Related papers: On the Similarity between von Neumann Graph Entrop…
Learning meaningful graphs from data plays important roles in many data mining and machine learning tasks, such as data representation and analysis, dimension reduction, data clustering, and visualization, etc. In this work, for the first…
Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and…
Graph Neural Networks (GNNs) are de facto solutions to structural data learning. However, it is susceptible to low-quality and unreliable structure, which has been a norm rather than an exception in real-world graphs. Existing graph…
We propose a pair of completely data-driven algorithms for unsupervised classification and dimension reduction, and we empirically study their performance on a number of data sets, both simulated data in three-dimensions and images from the…
Graph signal processing (GSP) is a prominent framework for analyzing signals on non-Euclidean domains. The graph Fourier transform (GFT) uses the combinatorial graph Laplacian matrix to reveal the spectral decomposition of signals in the…
Entropic causal inference is a recent framework for learning the causal graph between two variables from observational data by finding the information-theoretically simplest structural explanation of the data, i.e., the model with smallest…
Effective resistance (ER) is an attractive way to interrogate the structure of graphs. It is an alternative to computing the eigen-vectors of the graph Laplacian. Graph laplacians are used to find low dimensional structures in high…
In recent years, kernel methods are widespread in tasks of similarity measuring. Specifically, graph kernels are widely used in fields of bioinformatics, chemistry and financial data analysis. However, existing methods, especially entropy…
Machine learning on graph-structured data has attracted high research interest due to the emergence of Graph Neural Networks (GNNs). Most of the proposed GNNs are based on the node homophily, i.e neighboring nodes share similar…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
The chain rule for the Shannon and von Neumann entropy, which relates the total entropy of a system to the entropies of its parts, is of central importance to information theory. Here we consider the chain rule for the more general smooth…
Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…
In information theory, one major goal is to find useful functions that summarize the amount of information contained in the interaction of several random variables. Specifically, one can ask how the classical Shannon entropy, mutual…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
The entropy of a graph was first introduced by Rashevsky \cite{Rashevsky} and Trucco \cite{Trucco} to interpret as the structural information content of the graph and serve as a complexity measure. In this paper, we first state a number of…
Graph neural networks (GNNs) achieve strong performance on graph learning tasks, but training on large-scale networks remains computationally challenging. Transferability results show that GNNs with fixed weights can generalize from smaller…
We study the richness of the ensemble of graphical structures (i.e., unlabeled graphs) of the one-dimensional random geometric graph model defined by $n$ nodes randomly scattered in $[0,1]$ that connect if they are within the connection…
Graph signals offer a very generic and natural representation for data that lives on networks or irregular structures. The actual data structure is however often unknown a priori but can sometimes be estimated from the knowledge of the…
Network architecture design is very important for the optimization of industrial networks. The type of network architecture can be divided into small-scale network and large-scale network according to its scale. Graph theory is an efficient…
Graph neural networks (GNNs) have emerged as a fundamental tool for learning from graph-structured data, achieving strong performance across a wide range of applications. However, understanding their generalization capabilities remains…