Manifold-regression to predict from MEG/EEG brain signals without source modeling
Manifold-regression to predict from MEG/EEG brain signals without source modeling
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发表时间：
2019-06
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通讯作者：
D. Sabbagh;Pierre Ablin;G. Varoquaux;Alexandre Gramfort;D. Engemann
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作者：
D. Sabbagh;Pierre Ablin;G. Varoquaux;Alexandre Gramfort;D. Engemann
脑磁图和脑电图（M/EEG）可以实时无创地揭示神经元动力学，因此在医学和神经科学中受到重视。最近的进展，在建模脑行为的关系，突出了黎曼几何总结的空间相关的时间序列从M/EEG的协方差方面的有效性。然而，伪迹抑制后，M/EEG数据往往是秩亏的，这限制了黎曼概念的应用。在这篇文章中，我们专注于秩降维协方差矩阵的回归任务。我们研究了两种黎曼方法，矢量化的M/EEG传感器之间的协方差通过投影到一个切空间。Wasserstein距离很容易适用于秩缩减的数据，但缺乏仿射不变性。这可以通过找到一个共同的子空间，其中协方差矩阵是满秩，使仿射不变的几何距离。我们研究了这两种方法在合成生成模型中的意义，这使我们能够控制线性模型预测的估计偏差。我们表明，Wasserstein和几何距离允许生成模型上的完美样本外预测。然后，我们评估的方法对真实的数据的有效性，从M/EEG协方差矩阵预测年龄。研究结果表明，数据驱动的黎曼方法优于不同的传感器空间估计器，并且它们接近需要MRI采集和繁琐的数据处理的生物制药驱动的源定位模型的性能。我们的研究表明，所提出的黎曼方法可以作为基本的积木自动化大规模分析M/EEG。
Magnetoencephalography and electroencephalography (M/EEG) can reveal neuronal dynamics non-invasively in real-time and are therefore appreciated methods in medicine and neuroscience. Recent advances in modeling brain-behavior relationships have highlighted the effectiveness of Riemannian geometry for summarizing the spatially correlated time-series from M/EEG in terms of their covariance. However, after artefact-suppression, M/EEG data is often rank deficient which limits the application of Riemannian concepts. In this article, we focus on the task of regression with rank-reduced covariance matrices. We study two Riemannian approaches that vectorize the M/EEG covariance between-sensors through projection into a tangent space. The Wasserstein distance readily applies to rank-reduced data but lacks affine-invariance. This can be overcome by finding a common subspace in which the covariance matrices are full rank, enabling the affine-invariant geometric distance. We investigated the implications of these two approaches in synthetic generative models, which allowed us to control estimation bias of a linear model for prediction. We show that Wasserstein and geometric distances allow perfect out-of-sample prediction on the generative models. We then evaluated the methods on real data with regard to their effectiveness in predicting age from M/EEG covariance matrices. The findings suggest that the data-driven Riemannian methods outperform different sensor-space estimators and that they get close to the performance of biophysics-driven source-localization model that requires MRI acquisitions and tedious data processing. Our study suggests that the proposed Riemannian methods can serve as fundamental building-blocks for automated large-scale analysis of M/EEG.