Unsupervised separation of nonlinearly mixed event-related potentials using manifold clustering and non-negative matrix factorization

Event-related potentials (ERPs) can quantify brain responses to reveal the neural mechanisms of sensory perception. However, ERPs often reflect nonlinear mixture responses to multiple sources of sensory stimuli, and an accurate separation of the response to each stimulus remains a challenge. This study aimed to separate the ERP into nonlinearly mixed source components specific to individual stimuli. We developed an unsupervised learning method based on clustering of manifold structures of mixture signals combined with channel optimization for signal source reconstruction using non-negative matrix factorization (NMF). Specifically, we first implemented manifold learning based on Local Tangent Space Alignment (LTSA) to extract the spatial manifold structure of multi-resolution sub-signals separated via wavelet packet transform. We then used fuzzy entropy to extract the dynamical process of the manifold structures and performed a k-means clustering to separate different sources. Lastly, we used NMF to obtain the optimal contributions of multiple channels to ensure accurate source reconstructions. We evaluated our developed approach using a simulated ERP dataset with known ground truth of two components of ERP mixture signals. Our results show that the correlation coefficient between the reconstructed source signal and the true source signal was 92.8 % and that the separation accuracy in ERP amplitude was 91.6 %. The results show that our unsupervised separation approach can accurately separate ERP signals from nonlinear mixture source components. The outcomes provide a promising way to isolate brain responses to multiple stimulus sources during multisensory perception.