Related papers: A Graph Convolution for Signed Directed Graphs
In this paper, we develop a new aligned vertex convolutional network model to learn multi-scale local-level vertex features for graph classification. Our idea is to transform the graphs of arbitrary sizes into fixed-sized aligned vertex…
Signed graphs have their edges labeled either as positive or negative. Here we introduce two types of signed distance matrix for signed graphs. We characterize balance in signed graphs using these matrices and we obtain explicit formulae…
Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In…
Graph Neural Networks (GNNs) have become the de-facto standard tool for modeling relational data. However, while many real-world graphs are directed, the majority of today's GNN models discard this information altogether by simply making…
The paper gives a thorough introduction to spectra of digraphs via its Hermitian adjacency matrix. This matrix is indexed by the vertices of the digraph, and the entry corresponding to an arc from $x$ to $y$ is equal to the complex unity…
A graph is a powerful concept for representation of relations between pairs of entities. Data with underlying graph structure can be found across many disciplines and there is a natural desire for understanding such data better. Deep…
A mixed graph is a graph with undirected and directed edges. Guo and Mohar in 2017 determined all mixed graphs whose Hermitian spectral radii are less than $2$. In this paper, we give a sufficient condition which can make Hermitian spectral…
Graph representation learning is a fundamental problem for modeling relational data and benefits a number of downstream applications. Traditional Bayesian-based graph models and recent deep learning based GNN either suffer from…
Recent advent in graph signal processing (GSP) has led to the development of new graph-based transforms and wavelets for image / video coding, where the underlying graph describes inter-pixel correlations. In this paper, we develop a new…
We propose a symmetric graph convolutional autoencoder which produces a low-dimensional latent representation from a graph. In contrast to the existing graph autoencoders with asymmetric decoder parts, the proposed autoencoder has a newly…
Geometric variations like rotation, scaling, and viewpoint changes pose a significant challenge to visual understanding. One common solution is to directly model certain intrinsic structures, e.g., using landmarks. However, it then becomes…
Signature is an infinite graded sequence of statistics known to characterize geometric rough paths, which includes the paths with bounded variation. This object has been studied successfully for machine learning with mostly applications in…
An oriented hypergraph is an oriented incidence structure that generalizes and unifies graph and hypergraph theoretic results by examining its locally signed graphic substructure. In this paper we obtain a combinatorial characterization of…
Signed Graph Neural Networks (SGNNs) have been shown to be effective in analyzing complex patterns in real-world situations where positive and negative links coexist. However, SGNN models suffer from poor explainability, which limit their…
Recent spectral graph sparsification research allows constructing nearly-linear-sized subgraphs that can well preserve the spectral (structural) properties of the original graph, such as the first few eigenvalues and eigenvectors of the…
Graph machine learning has been widely explored in various domains, such as community detection, transaction analysis, and recommendation systems. In these applications, anomaly detection plays an important role. Recently, studies have…
Directed graphs are widely used to model asymmetric relationships in real-world systems. However, existing directed graph neural networks often struggle to jointly capture directional semantics and global structural patterns due to their…
Convolution operations designed for graph-structured data usually utilize the graph Laplacian, which can be seen as message passing between the adjacent neighbors through a generic random walk. In this paper, we propose PAN, a new graph…
Spectral Graph Convolutional Networks (spectral GCNNs), a powerful tool for analyzing and processing graph data, typically apply frequency filtering via Fourier transform to obtain representations with selective information. Although…
A matching M is a dominating induced matching of a graph, if every edge of the graph is either in $M$ or has a common end-vertex with exactly one edge in $M$. The concept of complete dominating induced matching is introduced as graphs where…