Related papers: Simplicial Convolutional Filters
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…
We introduce the Deep Edge Filter, a novel approach that applies high-pass filtering to deep neural network features to improve model generalizability. Our method is motivated by our hypothesis that neural networks encode task-relevant…
We start out by demonstrating that an elementary learning task, corresponding to the training of a single linear neuron in a convolutional neural network, can be solved for feature spaces of very high dimensionality. In a second step,…
Bifiltered graphs are a versatile tool for modelling relations between data points across multiple grades of a two-dimensional scale. They are especially popular in topological data analysis, where the homological properties of the induced…
Simplicial complexes form an important class of topological spaces that are frequently used in many application areas such as computer-aided design, computer graphics, and simulation. Representation learning on graphs, which are just 1-d…
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…
Multiscale transforms designed to process analog and discrete-time signals and images cannot be directly applied to analyze high-dimensional data residing on the vertices of a weighted graph, as they do not capture the intrinsic geometric…
De Facto, signal processing is the interpolation and extrapolation of a sequence of observations viewed as a realization of a stochastic process. Its role in applied statistics ranges from scenarios in forecasting and time series analysis,…
Convolutional neural networks (CNNs) learn filters in order to capture local correlation patterns in feature space. We propose to learn these filters as combinations of preset spectral filters defined by the Discrete Cosine Transform (DCT).…
The efficient realization of linear space-variant (non-convolution) filters is a challenging computational problem in image processing. In this paper, we demonstrate that it is possible to filter an image with a Gaussian-like elliptic…
We propose wideband bandpass filters based on multipole resonances of spoof localized surface plasmons (SLSPs). The resonance characteristics and geometric tunability of SLSPs are investigated under microstrip excitations. Strong coupling…
We study the family of functions that are represented by a linear convolutional neural network (LCN). These functions form a semi-algebraic subset of the set of linear maps from input space to output space. In contrast, the families of…
Topological Signal Processing (TSP) over simplicial complexes is a framework that has been recently proposed, as a generalization of graph signal processing (GSP), to extend GSP to analyzing signals defined over sets of any order (i.e., not…
We introduce optical polarization-insensitive high pass filters based on total internal reflection of light at the interface of two dielectric media (1D) and Bragg reflection of a multilayer stack (2D) in transmission mode. The wavevectors…
Heterogeneous Graph Neural Networks (HGNNs) have gained significant popularity in various heterogeneous graph learning tasks. However, most existing HGNNs rely on spatial domain-based methods to aggregate information, i.e., manually…
Current learned image compression models typically exhibit high complexity, which demands significant computational resources. To overcome these challenges, we propose an innovative approach that employs hierarchical feature extraction…
In this work we introduce a convolution operation over the tangent bundle of Riemann manifolds in terms of exponentials of the Connection Laplacian operator. We define tangent bundle filters and tangent bundle neural networks (TNNs) based…
Joint image filters leverage the guidance image as a prior and transfer the structural details from the guidance image to the target image for suppressing noise or enhancing spatial resolution. Existing methods either rely on various…
Applying feature dependent network weights have been proved to be effective in many fields. However, in practice, restricted by the enormous size of model parameters and memory footprints, scalable and versatile dynamic convolutions with…
This paper introduces a reformulation of the classical convergence theorem for spectral sequences of filtered complexes which provides an algorithm to effectively compute the induced filtration on the total (co)homology, as soon as the…