed PCA is a dimensionality-reduction method that, unlike ordinary PCA, factors population activity into components each tied to a specific task parameter. It splits the trial-averaged data into marginalizations — the parts of the variance attributable to stimulus, to decision, to elapsed time, and to their interactions — and finds low-dimensional components that both capture variance and are demixed, so that a stimulus component varies with the stimulus but not with time, and so on. It aims to keep the interpretability of a supervised decomposition while retaining most of the explained variance of PCA.

dPCA is valuable when a population multiplexes several task variables and one wants a compact, labelled picture of how much of the activity reflects each, for example separating a condition-independent timing component from direction-dependent components. Its assumptions are that the relevant factors are known and discrete, that the design is (approximately) balanced across them, and that a linear decomposition is adequate; it operates on trial-averaged structure and does not, by itself, model single-trial dynamics, for which trajectory methods are more appropriate.