For neurological disorders and diseases, functional and anatomical connectomes of the human brain can be used to better inform targeted interventions and treatment strategies. Functional magnetic resonance imaging (fMRI) is a non-invasive neuroimaging technique that captures spatio-temporal brain function through blood flow over time. FMRI can be used to study the functional connectome through the functional connectivity matrix; that is, Pearson's correlation matrix between time series from the regions of interest of an fMRI image. One approach to analysing functional connectivity is using partial least squares (PLS), a multivariate regression technique designed for high-dimensional predictor data. However, analysing functional connectivity with PLS ignores a key property of the functional connectivity matrix; namely, these matrices are positive definite. To account for this, we introduce a generalisation of PLS to Riemannian manifolds, called R-PLS, and apply it to symmetric positive definite matrices with the affine invariant geometry. We apply R-PLS to two functional imaging datasets: COBRE, which investigates functional differences between schizophrenic patients and healthy controls, and; ABIDE, which compares people with autism spectrum disorder and neurotypical controls. Using the variable importance in the projection statistic on the results of R-PLS, we identify key functional connections in each dataset that are well represented in the literature. Given the generality of R-PLS, this method has potential to open up new avenues for multi-model imaging analysis linking structural and functional connectomics.

翻译：对于神经系统疾病和病症，人脑的功能和结构连接组可用于更有针对性地指导干预和治疗策略。功能磁共振成像（fMRI）是一种非侵入性神经成像技术，通过随时间变化的血流捕捉大脑的时空功能。fMRI可通过功能连接矩阵研究功能连接组；即fMRI图像感兴趣区域间时间序列的皮尔逊相关矩阵。分析功能连接的一种方法是使用偏最小二乘（PLS），这是一种专为高维预测变量数据设计的多元回归技术。然而，使用PLS分析功能连接忽略了功能连接矩阵的一个关键特性——即这些矩阵是正定的。为解决此问题，我们将PLS推广至黎曼流形，提出R-PLS方法，并将其应用于具有仿射不变几何结构的对称正定矩阵。我们将R-PLS应用于两个功能成像数据集：COBRE（探究精神分裂症患者与健康对照组的功能差异）和ABIDE（比较自闭症谱系障碍患者与神经典型对照组）。通过利用R-PLS结果中的投影变量重要性统计量，我们识别出每个数据集中文献已有充分记载的关键功能连接。鉴于R-PLS的普适性，该方法有望为连接结构和功能连接组学的多模态成像分析开辟新途径。