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Adversarial Graph Fusion for Incomplete Multi-view Semi-supervised Learning with Tensorial Imputation

Zhangqi Jiang, Tingjin Luo, Xu Yang, Xinyan Liang

TL;DR

The paper tackles the Sub-Cluster Problem (SCP) caused by missing views in graph-based multi-view semi-supervised learning and introduces AGF-TI, a method that combines Adversarial Graph Fusion with Tensorial Imputation. It frames graph fusion as a min-max optimization across anchor-based bipartite graphs and recovers missing local structure via a third-order tensor with Tensor Nuclear Norm (TNN), while using an anchor-based strategy for scalability. An ADMM-based alternating optimization, augmented with a reduced-gradient inner loop, ensures convergence to a stationary point. Empirical results on six public datasets across various view-missing and label-scarcity settings show that AGF-TI outperforms state-of-the-art baselines, validating its robustness, efficiency, and practical impact for incomplete multi-view data.

Abstract

View missing remains a significant challenge in graph-based multi-view semi-supervised learning, hindering their real-world applications. To address this issue, traditional methods introduce a missing indicator matrix and focus on mining partial structure among existing samples in each view for label propagation (LP). However, we argue that these disregarded missing samples sometimes induce discontinuous local structures, i.e., sub-clusters, breaking the fundamental smoothness assumption in LP. Consequently, such a Sub-Cluster Problem (SCP) would distort graph fusion and degrade classification performance. To alleviate SCP, we propose a novel incomplete multi-view semi-supervised learning method, termed AGF-TI. Firstly, we design an adversarial graph fusion scheme to learn a robust consensus graph against the distorted local structure through a min-max framework. By stacking all similarity matrices into a tensor, we further recover the incomplete structure from the high-order consistency information based on the low-rank tensor learning. Additionally, the anchor-based strategy is incorporated to reduce the computational complexity. An efficient alternative optimization algorithm combining a reduced gradient descent method is developed to solve the formulated objective, with theoretical convergence. Extensive experimental results on various datasets validate the superiority of our proposed AGF-TI as compared to state-of-the-art methods. Code is available at https://github.com/ZhangqiJiang07/AGF_TI.

Adversarial Graph Fusion for Incomplete Multi-view Semi-supervised Learning with Tensorial Imputation

TL;DR

The paper tackles the Sub-Cluster Problem (SCP) caused by missing views in graph-based multi-view semi-supervised learning and introduces AGF-TI, a method that combines Adversarial Graph Fusion with Tensorial Imputation. It frames graph fusion as a min-max optimization across anchor-based bipartite graphs and recovers missing local structure via a third-order tensor with Tensor Nuclear Norm (TNN), while using an anchor-based strategy for scalability. An ADMM-based alternating optimization, augmented with a reduced-gradient inner loop, ensures convergence to a stationary point. Empirical results on six public datasets across various view-missing and label-scarcity settings show that AGF-TI outperforms state-of-the-art baselines, validating its robustness, efficiency, and practical impact for incomplete multi-view data.

Abstract

View missing remains a significant challenge in graph-based multi-view semi-supervised learning, hindering their real-world applications. To address this issue, traditional methods introduce a missing indicator matrix and focus on mining partial structure among existing samples in each view for label propagation (LP). However, we argue that these disregarded missing samples sometimes induce discontinuous local structures, i.e., sub-clusters, breaking the fundamental smoothness assumption in LP. Consequently, such a Sub-Cluster Problem (SCP) would distort graph fusion and degrade classification performance. To alleviate SCP, we propose a novel incomplete multi-view semi-supervised learning method, termed AGF-TI. Firstly, we design an adversarial graph fusion scheme to learn a robust consensus graph against the distorted local structure through a min-max framework. By stacking all similarity matrices into a tensor, we further recover the incomplete structure from the high-order consistency information based on the low-rank tensor learning. Additionally, the anchor-based strategy is incorporated to reduce the computational complexity. An efficient alternative optimization algorithm combining a reduced gradient descent method is developed to solve the formulated objective, with theoretical convergence. Extensive experimental results on various datasets validate the superiority of our proposed AGF-TI as compared to state-of-the-art methods. Code is available at https://github.com/ZhangqiJiang07/AGF_TI.

Paper Structure

This paper contains 35 sections, 9 theorems, 46 equations, 15 figures, 14 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminary and Related Work
  3. Graph-based Multi-view Semi-supervised Learning
  4. Accelerated GMvSSL with Bipartite Graphs
  5. Third-order Tensor for Multi-view Learning
  6. Methodology
  7. Proposed Formulation
  8. Optimization
  9. Experiments
  10. Experimental Settings
  11. Main Results
  12. Ablation Study
  13. Model Analysis
  14. Conclusion
  15. Basic Tensor Operators
  16. ...and 20 more sections

Key Result

Theorem 1

$h(\boldsymbol{\alpha})$ is differentiable, and its gradient can be calculated as $\frac{\partial h(\boldsymbol{\alpha})}{\partial \alpha_v}{=}2\lambda\alpha_v\text{Tr}(\mathbf{P}^{\star\top}\mathbf{Z}_v\mathbf{T}_v)$, where $\mathbf{P}^{\star}$ is the optimal solution of the inner maximization prob

Figures (15)

  • Figure 1: (A)--(D) is an example for the Sub-Cluster Problem (SCP), and (E) shows the proposed AGF-TI. SCP: sub-clusters caused by the missing samples break the smoothness assumption in Label Propagation (LP). To address SCP, AGF-TI comprises an adversarial graph fusion operator to learn a robust fused graph, and tensor learning to recover similarity relationships of missing samples.
  • Figure 2: ACC results on six datasets with LAR varying in {1%, 2%, 4%, 8%} when VMR is 60%.
  • Figure 3: Ablation study of AGF-TI under LAR is 5%.
  • Figure 4: The iterative error and classification performance of AGF-TI during optimization process.
  • Figure 5: Parameter sensitivity analysis of $\beta_\lambda$ and $\rho$ in terms of Accuracy.
  • ...and 10 more figures

Theorems & Definitions (13)

  • Definition 1: Tensor Nuclear Norm
  • Remark 1: Benefits of AGF
  • Theorem 1
  • Theorem 2
  • Definition 2: Orthogonal Tensor
  • Definition 3: t-SVD
  • Theorem 3
  • Lemma 1
  • Theorem 4
  • Corollary 1
  • ...and 3 more