基于距离保持到局部均值的距离降维（DPLM）的SPD矩阵及其在BCI中的应用
Dimensionality reduction based on Distance Preservation to Local Mean (DPLM) for SPD matrices and its application in BCI
AI总结：
本文提出了一种非线性降维算法，用于对对称正定（SPD）矩阵流形进行处理，通过保持数据的局部结构和局部均值距离（DPLM）来提供高类间区分的低维表示。实验表明，DPLM在BCI竞赛IV的多类数据集IIa上优于其他方法，因其对异常值具有鲁棒性。
摘要：
本文提出了一种非线性降维算法，用于对称正定（SPD）矩阵流形。该算法考虑了SPD矩阵的几何特性，并通过保持距离到局部均值（DPLM）来提供高类间区分的低维表示。DPLM在训练样本数量上是线性的，并且可以利用可用的标签信息以提高分类任务的性能。我们在BCI竞赛IV的多类数据集IIa上进行了多项实验。结果表明，我们的方法在与其他文献中方法相比时，由于其对异常值的鲁棒性而表现更优。实验还确认，DPLM与FGMDM作为分类器的结合在该数据集上实现了最先进的性能。
英文摘要：
In this paper, we propose a nonlinear dimensionality reduction algorithm for the manifold of Symmetric Positive Definite (SPD) matrices that considers the geometry of SPD matrices and provides a low dimensional representation of the manifold with high class discrimination. The proposed algorithm, tries to preserve the local structure of the data by preserving distance to local mean (DPLM) and also provides an implicit projection matrix. DPLM is linear in terms of the number of training samples and may use the label information when they are available in order to performance improvement in classification tasks. We performed several experiments on the multi-class dataset IIa from BCI competition IV. The results show that our approach as dimensionality reduction technique - leads to superior results in comparison with other competitor in the related literature because of its robustness against outliers. The experiments confirm that the combination of DPLM with FGMDM as the classifier leads to the state of the art performance on this dataset.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
