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

We propose a method of analysis of dynamical networks based on a recent
measure of Granger causality between time series, based on kernel methods. The
generalization of kernel Granger causality to the multivariate case, here
presented, shares the following features with the bivariate measures: (i) the
nonlinearity of the regression model can be controlled by choosing the kernel
function and (ii) the problem of false-causalities, arising as the complexity
of the model increases, is addressed by a selection strategy of the
eigenvectors of a reduced Gram matrix whose range represents the additional
features due to the second time series. Moreover, there is no {\it a priori}
assumption that the network must be a directed acyclic graph. We apply the
proposed approach to a network of chaotic maps and to a simulated genetic
regulatory network: it is shown that the underlying topology of the network can
be reconstructed from time series of node's dynamics, provided that a
sufficient number of samples is available. Considering a linear dynamical
network, built by preferential attachment scheme, we show that for limited data
use of bivariate Granger causality is a better choice w.r.t methods using $L1$
minimization. Finally we consider real expression data from HeLa cells, 94
genes and 48 time points. The analysis of static correlations between genes
reveals two modules corresponding to well known transcription factors; Granger
analysis puts in evidence nineteen causal relationships, all involving genes
related to tumor development.

本文提出了一种基于核方法的分析动态网络的方法，该方法不需要先验假设网络是有向无环图。提出的方法已应用于混沌映射、模拟基因调控网络和真实表达数据中，针对肿瘤发展研究了 19 种涉及肿瘤发展相关基因的因果关系。