Related papers: Convolutional Filtering in Simplicial Complexes

Topological filters via sheaves generalize the classical linear translation-invariant filter theory by attaching the filter computation locally to a simplicial topological space. This paper develops topological filters for causal signal…

Spectral graph convolution, an important tool of data filtering on graphs, relies on two essential decisions: selecting spectral bases for signal transformation and parameterizing the kernel for frequency analysis. While recent techniques…

Within the graph learning community, conventional wisdom dictates that spectral convolutional networks may only be deployed on undirected graphs: Only there could the existence of a well-defined graph Fourier transform be guaranteed, so…

In this paper, we introduce a new regularization technique for transfer learning. The aim of the proposed approach is to capture statistical relationships among convolution filters learned from a well-trained network and transfer this…

Graph signal processing (GSP) uses a shift operator to define a Fourier basis for the set of graph signals. The shift operator is often chosen to capture the graph topology. However, in many applications, the graph topology may be unknown a…

We first establish a kernel theorem that characterizes all linear shift-invariant (LSI) operators acting on discrete multicomponent signals. This result naturally leads to the identification of the Parseval convolution operators as the…

The increasing availability of geometric data has motivated the need for information processing over non-Euclidean domains modeled as manifolds. The building block for information processing architectures with desirable theoretical…

In the co-sparse analysis model a set of filters is applied to a signal out of the signal class of interest yielding sparse filter responses. As such, it may serve as a prior in inverse problems, or for structural analysis of signals that…

Last decade has seen the emergence of numerous methods for learning on graphs, particularly Graph Neural Networks (GNNs). These methods, however, are often not directly applicable to more complex structures like bipartite graphs (equivalent…

Convolutional Neural Networks (CNNs) have recently led to incredible breakthroughs on a variety of pattern recognition problems. Banks of finite impulse response filters are learned on a hierarchy of layers, each contributing more abstract…

We design a critically-sampled compact-support biorthogonal transform for graph signals, via graph filterbanks. Instead of partitioning the nodes in two sets so as to remove one every two nodes in the filterbank downsampling operations, the…

We present a novel surface convolution operator acting on vector fields that is based on a simple observation: instead of combining neighboring features with respect to a single coordinate parameterization defined at a given point, we have…

Convolutional networks are large linear systems divided into layers and connected by non-linear units. These units are the "articulations" that allow the network to adapt to the input. To understand how a network manages to solve a problem…

The use of graph convolution in the development of recommender system algorithms has recently achieved state-of-the-art results in the collaborative filtering task (CF). While it has been demonstrated that the graph convolution operation is…

This paper focuses on spectral filters on graphs, namely filters defined as elementwise multiplication in the frequency domain of a graph. In many graph signal processing settings, it is important to transfer a filter from one graph to…

Convolutional Sparse Coding (CSC) is an increasingly popular model in the signal and image processing communities, tackling some of the limitations of traditional patch-based sparse representations. Although several works have addressed the…

Convolutional Sparse Coding (CSC) is a well-established image representation model especially suited for image restoration tasks. In this work, we extend the applicability of this model by proposing a supervised approach to convolutional…

Simplicial complex (SC) representation is an elegant mathematical framework for representing the effect of complexes or groups with higher-order interactions in a variety of complex systems ranging from brain networks to social…

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…

In this paper, we introduce a convolutional architecture to perform learning when information is supported on multigraphs. Exploiting algebraic signal processing (ASP), we propose a convolutional signal processing model on multigraphs…