论文标题
通过三因素SVD型歧管优化的部分最小二乘回归用于EEG解码
Partial Least Square Regression via Three-factor SVD-type Manifold Optimization for EEG Decoding
论文作者
论文摘要
部分最小二平方回归（PLSR）是一个广泛使用的统计模型，可揭示来自自变量和因变量的潜在因子的线性关系。但是，解决PLSR模型的传统方法通常基于欧几里得空间，并且很容易被卡住。为此，我们提出了一种新方法来解决部分最小平方回归，该方法通过对Bi-Grassmann歧管（PLSRBIGR）的优化来命名为PLSR。具体而言，我们首先利用在Bi-Grassmann歧管上定义的交叉稳态矩阵的三因素SVD型分解，将正交约束的优化问题转换为Bi-Grassmann歧管上不受限制的优化问题，然后将riemannian的预定在矩阵量表中，然后将riemann condrianian condrienann condricann condricann condricann condricann condricann condricann condricann condricann condricann condricann condricann。 PLSRBIGR通过各种实验进行了验证，以解码运动图像（MI）和稳态视觉诱发电位（SSVEP）任务。实验结果表明，PLSRBIGR在多个EEG解码任务中的表现优于竞争算法，这将极大地促进小样本数据学习。
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.
