PhaseICA: Complex-Valued Decomposition of Spatially Independent Brain Waves

Understanding complex dynamics from spatiotemporal signals requires robust tools capable of decoding reoccurring patterns. Traditional ICA methods often overlook the spatially non-stationarity nature of brain activity across both the frequency and spatial domains. We propose a novel data-driven approach, named PhaseICA, designed to extract reoccurring spatiotemporal patterns, referred to as brain waves. Unlike conventional ICA methods that focus solely on amplitude, PhaseICA incorporates phase information directly into the component estimation, preserving the nonstationary property that real-valued ICA methods typically discard. The method performs spatial independence optimization in the complex domain by minimizing a complex entropy bound over the eigenvectors of Hilbert-transformed signals. The proposed method captures spatial propagation across brain regions with interpretable and compact representations, offering a promising foundation for decoding brain dynamic systems and revealing the temporal relationship of regions.