Key Laboratory for NeuroInformation of Ministry of Education, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu, China.
PLoS One. 2013 Sep 13;8(9):e74433. doi: 10.1371/journal.pone.0074433. eCollection 2013.
Linear discriminant analysis (LDA) is one of the most popular classification algorithms for brain-computer interfaces (BCI). LDA assumes Gaussian distribution of the data, with equal covariance matrices for the concerned classes, however, the assumption is not usually held in actual BCI applications, where the heteroscedastic class distributions are usually observed. This paper proposes an enhanced version of LDA, namely z-score linear discriminant analysis (Z-LDA), which introduces a new decision boundary definition strategy to handle with the heteroscedastic class distributions. Z-LDA defines decision boundary through z-score utilizing both mean and standard deviation information of the projected data, which can adaptively adjust the decision boundary to fit for heteroscedastic distribution situation. Results derived from both simulation dataset and two actual BCI datasets consistently show that Z-LDA achieves significantly higher average classification accuracies than conventional LDA, indicating the superiority of the new proposed decision boundary definition strategy.
线性判别分析（LDA）是脑机接口（BCI）中最流行的分类算法之一。LDA 假设数据服从高斯分布，且相关类别的协方差矩阵相等，但在实际的 BCI 应用中，通常不满足该假设，因为实际中通常观察到异方差类分布。本文提出了 LDA 的增强版本，即 z 分数线性判别分析（Z-LDA），它引入了一种新的决策边界定义策略来处理异方差类分布。Z-LDA 通过利用投影数据的均值和标准差信息来定义 z 分数决策边界，该方法可以自适应地调整决策边界以适应异方差分布情况。来自模拟数据集和两个实际 BCI 数据集的结果一致表明，Z-LDA 实现了明显更高的平均分类准确性，优于传统 LDA，这表明了新提出的决策边界定义策略的优越性。
