We observe that the view missing issue will incur unreliable neighbor relationships, thus breaking the key smoothness assumption in label propagation (LP). As shown in subfigures (A) and (B), missing samples in each view may generate multiple ''vacuum regions'' that fragment a complete category cluster into several sub-clusters, thereby distorting the smooth local structure on the common manifold. We term this phenomenon the Sub-Cluster Problem (SCP). Comparing subfigures (C) and (D), one could observe that SCP impedes the propagation of red label information to its corresponding sub-cluster, erroneously making the decision boundary recede into the vacuum region.

• MATLAB 2022a (64-bit)

• AGF_TI.m: the proposed AGF-TI method, whose optimization procedure is summarized in Algorithm 2.
• AGF_TI_grad.m: calculate the reduced gradient $\mathbf{g}$.
• AGF_TI_cost.m: update the fused bipartite graph $\mathbf{P}$ and compute the cost for optimal step length search $\theta$.
• AGF_TI_update.m: the implementation of the optimal step length search process and update the view weight coefficients $\boldsymbol{\alpha}$.

To classify the unlabeled instances in the incomplete multi-view semi-supervised learning task, you can run the following command in MATLAB:

[Ypred, Out] = AGF_TI(tensor_Z, num_class, Ll, existing_index, params)

• tensor_Z: third-order tensor of the bipartite graphs $\mathcal{Z}$, $(n, m, V)$.
• num_class: the number of classes, $c$.
• Ll: the label set of the labeled instances, ${y_i{\in}[c]}_{i=1}^\ell$.
• existing_index: the indicator matrix of size $n \times V$ to present the missing instance in each view, ${\pi_v, \omega_v}_{v=1}^V$.
• params: structure, parameters for the AGF-TI method, including:
  • params.maxIter: int, maximum number of iterations.
  • params.lambda: float, the trade-off parameter for the AGF.
  • params.beta: float, $\beta_\lambda$.
  • params.rho: float, the trade-off parameter for the Tensor Nuclear Norm.
  • params.seuildiffsigma: float, the threshold for convergence of Algorithm 1.
  • params.epson: float, the threshold for convergence of Algorithm 2.
  • params.goldensearch_deltmax: float, the initial precision of golden section search.
  • params.numericalprecision: float, the numerical precision weights below this value.
  • params.firstbasevariable: string, the tie breaking method for choosing the base.

• Ypred: the predicted labels of the unlabeled instances, $(n-\ell, 1)$
• Out: struct, the output of the algorithm
  • Out.F: the final representation of the fused labeled and unlabeled instances, $(n, c)$
  • Out.Q: the final representation of the fused anchors, $(m, c)$
  • Out.alpha: the final weights of the views, $(V, 1)$

More datasets can be found here.

Please cite our paper if it's helpful to your work!

@article{jiang2025AGF_TI,
  title={Adversarial Graph Fusion for Incomplete Multi-view Semi-supervised Learning with Tensorial Imputation},
  author={Jiang, Zhangqi and Luo, Tingjin and Yang, Xu and Xinyan, Liang},
  journal={arXiv preprint arXiv:2509.15955},
  year={2025}
}