Related papers: Transfer operators on graphs: Spectral clustering …

Graph Transformers, which incorporate self-attention and positional encoding, have recently emerged as a powerful architecture for various graph learning tasks. Despite their impressive performance, the complex non-convex interactions…

Embedding networks into a fixed dimensional feature space, while preserving its essential structural properties is a fundamental task in graph analytics. These feature vectors (graph descriptors) are used to measure the pairwise similarity…

A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…

Spectral algorithms are graph partitioning algorithms that partition a node set of a graph into groups by using a spectral embedding map. Clustering techniques based on the algorithms are referred to as spectral clustering and are widely…

Dynamical systems can be analyzed via their Frobenius-Perron transfer operator and its estimation from data is an active field of research. Recently entropic transfer operators have been introduced to estimate the operator of deterministic…

Open-world semi-supervised learning aims at inferring both known and novel classes in unlabeled data, by harnessing prior knowledge from a labeled set with known classes. Despite its importance, there is a lack of theoretical foundations…

Attention mechanisms have become a cornerstone in modern neural networks, driving breakthroughs across diverse domains. However, their application to graph structured data, where capturing topological connections is essential, remains…

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…

Within the graph learning community, conventional wisdom dictates that spectral convolutional networks may only be deployed on undirected graphs: Only there could the existence of a well-defined graph Fourier transform be guaranteed, so…

Graphs are widely used in various fields of computer science. They have also found application in unrelated areas, leading to a diverse range of problems. These problems can be modeled as relationships between entities in various contexts,…

In the graph clustering problem with a planted solution, the input is a graph on $n$ vertices partitioned into $k$ clusters, and the task is to infer the clusters from graph structure. A standard assumption is that clusters induce…

Graph clustering plays a pivotal role in unsupervised learning methods like spectral clustering, yet traditional methods for graph clustering often perpetuate bias through unfair graph constructions that may underrepresent some groups. The…

Graph clustering is a fundamental problem that has been extensively studied both in theory and practice. The problem has been defined in several ways in literature and most of them have been proven to be NP-Hard. Due to their high practical…

Connectivity is a fundamental property of quantum graphs, previously studied in the operator system model for matrix quantum graphs and via graph homomorphisms in the quantum adjacency matrix model. In this paper, we develop an algebraic…

The focus of Part I of this monograph has been on both the fundamental properties, graph topologies, and spectral representations of graphs. Part II embarks on these concepts to address the algorithmic and practical issues centered round…

Using graphs to model irregular information domains is an effective approach to deal with some of the intricacies of contemporary (network) data. A key aspect is how the data, represented as graph signals, depend on the topology of the…

Graph pooling is a family of operations which take graphs as input and produce shrinked graphs as output. Modern graph pooling methods are trainable and, in general inserted in Graph Neural Networks (GNNs) architectures as graph shrinking…

Spectral clustering is one of the most popular methods for community detection in graphs. A key step in spectral clustering algorithms is the eigen decomposition of the $n{\times}n$ graph Laplacian matrix to extract its $k$ leading…

Graph neural networks are powerful architectures for structured datasets. However, current methods struggle to represent long-range dependencies. Scaling the depth or width of GNNs is insufficient to broaden receptive fields as larger GNNs…

Graphons are infinite-dimensional objects that represent the limit of convergent sequences of graphs as their number of nodes goes to infinity. This paper derives a theory of graphon signal processing centered on the notions of graphon…