Partial Least Square Regression via Three-factor SVD-type Manifold Optimization for EEG Decoding

Partial least square regression (PLSR) is a widely-used statistical model to reveal the linear relationships of latent factors that comes from the independent variables and dependent variables. However, traditional methods \ql{ to solve PLSR models are usually based on the Euclidean space, and easily getting} stuck into a local minimum. To this end, we propose a new method to solve the partial least square regression, named PLSR via optimization on bi-Grassmann manifold (PLSRbiGr). \ql{Specifically, we first leverage} the three-factor SVD-type decomposition of the cross-covariance matrix defined on the bi-Grassmann manifold, converting the orthogonal constrained optimization problem into an unconstrained optimization problem on bi-Grassmann manifold, and then incorporate the Riemannian preconditioning of matrix scaling to regulate the Riemannian metric in each iteration. \ql{PLSRbiGr is validated} with a variety of experiments for decoding EEG signals at motor imagery (MI) and steady-state visual evoked potential (SSVEP) task. Experimental results demonstrate that PLSRbiGr outperforms competing algorithms in multiple EEG decoding tasks, which will greatly facilitate small sample data learning.