Related papers: On spectral embedding performance and elucidating …

Spectral graph sparsification is a classical tool for reducing graph complexity while preserving Laplacian quadratic forms. In graph neural networks (GNNs), sparsification is often used to accelerate computation while maintaining predictive…

Spectral graph convolutional networks are generalizations of standard convolutional networks for graph-structured data using the Laplacian operator. A common misconception is the instability of spectral filters, i.e. the impossibility to…

We present a novel spectral embedding of graphs that incorporates weights assigned to the nodes, quantifying their relative importance. This spectral embedding is based on the first eigenvectors of some properly normalized version of the…

We consider the stochastic block model where connection between vertices is perturbed by some latent (and unobserved) random geometric graph. The objective is to prove that spectral methods are robust to this type of noise, even if they are…

Contrastive learning has emerged as a premier method for learning representations with or without supervision. Recent studies have shown its utility in graph representation learning for pre-training. Despite successes, the understanding of…

Graph embedding provides a feasible methodology to conduct pattern classification for graph-structured data by mapping each data into the vectorial space. Various pioneering works are essentially coding method that concentrates on a…

Finding communities in networks is a problem that remains difficult, in spite of the amount of attention it has recently received. The Stochastic Block-Model (SBM) is a generative model for graphs with "communities" for which, because of…

The null space of the $k$-th order Laplacian $\mathbf{\mathcal L}_k$, known as the {\em $k$-th homology vector space}, encodes the non-trivial topology of a manifold or a network. Understanding the structure of the homology embedding can…

Graph is a highly generic and diverse representation, suitable for almost any data processing problem. Spectral graph theory has been shown to provide powerful algorithms, backed by solid linear algebra theory. It thus can be extremely…

The asymptotic behaviour of dynamical processes in networks can be expressed as a function of spectral properties of the corresponding adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of…

Connection graphs (CGs) extend traditional graph models by coupling network topology with orthogonal transformations, enabling the representation of global geometric consistency. They play a key role in applications such as synchronization,…

Despite being very successful within the pattern recognition and machine learning community, graph-based methods are often unusable because of the lack of mathematical operations defined in graph domain. Graph embedding, which maps graphs…

Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as…

Several state-of-the-art neural graph embedding methods are based on short random walks (stochastic processes) because of their ease of computation, simplicity in capturing complex local graph properties, scalability, and interpretibility.…

In this paper, we focus on learning sparse graphs with a core-periphery structure. We propose a generative model for data associated with core-periphery structured networks to model the dependence of node attributes on core scores of the…

Spectral embedding finds vector representations of the nodes of a network, based on the eigenvectors of a properly constructed matrix, and has found applications throughout science and technology. Many networks are multipartite, meaning…

The exploitation of graph structures is the key to effectively learning representations of nodes that preserve useful information in graphs. A remarkable property of graph is that a latent hierarchical grouping of nodes exists in a global…

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…

We consider graphs where edges and their signs are added independently at random from among all pairs of nodes. We establish strong concentration inequalities for adjacency and Laplacian matrices obtained from this family of random graph…

Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…