Related papers: Bespoke multiresolution analysis of graph signals
We study nonparametric methods for the setting where multiple distinct networks are observed on the same set of nodes. Such samples may arise in the form of replicated networks drawn from a common distribution, or in the form of…
The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…
We propose a novel deep learning framework for fast prediction of boundaries of two-dimensional simply connected domains using wavelets and Multi Resolution Analysis (MRA). The boundaries are modelled as (piecewise) smooth closed curves…
Haar wavelet is one of the best mathematical tools in image cryptography and analysis. Because of the specific structure, this wavelet has the ability which is combined with other mathematical tools such as chaotic maps. The rational order…
Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are…
We introduce a novel framework for graph signal processing (GSP) that models signals as graph distribution-valued signals (GDSs), which are probability distributions in the Wasserstein space. This approach overcomes key limitations of…
This paper aims to provide a novel design of a multiscale framelet convolution for spectral graph neural networks (GNNs). While current spectral methods excel in various graph learning tasks, they often lack the flexibility to adapt to…
We construct a directional spin wavelet framework on the sphere by generalising the scalar scale-discretised wavelet transform to signals of arbitrary spin. The resulting framework is the only wavelet framework defined natively on the…
In this paper, we introduce a generalization of graphlets to heterogeneous networks called typed graphlets. Informally, typed graphlets are small typed induced subgraphs. Typed graphlets generalize graphlets to rich heterogeneous networks…
Graph representation learning is a fast-growing field where one of the main objectives is to generate meaningful representations of graphs in lower-dimensional spaces. The learned embeddings have been successfully applied to perform various…
Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. In recent years great progress has been made by augmenting `traditional' network theory.…
We consider the problem of offline, pool-based active semi-supervised learning on graphs. This problem is important when the labeled data is scarce and expensive whereas unlabeled data is easily available. The data points are represented by…
Spectral-based graph neural networks (SGNNs) have been attracting increasing attention in graph representation learning. However, existing SGNNs are limited in implementing graph filters with rigid transforms (e.g., graph Fourier or…
Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…
An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…
Graph alignment, the problem of identifying corresponding nodes across multiple graphs, is fundamental to numerous applications. Most existing unsupervised methods embed node features into latent representations to enable cross-graph…
We consider the problem of constructing embeddings of large attributed graphs and supporting multiple downstream learning tasks. We develop a graph embedding method, which is based on extending deep metric and unbiased contrastive learning…
Given an undirected and connected graph $G$ on $T$ vertices, suppose each vertex $t$ has a latent signal $x_t \in \mathbb{R}^n$ associated to it. Given partial linear measurements of the signals, for a potentially small subset of the…
Graph-based models require aggregating information in the graph from neighbourhoods of different sizes. In particular, when the data exhibit varying levels of smoothness on the graph, a multi-scale approach is required to capture the…
Many real-world applications give rise to large heterogeneous networks where nodes and edges can be of any arbitrary type (e.g., user, web page, location). Special cases of such heterogeneous graphs include homogeneous graphs, bipartite,…