Related papers: Convolutional Filtering in Simplicial Complexes

Conventionally, convolutional neural networks (CNNs) process different images with the same set of filters. However, the variations in images pose a challenge to this fashion. In this paper, we propose to generate sample-specific filters…

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…

In this paper, a new class of circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the…

Simplicial complexes are higher-order combinatorial structures which have been used to represent real-world complex systems. In this paper, we concentrate on the local patterns in simplicial complexes called simplets, a generalization of…

Basic operations in graph signal processing consist in processing signals indexed on graphs either by filtering them, to extract specific part out of them, or by changing their domain of representation, using some transformation 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)…

It is increasingly common for data to possess intricate structure, necessitating new models and analytical tools. Graphs, a prominent type of structure, can encode the relationships between any two entities (nodes). However, graphs neither…

Many neural networks for graphs are based on the graph convolution operator, proposed more than a decade ago. Since then, many alternative definitions have been proposed, that tend to add complexity (and non-linearity) to the model. In this…

Graph convolution networks, like message passing graph convolution networks (MPGCNs), have been a powerful tool in representation learning of networked data. However, when data is heterogeneous, most architectures are limited as they employ…

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…

We propose a simple and generic layer formulation that extends the properties of convolutional layers to any domain that can be described by a graph. Namely, we use the support of its adjacency matrix to design learnable weight sharing…

Simplicial complexes (SCs) have become a popular abstraction for analyzing complex data using tools from topological data analysis or topological signal processing. However, the analysis of many real-world datasets often leads to dense SCs,…

Superior performance and ease of implementation have fostered the adoption of Convolutional Neural Networks (CNNs) for a wide array of inference and reconstruction tasks. CNNs implement three basic blocks: convolution, pooling and pointwise…

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…

This paper focuses on spectral graph convolutional neural networks (ConvNets), where filters are defined as elementwise multiplication in the frequency domain of a graph. In machine learning settings where the dataset consists of signals…

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…

Weight pruning is among the most popular approaches for compressing deep convolutional neural networks. Recent work suggests that in a randomly initialized deep neural network, there exist sparse subnetworks that achieve performance…

Group convolutional layers with respect to some group $G$ are modeled by convolutions or cross-correlations with a filter, and they provide the fundamental building block for group convolutional neural networks. For entirely unconstrained…

We present an efficient alternative to the convolutional layer using cheap spatial transformations. This construction exploits an inherent spatial redundancy of the learned convolutional filters to enable a much greater parameter…

Theoretical development and applications of graph signal processing (GSP) have attracted much attention. In classical GSP, the underlying structures are restricted in terms of dimensionality. A graph is a combinatorial object that models…