Related papers: Fused $\ell_{1}$ Trend Filtering on Graphs

We analyse a new notion of total anisotropic higher-order variation which, differently from the Total Generalized Variation by Bredies et al., quantifies for possibly non-symmetric tensor fields their variations at arbitrary order weighted…

Federated Learning (FL) is a machine learning paradigm that enables clients to jointly train a global model by aggregating the locally trained models without sharing any local training data. In practice, there can often be substantial…

While deep learning (DL) architectures like convolutional neural networks (CNNs) have enabled effective solutions in image denoising, in general their implementations overly rely on training data, lack interpretability, and require tuning…

We present the group fused Lasso for detection of multiple change-points shared by a set of co-occurring one-dimensional signals. Change-points are detected by approximating the original signals with a constraint on the multidimensional…

Graph machine learning has gained great attention in both academia and industry recently. Most of the graph machine learning models, such as Graph Neural Networks (GNNs), are trained over massive graph data. However, in many real-world…

This paper proves limit theorems for the number of monochromatic edges in uniform random colorings of general random graphs. These can be seen as generalizations of the birthday problem (what is the chance that there are two friends with…

For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems,…

The \emph{generalized sorting problem} is a restricted version of standard comparison sorting where we wish to sort $n$ elements but only a subset of pairs are allowed to be compared. Formally, there is some known graph $G = (V, E)$ on the…

There have been rapid developments in model-based clustering of graphs, also known as block modelling, over the last ten years or so. We review different approaches and extensions proposed for different aspects in this area, such as the…

This paper tackles the challenging problem of jointly inferring time-varying network topologies and imputing missing data from partially observed graph signals. We propose a unified non-convex optimization framework to simultaneously…

Path and boundary-path groupoids of finitely aligned higher-rank graphs are often constructed using either filters or graph morphisms. We generalise the graph morphism approach to finitely aligned P-graphs where (Q, P) is a weakly…

Planar drawings of graphs tend to be favored over non-planar drawings. Testing planarity and creating a planar layout of a planar graph can be done in linear time. However, creating readable drawings of nearly planar graphs remains a…

A traversal of a connected graph is a linear ordering of its vertices all of whose initial segments induce connected subgraphs. Traversals, and their refinements such as breadth-first and depth-first traversals, are computed by various…

We study entanglement properties of mixed density matrices obtained from combinatorial Laplacians. This is done by introducing the notion of the density matrix of a graph. We characterize the graphs with pure density matrices and show that…

A graph is regularizable if it is possible to assign weights to its edges so that all nodes have the same degree. Weights can be positive, nonnegative or arbitrary as soon as the regularization degree is not null. Positive and nonnegative…

This work establishes rigorous, novel and widely applicable stability guarantees and transferability bounds for graph convolutional networks -- without reference to any underlying limit object or statistical distribution. Crucially,…

We consider the problem of spectral clustering under group fairness constraints, where samples from each sensitive group are approximately proportionally represented in each cluster. Traditional fair spectral clustering (FSC) methods…

Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…

This paper proposes a novel consensus-based distributed filter over directed graphs under the collectively observability condition. The distributed filter is designed using an augmented leader-following information fusion strategy, and the…

Many problems can be presented in an abstract form through a wide range of binary objects and relations which are defined over problem domain. In these problems, graphical demonstration of defined binary objects and solutions is the most…