Deflation properties in tensor-based eye blink removal algorithm

Blind source separation refers to a set of techniques designed to uncover latent (i.e. directly unobservable) structures in data. Depending on user preferences and the chosen algorithm, latent components can be estimated either simultaneously or iteratively, one at a time. The latter approach is typically performed using component deflation. However, Camacho et al. (Chemom Intell Lab Syst 208:104212, 2021) showed that deflation can introduce spurious artefacts into the data, particularly when the latent components are estimated under constraints. This study explored the theoretical properties of deflation in the context of higher-order arrays and tensor decomposition. In certain cases, the tensor latent components may represent noise and must be removed before further decomposition to accurately reveal the underlying structure of the data. Building on the ideas presented in Camacho et al. (Chemom Intell Lab Syst 208:104212, 2021), we investigated whether specific forms of deflation can generate spurious artefacts in electroencephalogram (EEG) tensor data, particularly under nonnegativity or unimodality constraints, where orthogonality may lack a natural interpretation. Our results are demonstrated using two real EEG datasets and one simulated dataset.