From Signals to Trajectories: A Primer on Low-Dimensional Dynamics in Human EEG and MEG
TL;DR
This primer explains how EEG/MEG activity can be organized into neural state representations, projected onto axes organized by decreasing covariance, truncated into low-dimensional representations, and visualized as trajectories that capture how distributed activity evolves over time.
Abstract
Neural activity unfolds not as a set of independent signals, but as a coordinated dynamical process that can be described as a point moving through a high-dimensional state space. This perspective has contributed substantially to recent developments in systems neuroscience, especially through studies of directly recorded neuronal population activity, but remains comparatively underused in non-invasive human recordings such as EEG and MEG. In this primer, we present a neural trajectory analysis based on Principal Component Analysis (PCA) as an accessible route into extending the concepts of neural trajectories in state space to human electrophysiology. We explain how EEG/MEG activity can be organized into neural state representations, projected onto axes organized by decreasing covariance, truncated into low-dimensional representations, and visualized as trajectories that capture how distributed activity evolves over time. We show how trajectory geometry can be used to compare conditions and relate neural dynamics to behavior or clinical outcomes. An example of EEG motor execution and imagery, accompanied by a tutorial notebook, illustrates the workflow from conventional EEG summaries to trajectory-based analysis. We also clarify the limits of PCA, including its linear, variance-driven nature, and discuss EEG/MEG-specific challenges such as spatial mixing, preprocessing sensitivity, validation, and overinterpretation. Finally, we situate PCA within a broader family of state-space methods. By making neural trajectories practical and interpretable, this primer offers a guide for bringing the conceptual framework of population-level dynamics into mainstream human cognitive neuroscience.