Dynamic mode decomposition (DMD)

DMD is a data-driven algorithm that fits a single best-fit linear operator A to a sequence of state snapshots, X' ~ A X, and then reads out its eigenvalues and eigenvectors as spatiotemporal modes — each mode a spatial pattern with an associated oscillation frequency and growth or decay rate. It is computed efficiently through the singular value decomposition of the snapshot matrix, and is closely tied to Koopman theory: DMD is, in effect, a finite-dimensional numerical approximation of the Koopman operator restricted to linear observables.

In neuroscience DMD and its variants have been used to extract coherent traveling waves and transient oscillatory modes from ECoG and LFP arrays, offering a decomposition that respects both space and time in a way channel-by-channel spectral analysis does not. Extensions matter in practice: exact vs projected DMD, time-delay embedding (Hankel-DMD) to capture dynamics not linear in the raw state, and optimized / bagging variants that are more robust to the short, noisy, low-signal regime typical of neural recordings. As a linear method it will misrepresent strongly nonlinear or multistable dynamics.