Related papers: Sampling perspectives on sparse exchangeable graph…
We propose a desigining method of a flexible sampling operator for graph signals via a difference-of-convex (DC) optimization algorithm. A fundamental challenge in graph signal processing is sampling, especially for graph signals that are…
Theoretical analyses for graph learning methods often assume a complete observation of the input graph. Such an assumption might not be useful for handling any-size graphs due to the scalability issues in practice. In this work, we develop…
We develop a clear connection between deFinetti's theorem for exchangeable arrays (work of Aldous--Hoover--Kallenberg) and the emerging area of graph limits (work of Lovasz and many coauthors). Along the way, we translate the graph theory…
How might one "reduce" a graph? That is, generate a smaller graph that preserves the global structure at the expense of discarding local details? There has been extensive work on both graph sparsification (removing edges) and graph…
Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of efforts have been devoted to calculating graphlet statistics where random walk based approaches are…
Sampling technique has become one of the recent research focuses in the graph-related fields. Most of the existing graph sampling algorithms tend to sample the high degree or low degree nodes in the complex networks because of the…
Graph neural networks (GNNs) have become powerful tools for processing graph-based information in various domains. A desirable property of GNNs is transferability, where a trained network can swap in information from a different 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…
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…
Generalization and approximation capabilities of message passing graph neural networks (MPNNs) are often studied by defining a compact metric on a space of input graphs under which MPNNs are H\"older continuous. Such analyses are of two…
We introduce a general Bayesian framework for graph matching grounded in a new theory of exchangeable random permutations. Leveraging the cycle representation of permutations and the literature on exchangeable random partitions, we define,…
The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Graphons, as limits of graph sequences, provide an operator-theoretic framework for analyzing the asymptotic behavior of graph neural operators. Spectral convergence of sampled graphs to graphons induces convergence of the corresponding…
As large graph datasets become increasingly common across many fields, sampling is often needed to reduce the graphs into manageable sizes. This procedure raises critical questions about representativeness as no sample can capture the…
Network systems have become a ubiquitous modeling tool in many areas of science where nodes in a graph represent distributed processes and edges between nodes represent a form of dynamic coupling. When a network topology is already known…
With the objective of employing graphs toward a more generalized theory of signal processing, we present a novel sampling framework for (wavelet-)sparse signals defined on circulant graphs which extends basic properties of Finite Rate of…
Current methods of graph signal processing rely heavily on the specific structure of the underlying network: the shift operator and the graph Fourier transform are both derived directly from a specific graph. In many cases, the network is…
Graph neural networks (GNNs) achieve strong performance on graph learning tasks, but training on large-scale networks remains computationally challenging. Transferability results show that GNNs with fixed weights can generalize from smaller…
A new scheme to sample signals defined in the nodes of a graph is proposed. The underlying assumption is that such signals admit a sparse representation in a frequency domain related to the structure of the graph, which is captured by the…