Co-Hub Node Based Multiview Graph Learning with Theoretical Guarantees
This addresses the need for more accurate and interpretable graph learning in applications like neuroscience, though it is incremental by extending existing multiview methods with a node-based approach.
The paper tackles the problem of learning multiple related graphs from heterogeneous multiview data by proposing a co-hub node model that assumes shared hub nodes across views, and it demonstrates improved precision with theoretical guarantees and validation on synthetic and fMRI data.
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.