相关论文: Signal processing on simplicial complexes

Higher-order information is crucial for relational learning in many domains where relationships extend beyond pairwise interactions. Hypergraphs provide a natural framework for modeling such relationships, which has motivated recent…

Predicting the labels of graph-structured data is crucial in scientific applications and is often achieved using graph neural networks (GNNs). However, when data is scarce, GNNs suffer from overfitting, leading to poor performance.…

Recently there has been an increasing interest in studying dynamical processes on networks exhibiting higher-order structures, such as simplicial complexes, where the dynamics acts above and beyond dyadic interactions. Using simulations or…

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)…

Traditional graph signal processing (GSP) methods applied to brain networks focus on signals defined on the nodes. Thus, they are unable to capture potentially important dynamics occurring on the edges. In this work, we adopt an…

Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for…

The study of the interactions among different types of interconnected systems in complex networks has attracted significant interest across many research fields. However, effective signal processing over layered networks requires…

Traditionally, interaction systems have been described as networks, where links encode information on the pairwise influences among the nodes. Yet, in many systems, interactions take place in larger groups. Recent work has shown that…

Recently, neural network architectures have been developed to accommodate when the data has the structure of a graph or, more generally, a hypergraph. While useful, graph structures can be potentially limiting. Hypergraph structures in…

Recent work in Topological Deep Learning (TDL) seeks to generalize graph learning's preeminent $message \ passing$ paradigm to more complex relational structures: simplicial complexes, cell complexes, hypergraphs, and combinations thereof.…

Focusing on coupling between edges, we generalize the relationship between the normalized graph Laplacian and random walks on graphs by devising an appropriate normalization for the Hodge Laplacian -- the generalization of the graph…

Modeling higher-order interactions (HOI) has emerged as a crucial challenge in complex systems analysis, as many phenomena cannot be fully captured by pairwise relationships alone. Hypergraphs, which generalize graphs by allowing…

A simplex-based network is referred to as a higher-order network, in which describe that the interactions can include more than two nodes. Many multicomponent interactions can be grasped through simplicial complexes, which have recently…

Obtaining sparse, interpretable representations of observable data is crucial in many machine learning and signal processing tasks. For data representing flows along the edges of a graph, an intuitively interpretable way to obtain such…

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…

For deep learning problems on graph-structured data, pooling layers are important for down sampling, reducing computational cost, and to minimize overfitting. We define a pooling layer, nervePool, for data structured as simplicial…

The study of complex systems benefits from graph models and their analysis. In particular, the eigendecomposition of the graph Laplacian lets emerge properties of global organization from local interactions; e.g., the Fiedler vector has the…

The notion of Laplacian of a graph can be generalized to simplicial complexes and hypergraphs, and contains information on the topology of these structures. Even for a graph, the consideration of associated simplicial complexes is…

Current methods of graph signal processing rely heavily on the specific structure of the underlying network: the shift operator and the graph Fourier transform are both derived directly from a specific graph. In many cases, the network is…

The propagation of information in social, biological and technological systems represents a crucial component in their dynamic behavior. When limited to pairwise interactions, a rather firm grip is available on the relevant parameters and…