用几何方法分析脑影像数据，让模型更懂大脑结构。
SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challenges
- 将脑影像数据建模为对称正定矩阵，利用黎曼几何进行学习。
- 在多种脑成像任务中表现稳定，保持了矩阵的对称与正定性。
- 适合做脑机接口、神经疾病分析的研究者参考。
脑影像技术通过不同模态捕捉大脑活动、结构和连接特征，这些测量可统一建模为对称正定（SPD）矩阵表示。借助黎曼几何，SPD流形为这类数据提供了非欧几里得的统计推断与机器学习框架。本文系统梳理了从特定模态表示到几何浅层与深层学习范式的发展，构建了一个统一的SPD矩阵学习框架，连接经典几何统计与现代机器学习。该框架在神经影像与神经生理应用中展现出良好的数学基础，能有效保留对称性与正定性等关键结构约束，并拓展至脑机接口等前沿人工智能应用。
原文摘要 · Abstract (English)
Neuroimaging provides essential tools for characterizing brain activity, structure, and connectivity through modalities that capture complementary aspects of brain organization. Across these diverse modalities, a unifying perspective arises when measurements are modeled as symmetric positive-definite (SPD)-valued representations through appropriate estimation or regularization procedures. Endowed with Riemannian geometry, the SPD manifold provides a non-Euclidean framework for principled statistical inference and machine learning on these representations. This review organizes these analytical and learning approaches within a framework for SPD matrix learning that connects classical geometric statistics with modern machine learning across neuroimaging and neurophysiological applications. We systematically survey the progression from modality-specific representations to geometric shallow and deep learning paradigms, highlighting how SPD matrix learning preserves underlying structural constraints while extending to modern AI applications in neuroimaging and brain-computer interfaces.
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