Related papers: Graph Laplacians, Riemannian Manifolds and their M…
Networks arise in many applications, such as in the analysis of text documents, social interactions and brain activity. We develop a general framework for extrinsic statistical analysis of samples of networks, motivated by networks…
Modern data introduces new challenges to classic signal processing approaches, leading to a growing interest in the field of graph signal processing. A powerful and well established model for real world signals in various domains is sparse…
According to a recent conjecture, isospectral objects have different nodal count sequences. We study generalized Laplacians on discrete graphs, and use them to construct the first non-trivial counter-examples to this conjecture. In…
We propose a general multi-class visual recognition model, termed the Classifier Graph, which aims to generalize and integrate ideas from many of today's successful hierarchical recognition approaches. Our graph-based model has the…
Many tasks require mapping continuous input data (e.g. images) to discrete task outputs (e.g. class labels). Yet, how neural networks learn to perform such discrete computations on continuous data manifolds remains poorly understood. Here,…
As key subjects in spectral geometry and combinatorial graph theory respectively, the (continuous) Hodge Laplacian and the combinatorial Laplacian share similarities in revealing the topological dimension and geometric shape of data and in…
The prevalence of graph-based data has spurred the rapid development of graph neural networks (GNNs) and related machine learning algorithms. Yet, despite the many datasets naturally modeled as directed graphs, including citation, website,…
We give inequalities relating the eigenvalues of the adjacency matrix and the Laplacian of a graph, and its minimum and maximum degrees. The results are applied to derive new conditions for quasi-randomness of graphs.
Learning to optimize is a rapidly growing area that aims to solve optimization problems or improve existing optimization algorithms using machine learning (ML). In particular, the graph neural network (GNN) is considered a suitable ML model…
Multilayer networks have permeated all the sciences as a powerful mathematical abstraction for interdependent heterogenous complex systems such as multimodal brain connectomes, transportation, ecological systems, and scientific…
In this Letter we supervisedly train neural networks to distinguish different topological phases in the context of topological band insulators. After training with Hamiltonians of one-dimensional insulators with chiral symmetry, the neural…
This paper aims to establish theoretical foundations of graph product multilayer networks (GPMNs), a family of multilayer networks that can be obtained as a graph product of two or more factor networks. Cartesian, direct (tensor), and…
We study topological Poincar\'e type inequalities on general graphs. We characterize graphs satisfying such inequalities and then turn to the best constants in these inequalities. Invoking suitable metrics we can interpret these constants…
Let $M^n$ be a compact orientable smooth Riemannian submanifold of dimension $n\geq 3$ in $\mathbb R^d$. We construct a family of deformed Hodge Laplacians $\Delta_t^*$, $t>0$, acting on differential forms and defined through the extrinsic…
To every Hermitian vector bundle with connection over a compact Riemannian manifold $M$ one can associate a corresponding connection Laplacian acting on the sections of the bundle. We define analogous combinatorial metric dependent…
Network data are increasingly available in various research fields, motivating statistical analysis for populations of networks where a network as a whole is viewed as a data point. Due to the non-Euclidean nature of networks, basic…
In this paper, we consider the weighted graph matching problem with partially disclosed correspondences between a number of anchor nodes. Our construction exploits recently introduced node signatures based on graph Laplacians, namely the…
Graph signal processing (GSP) is a key tool for satisfying the growing demand for information processing over networks. However, the success of GSP in downstream learning and inference tasks is heavily dependent on the prior identification…
Separating multiple graph signals from a single observed mixture is an inherently ill-posed problem that traditionally relies on restrictive and handcrafted priors. This letter addresses this challenge by proposing an unsupervised learnable…
Boundary detection has long been a fundamental tool for image processing and computer vision, supporting the analysis of static and time-varying data. In this work, we built upon the theory of Graph Signal Processing to propose a novel…