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Multiview Graph Learning with Consensus Graph

Abdullah Karaaslanli, Selin Aviyente

TL;DR

This work tackles the problem of inferring multiple related graphs from heterogeneous observations by introducing a consensus-based multiview graph learning framework. It jointly learns per-view graphs and a shared consensus graph under a smoothness prior on graph signals, via a general optimization with configurable consensus and regularization terms. Two concrete models, mvGL-l1 and mvGL-l2, illustrate the framework’s flexibility, and an ADMM-based solver enables scalable optimization. Empirical results on simulated data and EEG demonstrate improved view-edge recovery, meaningful shared structure across subjects, and improved cross-subject community consistency, highlighting the method’s potential for uncovering both common and subject-specific network features. The proposed approach provides a principled way to synthesize information across related graphs and can be extended to alternative similarity notions and larger-scale problems.

Abstract

Graph topology inference, i.e., learning graphs from a given set of nodal observations, is a significant task in many application domains. Existing approaches are mostly limited to learning a single graph assuming that the observed data is homogeneous. This is problematic because many modern datasets are heterogeneous or mixed and involve multiple related graphs, i.e., multiview graphs. Recent work proposing to learn multiview graphs ensures the similarity of learned view graphs through pairwise regularization, where each pair of views is encouraged to have similar structures. However, this approach cannot infer the shared structure across views. In this work, we propose an alternative method based on consensus regularization, where views are ensured to be similar through a learned consensus graph representing the common structure of the views. In particular, we propose an optimization problem, where graph data is assumed to be smooth over the multiview graph and the topology of the individual views and that of the consensus graph are learned, simultaneously. Our optimization problem is designed to be general in the sense that different regularization functions can be used depending on what the shared structure across views is. Moreover, we propose two regularization functions that extend fused and group graphical lasso to consensus based regularization. Proposed multiview graph learning is evaluated on simulated data and shown to have better performance than existing methods. It is also employed to infer the functional brain connectivity networks of multiple subjects from their electroencephalogram (EEG) recordings. The proposed method reveals the structure shared by subjects as well as the characteristics unique to each subject.

Multiview Graph Learning with Consensus Graph

TL;DR

This work tackles the problem of inferring multiple related graphs from heterogeneous observations by introducing a consensus-based multiview graph learning framework. It jointly learns per-view graphs and a shared consensus graph under a smoothness prior on graph signals, via a general optimization with configurable consensus and regularization terms. Two concrete models, mvGL-l1 and mvGL-l2, illustrate the framework’s flexibility, and an ADMM-based solver enables scalable optimization. Empirical results on simulated data and EEG demonstrate improved view-edge recovery, meaningful shared structure across subjects, and improved cross-subject community consistency, highlighting the method’s potential for uncovering both common and subject-specific network features. The proposed approach provides a principled way to synthesize information across related graphs and can be extended to alternative similarity notions and larger-scale problems.

Abstract

Graph topology inference, i.e., learning graphs from a given set of nodal observations, is a significant task in many application domains. Existing approaches are mostly limited to learning a single graph assuming that the observed data is homogeneous. This is problematic because many modern datasets are heterogeneous or mixed and involve multiple related graphs, i.e., multiview graphs. Recent work proposing to learn multiview graphs ensures the similarity of learned view graphs through pairwise regularization, where each pair of views is encouraged to have similar structures. However, this approach cannot infer the shared structure across views. In this work, we propose an alternative method based on consensus regularization, where views are ensured to be similar through a learned consensus graph representing the common structure of the views. In particular, we propose an optimization problem, where graph data is assumed to be smooth over the multiview graph and the topology of the individual views and that of the consensus graph are learned, simultaneously. Our optimization problem is designed to be general in the sense that different regularization functions can be used depending on what the shared structure across views is. Moreover, we propose two regularization functions that extend fused and group graphical lasso to consensus based regularization. Proposed multiview graph learning is evaluated on simulated data and shown to have better performance than existing methods. It is also employed to infer the functional brain connectivity networks of multiple subjects from their electroencephalogram (EEG) recordings. The proposed method reveals the structure shared by subjects as well as the characteristics unique to each subject.
Paper Structure (22 sections, 10 equations, 6 figures, 1 table)

This paper contains 22 sections, 10 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Background
  4. Notations
  5. Graphs and Graph Signals
  6. Single Graph Learning
  7. Multiview Graph Learning
  8. Problem Formulation
  9. Optimization
  10. Selection of $c(\cdot)$ and $r(\cdot)$
  11. Convergence and Computational Complexity
  12. Results
  13. Simulated Datasets
  14. EEG Dataset
  15. Data Description
  16. ...and 7 more sections

Figures (6)

  • Figure 1: Performance of methods when learning view graphs. a., b. and c. show the results when the consensus graph is generated using Erdős–Rényi. d., e. and f. show the performance when the consensus graph is drawn from Barabási–Albert. Changes in performance with respect to number of views (a. and d.), number of signals (b. and e.) and the amount on noise (c. and f.) are plotted. Shaded area is the $95\%$ confidence interval calculated from $10$ realizations of simulated data.
  • Figure 2: Performance of methods when learning the consensus graphs. a., b. and c. show the results when consensus graph is generated with Erdős–Rényi; and d., e. and f. show the performance for Barabási–Albert model. Changes in performance with respect to number of views (a. and d.), number of signals (b. and e.) and the amount on noise (c. and f.) are plotted. Shaded area is the $95\%$ confidence interval calculated from $10$ realizations of simulated data.
  • Figure 3: Run times of methods with increasing number of nodes (a.) and number of views (b.). For svGL, we report total run time to learn all views.
  • Figure 4: Performance of different methods when "ground-truth" graphs are constructed with $\textrm{svGL}$ using all EEG trials. a) A "ground-truth" graph is constructed for each subject using all available trials of the subject. b) A single "ground-truth" graph is constructed across all trials and subjects.
  • Figure 5: Total variation of test data on subject graphs learned by different methods.
  • ...and 1 more figures