Unsupervised discovery of neural events by dynamic matrix factorization

Neural events are characteristic transient, coordinated neural activities observable in the brain’s aggregate signals, such as local field potentials (LFPs). It was shown that certain neural events, like sharp wave-ripples (SWR) [1], play a crucial role in various cognitive functions, including memory consolidation and both offline and online planning. These events have signatures across nearly all scales, from microscopic coordination at the level of individual spiking activity and synaptic dynamics [2] to macroscopic regulation in the thalamocortical system [3]. Despite the growing recognition of the importance of transient dynamics in cognitive processes, a comprehensive and multi-faceted characterization of neural events remains elusive. We develop an unsupervised method to discover neural events with minimal prior knowledge and assumptions. Transient oscillations are short-lived events best characterized by their occurrence rate, timing, duration, and amplitude, or by combined metrics. We employ data-driven dynamical modeling and unsupervised machine learning algorithms to identify and characterize transient neural dynamics. Our event detection method combines multi-resolution dynamic mode decomposition (mrDMD) and non-negative matrix factorization (NMF). First, we employ mrDMD to decompose the time series into dynamical modes with a hierarchy of timescale [4]. Through mrDMD, we estimate the timing, frequency, and intensity of putative events in each channel. We then used the resulting modes from mrDMD to initialize Itakura-saito non-negative matrix factorization (IS-NMF) which decomposes the time series into a superposition of sparse events [5]. Since IS-NMF solves a non-convex optimization problem, it is highly sensitive to initialization, thus using modes from mrDMD allowed us to have meaningful initialization of the temporal and frequency matrices in IS-NMF, and facilitate the convergence of IS-NMF optimization. We evaluated our method using multi-channel synthetic data, which consisted of distinctive transient events with various frequencies and baseline noise, resembling LFPs. The results from IS-NMF enabled us to capture both the temporal dynamics of events and their spectral characteristics. With mrDMD, we could reconstruct each event's original signal for further analysis, including shape and other features. Overall, with our method, we can detect neural events and characterize them with minimal prior knowledge about the underlying structure.