In this paper, we study the problem of unsupervised graph representation
learning by harnessing the control properties of dynamical networks defined on
graphs. Our approach introduces a novel framework for contrastive learning, a
widely prevalent technique for unsupervised representation learning. A crucial
step in contrastive learning is the creation of 'augmented' graphs from the
input graphs. Though different from the original graphs, these augmented graphs
retain the original graph's structural characteristics. Here, we propose a
unique method for generating these augmented graphs by leveraging the control
properties of networks. The core concept revolves around perturbing the
original graph to create a new one while preserving the controllability
properties specific to networks and graphs. Compared to the existing methods,
we demonstrate that this innovative approach enhances the effectiveness of
contrastive learning frameworks, leading to superior results regarding the
accuracy of the classification tasks. The key innovation lies in our ability to
decode the network structure using these control properties, opening new
avenues for unsupervised graph representation learning.

通过利用动态网络的控制特性对无监督图表示学习问题进行研究，我们提出了一种基于对比学习的新框架。我们通过利用网络的控制特性生成扩展图，保留了原始图的结构特征，提高了分类任务准确性。这种创新方法的关键在于利用控制特性解码网络结构，为无监督图表示学习开辟了新的方向。

基于控制的数据增强对比学习中的图嵌入

Control-based Graph Embeddings with Data Augmentation for Contrastive  Learning

Augmented graphs play a vital role in regularizing Graph Neural Networks
(GNNs), which leverage information exchange along edges in graphs, in the form
of message passing, for learning. Due to their effectiveness, simple edge and
node manipulations (e.g., addition and deletion) have been widely used in graph
augmentation. Nevertheless, such common augmentation techniques can
dramatically change the semantics of the original graph, causing overaggressive
augmentation and thus under-fitting in the GNN learning. To address this
problem arising from dropping or adding graph edges and nodes, we propose
SoftEdge, which assigns random weights to a portion of the edges of a given
graph for augmentation. The synthetic graph generated by SoftEdge maintains the
same nodes and their connectivities as the original graph, thus mitigating the
semantic changes of the original graph. We empirically show that this simple
method obtains superior accuracy to popular node and edge manipulation
approaches and notable resilience to the accuracy degradation with the GNN
depth.

通过在给定图的一部分边缘分配随机权值的方式生成合成图，SoftEdge 方法可以缓解对原始图的语义更改，从而提高了图神经网络（GNN）的学习精确度和深度鲁棒性。