Identical fits of nonnegative matrix/tensor factorization may correspond to different extracted event-related potentials

Nonnegative Matrix/Tensor factorization (NMF/NTF) have been used in the study of EEG, and the fit (explained variation) is often used to evaluate the performance of a nonnegative decomposition algorithm. However, this parameter only reveals the information derived from the mathematical model and just exhibits the reliability of the algorithms, and the property of EEG can not be reflected. If fits of two algorithms are identical, it is necessary to examine whether the desired components extracted by them are identical too. In order to verify this doubt, we performed NMF and NTF on the same dataset of an auditory event-related potentials (ERPs), and found that the identical fits of NMF and NTF under the hierarchical alternating least squares algorithms corresponded to different desired ERPs extracted by NMF and NTF, moreover, NTF contributed the ERP with much better timing and spectral properties. Such analysis implies that to combine the fit and property of the desired ERP component together helps evaluate the performance of NMF and NTF algorithms in the study of ERPs.