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

TL;DR

This paper introduces a novel Riemannian manifold optimization approach for partial least squares regression, specifically designed to improve EEG decoding accuracy by avoiding local minima in the optimization process.

Contribution

It proposes PLSRbiGr, a new method using three-factor SVD decomposition on bi-Grassmann manifold with Riemannian preconditioning, enhancing EEG decoding performance.

Findings

Outperforms existing algorithms in EEG decoding tasks

Effective in small sample data learning

Improves convergence by avoiding local minima

Abstract

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 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). 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. 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.