Related papers: Bespoke multiresolution analysis of graph signals
The scattering transform is a multilayered wavelet-based deep learning architecture that acts as a model of convolutional neural networks. Recently, several works have introduced generalizations of the scattering transform for non-Euclidean…
One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric…
We introduce a novel harmonic analysis for functions defined on the vertices of a strongly connected directed graph of which the random walk operator is the cornerstone. As a first step, we consider the set of eigenvectors of the random…
Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…
Signal processing on graph is attracting more and more attentions. For a graph signal in the low-frequency subspace, the missing data associated with unsampled vertices can be reconstructed through the sampled data by exploiting the…
To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Frechet mean. In this work,…
Deep unfolding networks have gained increasing attention in the field of compressed sensing (CS) owing to their theoretical interpretability and superior reconstruction performance. However, most existing deep unfolding methods often face…
We propose new scattering networks for signals measured on simplicial complexes, which we call \emph{Multiscale Hodge Scattering Networks} (MHSNs). Our construction builds on multiscale basis dictionaries on simplicial complexes -- namely,…
In this paper we present the Markov variation, a smoothness measure which offers a probabilistic interpretation of graph signal smoothness. This measure is then used to develop an optimization framework for graph signal interpolation. Our…
We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph…
The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of time-series containing non-uniform structures with only isolated…
One of the emerging techniques in node classification in heterogeneous graphs is to restrict message aggregation to pre-defined, semantically meaningful structures called metapaths. This work is the first attempt to incorporate attention…
While deep convolutional architectures have achieved remarkable results in a gamut of supervised applications dealing with images and speech, recent works show that deep untrained non-convolutional architectures can also outperform…
Scene graphs represent the key components of a scene in a compact and semantically rich way, but are difficult to build during incremental SLAM operation because of the challenges of robustly identifying abstract scene elements and…
We propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a…
We introduce a multi-windowed graph Fourier transform (MWGFT) for the joint vertex-frequency analysis of signals defined on graphs. Building on generalized translation and modulation induced by the graph Laplacian, the proposed framework…
We introduce a novel method, called Dispersion Entropy for Graph Signals, $DE_G$, as a powerful tool for analysing the irregularity of signals defined on graphs. We demonstrate the effectiveness of $DE_G$ in detecting changes in the…
We propose a new framework for manifold denoising based on processing in the graph Fourier frequency domain, derived from the spectral decomposition of the discrete graph Laplacian. Our approach uses the Spectral Graph Wavelet transform in…
Collaborative filtering is a popular approach in recommender systems, whose objective is to provide personalized item suggestions to potential users based on their purchase or browsing history. However, personalized recommendations require…
The past decade has seen a flourishing of advances in harmonic analysis of graphs. They lie at the crossroads of graph theory and such analytical tools as graph Laplacians, Markov processes and associated boundaries, analysis of path-space,…