相关论文: Homogeneity vs. Adjacency: generalising some graph…

The total generalized variation extends the total variation by incorporating higher-order smoothness. Thus, it can also suffer from similar discretization issues related to isotropy. Inspired by the success of novel discretization schemes…

We study the problem of learning features through self-supervision that are generalisable to multiple graphs. State-of-the-art graph self-supervision restricts training to only one graph, resulting in graph-specific models that are…

(Hyper)Graph decomposition is a family of problems that aim to break down large (hyper)graphs into smaller sub(hyper)graphs for easier analysis. The importance of this lies in its ability to enable efficient computation on large and complex…

When writing programs, people have the ability to tackle a new complex task by decomposing it into smaller and more familiar subtasks. While it is difficult to measure whether neural program synthesis methods have similar capabilities, what…

Many complex tasks can be decomposed into simpler, independent parts. Discovering such underlying compositional structure has the potential to enable compositional generalization. Despite progress, our most powerful systems struggle to…

Downsampling produces coarsened, multi-resolution representations of data and it is used, for example, to produce lossy compression and visualization of large images, reduce computational costs, and boost deep neural representation…

In this paper we consider module-composed graphs, i.e. graphs which can be defined by a sequence of one-vertex insertions v_1,...,v_n, such that the neighbourhood of vertex v_i, 2<= i<= n, forms a module (a homogeneous set) of the graph…

We extend the theory of decomposable maps by giving a detailed description of k-positive maps. A relation between transposition and modular theory is established. The structure of positive maps in terms of modular theory (the generalized…

In the present paper a novel graph-based approach to the shape decomposition problem is addressed. The shape is appropriately transformed into a visibility graph enriched with local neighborhood information. A two-step diffusion process is…

Community detection, the decomposition of a graph into essential building blocks, has been a core research topic in network science over the past years. Since a precise notion of what constitutes a community has remained evasive, community…

Image denoising is still a challenging issue in many computer vision sub-domains. Recent studies show that significant improvements are made possible in a supervised setting. However, few challenges, such as spatial fidelity and…

Finding dense subgraphs of a large graph is a standard problem in graph mining that has been studied extensively both for its theoretical richness and its many practical applications. In this paper we introduce a new family of dense…

In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…

The decomposition of undirected graphs simplifies complex problems by breaking them into solvable subgraphs, following the philosophy of divide and conquer. This paper investigates the relationship between atom decomposition and the maximum…

Recently, we have introduced and modified two graph-decomposition theorems based on a new graph product, motivated by applications in the context of synchronising periodic real-time processes. This vertex-removing synchronised product…

Higher-order connectivity patterns such as small induced sub-graphs called graphlets (network motifs) are vital to understand the important components (modules/functional units) governing the configuration and behavior of complex networks.…

In this paper, the problem of decentralized eigenvalue decomposition of a general symmetric matrix that is important, e.g., in Principal Component Analysis, is studied, and a decentralized online learning algorithm is proposed. Instead of…

Finding dense substructures in a graph is a fundamental graph mining operation, with applications in bioinformatics, social networks, and visualization to name a few. Yet most standard formulations of this problem (like clique, quasiclique,…

Multilayer networks are a powerful paradigm to model complex systems, where multiple relations occur between the same entities. Despite the keen interest in a variety of tasks, algorithms, and analyses in this type of network, the problem…

This paper develops the exact linear relationship between the leading eigenvector of the unnormalized modularity matrix and the eigenvectors of the adjacency matrix. We propose a method for approximating the leading eigenvector of the…