To overcome this limitation, we propose fast heuristics based on graph convolutional networks (GCNs) that can be implemented in centralized and distributed manners.
We begin by introducing three practical properties associated with the notion of robustness in hierarchical clustering: linear scale preservation, stability, and excisiveness.
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.
When either the input or the filter coefficients are known, this is tantamount to assuming that the signals of interest live on a subspace defined by the supporting graph.
With the increasing popularity of graph-based methods for dimensionality reduction and representation learning, node embedding functions have become important objects of study in the literature.
On the other hand, we propose a matrix factorization method based on a loss function that generalizes that of the skip-gram model with negative sampling to arbitrary similarity matrices.
The graph convolutional network (GCN) is a go-to solution for machine learning on graphs, but its training is notoriously difficult to scale both in terms of graph size and the number of model parameters.
We propose a novel method to co-cluster the vertices and hyperedges of hypergraphs with edge-dependent vertex weights (EDVWs).
In the context of simplicial complexes, we specifically focus on signal processing using the Hodge Laplacian matrix, a multi-relational operator that leverages the special structure of simplicial complexes and generalizes desirable properties of the Laplacian matrix in graph signal processing.
Using graphs to model irregular information domains is an effective approach to deal with some of the intricacies of contemporary (network) data.
We study the role of the constraint set in determining the solution to low-rank, positive semidefinite (PSD) matrix sensing problems.
We study the problem of optimal power allocation in a single-hop ad hoc wireless network.
In small- to middle-sized wireless networks with tens of links, even a shallow GCN-based MWIS scheduler can leverage the topological information of the graph to reduce in half the suboptimality gap of the distributed greedy solver with good generalizability across graphs and minimal increase in complexity.
We assume that signals on the nodes of the graph are regularized by the underlying graph structure via a graph filtering model, which we then leverage to distill the graph topology change-point detection problem to a subspace detection problem.
Inferring graph structure from observations on the nodes is an important and popular network science task.
In particular, we consider the case where the graph was drawn from a graphon model, and we supplement our convex optimization problem with a provably-valid regularizer on the spectrum of the graph to be recovered.
While deep convolutional architectures have achieved remarkable results in a gamut of supervised applications dealing with images and speech, recent works show that deep untrained non-convolutional architectures can also outperform state-of-the-art methods in several tasks such as image compression and denoising.
We consider a blind identification problem in which we aim to recover a statistical model of a network without knowledge of the network's edges, but based solely on nodal observations of a certain process.
The first strategy selects edges to minimize the reconstruction error bound and works well on flows that are approximately divergence-free.
We discuss a variant of `blind' community detection, in which we aim to partition an unobserved network from the observation of a (dynamical) graph signal defined on the network.
The paper shows that communities can be detected by applying a spectral method to the covariance matrix of graph signals.
Using the theory of linear integral operators, we define degree, eigenvector, Katz and PageRank centrality functions for graphons and establish concentration inequalities demonstrating that graphon centrality functions arise naturally as limits of their counterparts defined on sequences of graphs of increasing size.
This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation.
We introduce two practical properties of hierarchical clustering methods for (possibly asymmetric) network data: excisiveness and linear scale preservation.
This paper introduces hierarchical quasi-clustering methods, a generalization of hierarchical clustering for asymmetric networks where the output structure preserves the asymmetry of the input data.
Our construction of hierarchical clustering methods is based on defining admissible methods to be those methods that abide by the axioms of value - nodes in a network with two nodes are clustered together at the maximum of the two dissimilarities between them - and transformation - when dissimilarities are reduced, the network may become more clustered but not less.