Joint Model Order Estimation for Multiple Tensors with A Coupled Mode and Applications to the Joint Decomposition of EEG, MEG Magnetometer, and Gradiometer Tensors

The efficient estimation of an approximate model order is essential for applications with multidimensional data if the observed low-rank data is corrupted by additive noise. Certain signal processing applications such as biomedical studies, where the data are collected simultaneously through heterogeneous sensors, share some common features, i.e., coupled factors among multiple tensors. The exploitation of this coupling can lead to a better model order estimation, especially in case of low SNRs. In this paper, we extend the rank estimation techniques, designed for a single tensor, to noise-corrupted coupled low-rank tensors that share one of their factor matrices. To this end, we consider the joint effect of the global eigenvalues (calculated from the coupled HOSVD) and exploit the exponential behavior of the resulting coupled global eigenvalues. We show that the proposed method outperforms the classical criteria and can be successfully applied to EEG, MEG Magnetometer, and Gradiometer measurements. Our real data simulation results show that the estimated rank is highly reliable in terms of dominant components extraction.