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Graph neural networks (GNNs) are the most widely adopted model in graph-structured data oriented learning and representation. Despite their extraordinary success in real-world applications, understanding their working mechanism by theory is…
Neural networks efficiently encode learned information within their parameters. Consequently, many tasks can be unified by treating neural networks themselves as input data. When doing so, recent studies demonstrated the importance of…
Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over…
Defining a sound shift operator for signals existing on a certain graph structure, similar to the well-defined shift operator in classical signal processing, is a crucial problem in graph signal processing, since almost all operations, such…
Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a broad spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and…
Higher-order networks have so far been considered primarily in the context of studying the structure of complex systems, i.e., the higher-order or multi-way relations connecting the constituent entities. More recently, a number of studies…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
This paper is devoted to signal processing on point-clouds by means of neural networks. Nowadays, state-of-the-art in image processing and computer vision is mostly based on training deep convolutional neural networks on large datasets.…
The problem of classifying graphs is ubiquitous in machine learning. While it is standard to apply graph neural networks or graph kernel methods, Gaussian processes can be employed by transforming spatial features from the graph domain into…
Filters are fundamental in extracting information from data. For time series and image data that reside on Euclidean domains, filters are the crux of many signal processing and machine learning techniques, including convolutional neural…
The goal of this paper is to propose novel strategies for adaptive learning of signals defined over graphs, which are observed over a (randomly time-varying) subset of vertices. We recast two classical adaptive algorithms in the graph…
Finding important edges in a graph is a crucial problem for various research fields, such as network epidemics, signal processing, machine learning, and sensor networks. In this paper, we tackle the problem based on sampling theory on…
A continuous-time graph signal can be viewed as a time series of graph signals. It generalizes both the classical continuous-time signal and ordinary graph signal. Therefore, such a signal can be considered as a function on two domains: the…
On finite metric graphs the set of all realizations of the Laplace operator in the edgewise defined $L^2$-spaces are studied. These are defined by coupling boundary conditions at the vertices most of which define non-self-adjoint operators.…
We give a probabilistic interpretation of sampling theory of graph signals. To do this, we first define a generative model for the data using a pairwise Gaussian random field (GRF) which depends on the graph. We show that, under certain…
Graph signal processing (GSP) is a prominent framework for analyzing signals on non-Euclidean domains. The graph Fourier transform (GFT) uses the combinatorial graph Laplacian matrix to reveal the spectral decomposition of signals in the…
Sampling random graphs is essential in many applications, and often algorithms use Markov chain Monte Carlo methods to sample uniformly from the space of graphs. However, often there is a need to sample graphs with some property that we are…
The notion of graph filters can be used to define generative models for graph data. In fact, the data obtained from many examples of network dynamics may be viewed as the output of a graph filter. With this interpretation, classical signal…
Distributed processing of large-scale graph data has many practical applications and has been widely studied. In recent years, a lot of distributed graph processing frameworks and algorithms have been proposed. While many efforts have been…
Graph convolutional neural networks (GCNN) have numerous applications in different graph based learning tasks. Although the techniques obtain impressive results, they often fall short in accounting for the uncertainty associated with the…