A Comparative Study of Principal Component Analysis (PCA) and Dynamic Mode Decomposition (DMD) Variants

Abstract

This study evaluates the performance of the Exact Dynamic Mode Decomposition (DMD), Optimized DMD, and Modified Optimized DMD algorithms under various noise conditions, with a specific focus on magnetoencephalography (MEG) data. DMD is a data-driven method used to decompose complex datasets into dynamic modes, which represent the un- derlying structures and dynamics of the data system. We found that the Modified Optimized DMD consistently outperformed the other methods in estimating the real parts of eigenvalues that describe time dynamics, significantly reducing bias and empirical variance. Addition- ally, Optimized DMD and Modified Optimized DMD are able to capture more complex spatial and temporal patterns from MEG data. These results emphasize the robustness and reliability of the Modified Optimized DMD, making it a valuable tool for diverse scientific applications that require accurate dynamic mode decomposition in noisy data.