提出共享枢纽节点的多视图图学习模型，提升结构识别精度。
Co-Hub Node Based Multiview Graph Learning with Theoretical Guarantees
- 假设不同视图共享一组枢纽节点，通过结构稀疏性约束建模。
- 在合成数据和多被试fMRI数据上成功识别出多个相关图结构。
- 理论证明了层可识别性并给出估计误差上界，适合图神经网络研究者。
揭示多变量数据背后的图结构在众多应用中至关重要。现有方法大多假设观测数据一致，仅推断单一图结构，但实际中常存在多个密切相关图（即多视图图）。以往多视图图学习多通过成对或共识正则化强化视图间边的相似性，然而多视图图常具有共享的节点级架构，如共同的枢纽节点，此类共性可提升学习精度并提供可解释性。本文提出一种共枢纽节点模型，假设不同视图共享一组枢纽节点，通过在这些共枢纽节点的连接上施加结构稀疏性来构建优化框架。此外，我们对层可识别性进行了理论分析，并给出了估计误差的上界。所提方法在合成图数据与多被试fMRI时间序列数据上验证，成功辨识出多个紧密相关的图结构。
原文摘要 · Abstract (English)
Identifying the graphical structure underlying the observed multivariate data is essential in numerous applications. Current methodologies are predominantly confined to deducing a singular graph under the presumption that the observed data are uniform. However, many contexts involve heterogeneous datasets that feature multiple closely related graphs, typically referred to as multiview graphs. Previous research on multiview graph learning promotes edge-based similarity across layers using pairwise or consensus-based regularizers. However, multiview graphs frequently exhibit a shared node-based architecture across different views, such as common hub nodes. Such commonalities can enhance the precision of learning and provide interpretive insight. In this paper, we propose a co-hub node model, positing that different views share a common group of hub nodes. The associated optimization framework is developed by enforcing structured sparsity on the connections of these co-hub nodes. Moreover, we present a theoretical examination of layer identifiability and determine bounds on estimation error. The proposed methodology is validated using both synthetic graph data and fMRI time series data from multiple subjects to discern several closely related graphs.
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