Related papers: Simplicial Convolutional Filters
In this paper, we study linear filters to process signals defined on simplicial complexes, i.e., signals defined on nodes, edges, triangles, etc. of a simplicial complex, thereby generalizing filtering operations for graph signals. We…
This paper proposes convolutional filtering for data whose structure can be modeled by a simplicial complex (SC). SCs are mathematical tools that not only capture pairwise relationships as graphs but account also for higher-order network…
In this tutorial, we provide a didactic treatment of the emerging topic of signal processing on higher-order networks. Drawing analogies from discrete and graph signal processing, we introduce the building blocks for processing data on…
Weighing the topological domain over which data can be represented and analysed is a key strategy in many signal processing and machine learning applications, enabling the extraction and exploitation of meaningful data features and their…
The processing of signals supported on non-Euclidean domains has attracted large interest recently. Thus far, such non-Euclidean domains have been abstracted primarily as graphs with signals supported on the nodes, though the processing of…
Higher-order networks have so far been considered primarily in the context of studying the structure of complex systems, i.e., the higher-order or multi-way relations connecting the constituent entities. More recently, a number of studies…
We propose a simplicial complex convolutional neural network (SCCNN) to learn data representations on simplicial complexes. It performs convolutions based on the multi-hop simplicial adjacencies via common faces and cofaces independently…
We develop wavelet representations for edge-flows on simplicial complexes, using ideas rooted in combinatorial Hodge theory and spectral graph wavelets. We first show that the Hodge Laplacian can be used in lieu of the graph Laplacian to…
Our previous multiscale graph basis dictionaries/graph signal transforms -- Generalized Haar-Walsh Transform (GHWT); Hierarchical Graph Laplacian Eigen Transform (HGLET); Natural Graph Wavelet Packets (NGWPs); and their relatives -- were…
The goal of this paper is to introduce pooling strategies for simplicial convolutional neural networks. Inspired by graph pooling methods, we introduce a general formulation for a simplicial pooling layer that performs: i) local aggregation…
Simplicial complexes are generalizations of graphs that describe higher-order network interactions among nodes in the graph. Network dynamics described by graph Laplacian flows have been widely studied in network science and control theory,…
We establish a framework for signal processing on product spaces of simplicial and cellular complexes. For simplicity, we focus on the product of two complexes representing time and space, although our results generalize naturally to…
Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once. This concept is central towards detection of higher…
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…
Hypergraphs and simplical complexes both capture the higher-order interactions of complex systems, ranging from higher-order collaboration networks to brain networks. One open problem in the field is what should drive the choice of the…
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 propose principled Gaussian processes (GPs) for modeling functions defined over the edge set of a simplicial 2-complex, a structure similar to a graph in which edges may form triangular faces. This approach is intended for learning…
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…
Group convolutional neural networks are a useful tool for utilizing symmetries known to be in a signal; however, they require that the signal is defined on the group itself. Existing approaches either work directly with group signals, or…
This paper focuses on devising graph signal processing tools for the treatment of data defined on the edges of a graph. We first show that conventional tools from graph signal processing may not be suitable for the analysis of such signals.…