AI summaryⓘ
The authors developed PCA-DMD, a new method to accurately reconstruct brain signals called local field potentials, which are complex and vary a lot between subjects. Their approach breaks the data into smaller parts, reduces its complexity using PCA, and models its changes over time with a Koopman operator, then combines everything back together. They showed that PCA-DMD works better than other similar methods, generalizes well to new subjects without extra adjustments, and can handle very large datasets efficiently. The method also revealed meaningful patterns in brain activity through spectral analysis. Overall, the authors present PCA-DMD as a scalable and interpretable tool for understanding brain signal dynamics.
Local Field Potentials (LFPs)Principal Component Analysis (PCA)Dynamic Mode Decomposition (DMD)Koopman OperatorSignal ReconstructionNeural DynamicsZero-shot GeneralizationSpectral AnalysisOverlap-add Aggregation
Abstract
Accurate reconstruction of long-duration neural recordings is challenging because local field potentials (LFPs) are high-resolution, multichannel, transient, and variable across subjects. We present PCA-DMD, a scalable operator-theoretic framework that segments LFP recordings into overlapping windows, projects them into a compact PCA space, learns linear Koopman evolution in the latent space, and reconstructs continuous signals through inverse projection and overlap-add aggregation. On 200,000-sample hippocampal recordings, PCA-DMD outperformed Classical DMD, SpDMD, MrDMD, and HODMD, achieving KLD=0.0761 and HD=0.0847. In all-pair cross-subject zero-shot generalization at 300,000 samples, correlations were 0.9504-0.9800, with HD=0.0010-0.0072 and KLD=0.0005-0.0022, without target-subject fine-tuning. Out-of-sample temporal prediction showed close one-step agreement on temporally held-out LFP segments across the unseen interval and multiple channels. Scalability analysis from 400,000 to 900,000 samples showed stable zero-shot reconstruction, with mean correlation remaining about 0.965-0.968 while computational cost increased predictably. External validation on an independent 93-channel Allen Neuropixels recording yielded mean and median channel-wise correlations of 0.7427 and 0.7990, respectively. Koopman spectral and mode analyses revealed dominant eigenvalues concentrated near the unit circle. PCA-DMD therefore provides an interpretable, generalizable, and computationally scalable framework for reconstructing high-dimensional neural dynamics.