Related papers: Learning graphs and simplicial complexes from data
The myriad complex systems with multiway interactions motivate the extension of graph-based pairwise connections to higher-order relations. In particular, the simplicial complex has inspired generalizations of graph neural networks (GNNs)…
Classical unsupervised learning methods like clustering and linear dimensionality reduction parametrize large-scale geometry when it is discrete or linear, while more modern methods from manifold learning find low dimensional representation…
The construction of a meaningful graph topology plays a crucial role in the effective representation, processing, analysis and visualization of structured data. When a natural choice of the graph is not readily available from the data sets,…
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…
Graph learning aims to infer a network structure directly from observed data, enabling the analysis of complex dependencies in irregular domains. Traditional methods focus on scalar signals at each node, ignoring dependencies along…
Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics…
Graph learning problems are typically approached by focusing on learning the topology of a single graph when signals from all nodes are available. However, many contemporary setups involve multiple related networks and, moreover, it is…
The goal of this paper is to establish the fundamental tools to analyze signals defined over a topological space, i.e. a set of points along with a set of neighborhood relations. This setup does not require the definition of a metric and…
Hypergraph structure learning, which aims to learn the hypergraph structures from the observed signals to capture the intrinsic high-order relationships among the entities, becomes crucial when a hypergraph topology is not readily available…
Graphs are nowadays ubiquitous in the fields of signal processing and machine learning. As a tool used to express relationships between objects, graphs can be deployed to various ends: I) clustering of vertices, II) semi-supervised…
Graph neural networks have emerged as a powerful tool for learning spatiotemporal interactions. However, conventional approaches often rely on predefined graphs, which may obscure the precise relationships being modeled. Additionally,…
Inferring graph structure from observations on the nodes is an important and popular network science task. Departing from the more common inference of a single graph and motivated by social and biological networks, we study the problem of…
Many optimization, inference and learning tasks can be accomplished efficiently by means of decentralized processing algorithms where the network topology (i.e., the graph) plays a critical role in enabling the interactions among…
We propose a framework that learns the graph structure underlying a set of smooth signals. Given $X\in\mathbb{R}^{m\times n}$ whose rows reside on the vertices of an unknown graph, we learn the edge weights $w\in\mathbb{R}_+^{m(m-1)/2}$…
Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many…
The problem of graph learning concerns the construction of an explicit topological structure revealing the relationship between nodes representing data entities, which plays an increasingly important role in the success of many graph-based…
Real-world data is often times associated with irregular structures that can analytically be represented as graphs. Having access to this graph, which is sometimes trivially evident from domain knowledge, provides a better representation of…
Recent papers have formulated the problem of learning graphs from data as an inverse covariance estimation with graph Laplacian constraints. While such problems are convex, existing methods cannot guarantee that solutions will have specific…
The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…
Social learning algorithms provide models for the formation of opinions over social networks resulting from local reasoning and peer-to-peer exchanges. Interactions occur over an underlying graph topology, which describes the flow of…