Graph convolutional networks (GCN) leverage topology-driven graph convolutional operations to combine information across the graph for inference tasks. In our recent work, we have studied GCNs with covariance matrices as graphs in the form of coVariance neural networks (VNNs) that draw similarities with traditional PCA-driven data analysis approaches while offering significant advantages over them. In this paper, we first focus on theoretically characterizing the transferability of VNNs. The notion of transferability is motivated from the intuitive expectation that learning models could generalize to "compatible" datasets (possibly of different dimensionalities) with minimal effort. VNNs inherit the scale-free data processing architecture from GCNs and here, we show that VNNs exhibit transferability of performance over datasets whose covariance matrices converge to a limit object. Multi-scale neuroimaging datasets enable the study of the brain at multiple scales and hence, can validate the theoretical results on the transferability of VNNs. To gauge the advantages offered by VNNs in neuroimaging data analysis, we focus on the task of "brain age" prediction using cortical thickness features. In clinical neuroscience, there has been an increased interest in machine learning algorithms which provide estimates of "brain age" that deviate from chronological age. We leverage the architecture of VNNs to extend beyond the coarse metric of brain age gap in Alzheimer's disease (AD) and make two important observations: (i) VNNs can assign anatomical interpretability to elevated brain age gap in AD, and (ii) the interpretability offered by VNNs is contingent on their ability to exploit specific principal components of the anatomical covariance matrix. We further leverage the transferability of VNNs to cross validate the above observations across different datasets.

翻译：图卷积网络（GCN）利用拓扑驱动的图卷积操作，跨越图结构整合信息以完成推理任务。在近期工作中，我们研究了以协方差矩阵作为图的GCN，即协方差神经网络（VNN），其与传统PCA驱动的数据分析方法具有相似性，同时展现出显著优势。本文首先从理论上刻画VNN的迁移性。迁移性概念源于直观预期：学习模型能以最小代价泛化至“兼容”数据集（可能具有不同维度）。VNN从GCN继承了无标度数据处理架构，我们证明：当数据集的协方差矩阵收敛至极限对象时，VNN在这些数据集上展现出性能迁移性。多尺度神经影像数据集支持跨尺度脑研究，因而可验证VNN迁移性的理论结果。为评估VNN在神经影像数据分析中的优势，我们聚焦于利用皮层厚度特征进行“脑龄”预测任务。在临床神经科学中，能够提供偏离实际年龄的“脑龄”估计的机器学习算法日益受到关注。我们利用VNN架构，超越阿尔茨海默病中脑龄差距的粗略度量，获得两项重要发现：(i) VNN可将阿尔茨海默病中升高的脑龄差距赋予解剖学可解释性；(ii) VNN提供的可解释性取决于其利用解剖协方差矩阵特定主成分的能力。我们进一步利用VNN的迁移性，在不同数据集上交叉验证上述发现。