Recursive Exponentially Weighted N-way Partial Least Squares Regression with Recursive-Validation of Hyper-Parameters in Brain-Computer Interface Applications

A tensor-input/tensor-output Recursive Exponentially Weighted N-Way Partial Least Squares (REW-NPLS) regression algorithm is proposed for high dimension multi-way (tensor) data treatment and adaptive modeling of complex processes in real-time. The method unites fast and efficient calculation schemes of the Recursive Exponentially Weighted PLS with the robustness of tensor-based approaches. Moreover, contrary to other multi-way recursive algorithms, no loss of information occurs in the REW-NPLS. In addition, the Recursive-Validation method for recursive estimation of the hyper-parameters is proposed instead of conventional cross-validation procedure. The approach was then compared to state-of-the-art methods. The efficiency of the methods was tested in electrocorticography (ECoG) and magnetoencephalography (MEG) datasets. The algorithms are implemented in software suitable for real-time operation. Although the Brain-Computer Interface applications are used to demonstrate the methods, the proposed approaches could be efficiently used in a wide range of tasks beyond neuroscience uniting complex multi-modal data structures, adaptive modeling, and real-time computational requirements.