Related papers: Multiscale Transforms for Signals on Simplicial Co…
We present simplicial neural networks (SNNs), a generalization of graph neural networks to data that live on a class of topological spaces called simplicial complexes. These are natural multi-dimensional extensions of graphs that encode not…
In this paper, we focus on graph learning from multi-view data of shared entities for spectral clustering. We can explain interactions between the entities in multi-view data using a multi-layer graph with a common vertex set, which…
We propose a generalization of transformer neural network architecture for arbitrary graphs. The original transformer was designed for Natural Language Processing (NLP), which operates on fully connected graphs representing all connections…
In the past years, many signal processing operations have been successfully adapted to the graph setting. One elegant and effective approach is to exploit the eigendecomposition of a graph shift operator (GSO), such as the adjacency or…
Graph Neural Networks have a limitation of solely processing features on graph nodes, neglecting data on high-dimensional structures such as edges and triangles. Simplicial Convolutional Neural Networks (SCNN) represent higher-order…
We present a framework for representing and modeling data on graphs. Based on this framework, we study three typical classes of graph signals: smooth graph signals, piecewise-constant graph signals, and piecewise-smooth graph signals. For…
The common graph Laplacian regularizer is well-established in semi-supervised learning and spectral dimensionality reduction. However, as a first-order regularizer, it can lead to degenerate functions in high-dimensional manifolds. The…
In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and…
Graphs can model networked data by representing them as nodes and their pairwise relationships as edges. Recently, signal processing and neural networks have been extended to process and learn from data on graphs, with achievements in tasks…
Despite the vast literature on network dynamics, we still lack basic insights into dynamics on higher-order structures (e.g., edges, triangles, and more generally, $k$-dimensional "simplices") and how they are influenced through…
We introduce the computational problem of graphlet transform of a sparse large graph. Graphlets are fundamental topology elements of all graphs/networks. They can be used as coding elements to encode graph-topological information at…
Simplicial complexes constitute the underlying topology of interacting complex systems including among the others brain and social interaction networks. They are generalized network structures that allow to go beyond the framework of…
Topological Data Analysis (TDA) studies the shape of data. A common topological descriptor is the persistence diagram, which encodes topological features in a topological space at different scales. Turner, Mukeherjee, and Boyer showed that…
Graph signal processing (GSP) has become an important tool in many areas such as image processing, networking learning and analysis of social network data. In this paper, we propose a broader framework that not only encompasses traditional…
Current graph neural networks (GNNs) lack generalizability with respect to scales (graph sizes, graph diameters, edge weights, etc..) when solving many graph analysis problems. Taking the perspective of synthesizing graph theory programs,…
Graph Transformers have garnered significant attention for learning graph-structured data, thanks to their superb ability to capture long-range dependencies among nodes. However, the quadratic space and time complexity hinders the…
Modeling information that resides on vertices of large graphs is a key problem in several real-life applications, ranging from social networks to the Internet-of-things. Signal Processing on Graphs and, in particular, graph wavelets can…
We study Laplacians on general countable weighted simplicial complexes from a conceptual point of view. These operators will first be introduced formally before showing that those formal operators coincide with self-adjoint realizations of…
The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful…
Kernels on graphs have had limited options for node-level problems. To address this, we present a novel, generalized kernel for graphs with node feature data for semi-supervised learning. The kernel is derived from a regularization…