Co-Hub Node Based Multiview Graph Learning with Theoretical Guarantees

TL;DR

This paper introduces a co-hub node model for multiview graph learning, leveraging shared hub nodes to improve structure estimation and providing theoretical guarantees on identifiability and error bounds.

Contribution

It proposes a novel co-hub node framework for multiview graphs, incorporating structured sparsity and offering theoretical analysis of layer identifiability and estimation accuracy.

Findings

Successfully identifies shared hub nodes in synthetic and real data

Achieves improved graph learning accuracy over existing methods

Provides theoretical bounds on estimation error and layer identifiability

Abstract

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.