mSPD-NN: A Geometrically Aware Neural Framework for Biomarker Discovery from Functional Connectomics Manifolds
mSPD-NN: A Geometrically Aware Neural Framework for Biomarker Discovery from Functional Connectomics Manifolds
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DOI：
10.48550/arxiv.2303.14986
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发表时间：
2023-03
期刊：
影响因子：
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通讯作者：
N. S. D'Souza;A. Venkataraman
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文献类型：
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作者：
N. S. D'Souza;A. Venkataraman
连接组学已成为神经成像中的一个强大工具，并推动了连接数据统计和机器学习方法的最新进展。尽管连接体存在于矩阵流形中，但大多数分析框架忽略了底层的数据几何。这在很大程度上是因为简单的操作，如均值估计，没有容易计算的封闭形式的解决方案。我们提出了一个几何感知的神经框架连接体，即，mSPD-NN，旨在估计对称正定（SPD）矩阵集合的测地平均值。mSPD-NN是由双线性全连接层与捆绑的权重，并利用一种新的损失函数来优化矩阵法方程所产生的Fr\'echet平均估计。通过对合成数据的实验，我们证明了我们的mSPD-NN对SPD均值估计的常见替代方案的有效性，在可扩展性和对噪声的鲁棒性方面提供了有竞争力的性能。我们在rs-fMRI数据的多个实验中说明了mSPD-NN在现实世界中的灵活性，并证明了它揭示了与ADHD-ASD合并症患者和健康对照之间的微妙网络差异相关的稳定生物标志物。
Connectomics has emerged as a powerful tool in neuroimaging and has spurred recent advancements in statistical and machine learning methods for connectivity data. Despite connectomes inhabiting a matrix manifold, most analytical frameworks ignore the underlying data geometry. This is largely because simple operations, such as mean estimation, do not have easily computable closed-form solutions. We propose a geometrically aware neural framework for connectomes, i.e., the mSPD-NN, designed to estimate the geodesic mean of a collections of symmetric positive definite (SPD) matrices. The mSPD-NN is comprised of bilinear fully connected layers with tied weights and utilizes a novel loss function to optimize the matrix-normal equation arising from Fr\'echet mean estimation. Via experiments on synthetic data, we demonstrate the efficacy of our mSPD-NN against common alternatives for SPD mean estimation, providing competitive performance in terms of scalability and robustness to noise. We illustrate the real-world flexibility of the mSPD-NN in multiple experiments on rs-fMRI data and demonstrate that it uncovers stable biomarkers associated with subtle network differences among patients with ADHD-ASD comorbidities and healthy controls.