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Signal processing on graphs has received a lot of attention in the recent years. A lot of techniques have arised, inspired by classical signal processing ones, to allow studying signals on any kind of graph. A common aspect of these…
Graph is a prevalent discrete data structure, whose generation has wide applications such as drug discovery and circuit design. Diffusion generative models, as an emerging research focus, have been applied to graph generation tasks.…
In this paper, we present a novel convolution theorem which encompasses the well known convolution theorem in (graph) signal processing as well as the one related to time-varying filters. Specifically, we show how a node-wise convolution…
Graphs are mathematical tools that can be used to represent complex real-world interconnected systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently.…
Due to network operation and maintenance relying heavily on network traffic monitoring, traffic matrix analysis has been one of the most crucial issues for network management related tasks. However, it is challenging to reliably obtain the…
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 develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a large number of applications in areas ranging from transport…
Spectral graph convolutional networks are generalizations of standard convolutional networks for graph-structured data using the Laplacian operator. A common misconception is the instability of spectral filters, i.e. the impossibility to…
Graph learning plays a pivotal role and has gained significant attention in various application scenarios, from social network analysis to recommendation systems, for its effectiveness in modeling complex data relations represented by graph…
In this paper, we study the graph classification problem in vertex-labeled graphs. Our main goal is to classify the graphs comparing their higher-order structures thanks to heat diffusion on their simplices. We first represent…
Being the most cutting-edge generative methods, diffusion methods have shown great advances in wide generation tasks. Among them, graph generation attracts significant research attention for its broad application in real life. In our…
Diffusion models form an important class of generative models today, accounting for much of the state of the art in cutting edge AI research. While numerous extensions beyond image and video generation exist, few of such approaches address…
Design of filters for graph signal processing benefits from knowledge of the spectral decomposition of matrices that encode graphs, such as the adjacency matrix and the Laplacian matrix, used to define the shift operator. For shift matrices…
A diffusion taking value in probability measures on a graph with a vertex set $V$, $\sum_{i\in V}x_i\delta_i$, is studied. The masses on each vertices satisfy the stochastic differential equation of the form $dx_i=\sum_{j\in…
Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal…
Most real-world networks are noisy and incomplete samples from an unknown target distribution. Refining them by correcting corruptions or inferring unobserved regions typically improves downstream performance. Inspired by the impressive…
Denoising diffusion probabilistic models have recently received much research attention since they outperform alternative approaches, such as GANs, and currently provide state-of-the-art generative performance. The superior performance of…
Signals and datasets that arise in physical and engineering applications, as well as social, genetics, biomolecular, and many other domains, are becoming increasingly larger and more complex. In contrast to traditional time and image…
We introduce a family of adaptive estimators on graphs, based on penalizing the $\ell_1$ norm of discrete graph differences. This generalizes the idea of trend filtering [Kim et al. (2009), Tibshirani (2014)], used for univariate…
We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this…