Though graph representation learning (GRL) has made significant progress, it
is still a challenge to extract and embed the rich topological structure and
feature information in an adequate way. Most existing methods focus on local
structure and fail to fully incorporate the global topological structure. To
this end, we propose a novel Structure-Preserving Graph Representation Learning
(SPGRL) method, to fully capture the structure information of graphs.
Specifically, to reduce the uncertainty and misinformation of the original
graph, we construct a feature graph as a complementary view via k-Nearest
Neighbor method. The feature graph can be used to contrast at node-level to
capture the local relation. Besides, we retain the global topological structure
information by maximizing the mutual information (MI) of the whole graph and
feature embeddings, which is theoretically reduced to exchanging the feature
embeddings of the feature and the original graphs to reconstruct themselves.
Extensive experiments show that our method has quite superior performance on
semi-supervised node classification task and excellent robustness under noise
perturbation on graph structure or node features.

提出了一种新型的结构保持的图表示学习方法（SPGRL），通过构建特征图对原始图进行对比，在保留全局拓扑结构信息的同时最大化整幅图和特征嵌入的互信息，该方法在简单噪声扰动下表现优异，且针对半监督节点分类任务具有很高的性能。

结构保持图表示学习

Structure-Preserving Graph Representation Learning

Identifying an appropriate underlying graph kernel that reflects pairwise
similarities is critical in many recent graph spectral signal restoration
schemes, including image denoising, dequantization, and contrast enhancement.
Existing graph learning algorithms compute the most likely entries of a
properly defined graph Laplacian matrix $\mathbf{L}$, but require a large
number of signal observations $\mathbf{z}$'s for a stable estimate. In this
work, we assume instead the availability of a relevant feature vector
$\mathbf{f}_i$ per node $i$, from which we compute an optimal feature graph via
optimization of a feature metric. Specifically, we alternately optimize the
diagonal and off-diagonal entries of a Mahalanobis distance matrix $\mathbf{M}$
by minimizing the graph Laplacian regularizer (GLR) $\mathbf{z}^{\top}
\mathbf{L} \mathbf{z}$, where edge weight is $w_{i,j} = \exp\{-(\mathbf{f}_i -
\mathbf{f}_j)^{\top} \mathbf{M} (\mathbf{f}_i - \mathbf{f}_j) \}$, given a
single observation $\mathbf{z}$. We optimize diagonal entries via proximal
gradient (PG), where we constrain $\mathbf{M}$ to be positive definite (PD) via
linear inequalities derived from the Gershgorin circle theorem. To optimize
off-diagonal entries, we design a block descent algorithm that iteratively
optimizes one row and column of $\mathbf{M}$. To keep $\mathbf{M}$ PD, we
constrain the Schur complement of sub-matrix $\mathbf{M}_{2,2}$ of $\mathbf{M}$
to be PD when optimizing via PG. Our algorithm mitigates full
eigen-decomposition of $\mathbf{M}$, thus ensuring fast computation speed even
when feature vector $\mathbf{f}_i$ has high dimension. To validate its
usefulness, we apply our feature graph learning algorithm to the problem of 3D
point cloud denoising, resulting in state-of-the-art performance compared to
competing schemes in extensive experiments.

本文提出一种基于特征图的方法来学习图信号的复原，通过最小化图拉普拉斯正则项以优化马氏距离矩阵的带权图，在 3D 点云去噪问题上的实验证明，相较于已有的方案，该算法具有最先进的性能。