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This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance (i.e. that minimizes a…

Machine Learning · Statistics 2019-05-14 Titouan Vayer , Laetitia Chapel , Rémi Flamary , Romain Tavenard , Nicolas Courty

Graphs have been utilized as a powerful tool to model pairwise relationships between people or objects. Such structure is a special type of a broader concept referred to as hypergraph, in which each hyperedge may consist of an arbitrary…

Social and Information Networks · Computer Science 2020-06-15 Manh Tuan Do , Se-eun Yoon , Bryan Hooi , Kijung Shin

In this paper we develop a framework to study observability for uniform hypergraphs. Hypergraphs, being extensions of graphs, allow edges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in…

Dynamical Systems · Mathematics 2023-09-19 Joshua Pickard , Amit Surana , Anthony Bloch , Indika Rajapakse

A heterogeneous graph consists of different vertices and edges types. Learning on heterogeneous graphs typically employs meta-paths to deal with the heterogeneity by reducing the graph to a homogeneous network, guide random walks or capture…

Machine Learning · Statistics 2023-03-06 See Hian Lee , Feng Ji , Wee Peng Tay

Optimal transport has become part of the standard quantitative economics toolbox. It is the framework of choice to describe models of matching with transfers, but beyond that, it allows to: extend quantile regression; identify discrete…

General Economics · Economics 2021-07-13 Alfred Galichon

Current paper introduces a Hypergraph Graph model of data storage which can be represented as a hybrid data structure based on Hypergraph and Graph. The pro-posed data structure is claimed to realize complex combinatorial structures. The…

Data Structures and Algorithms · Computer Science 2013-12-02 Shiladitya Munshi , Ayan Chakraborty , Debajyoti Mukhopadhyay

Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…

Optimization and Control · Mathematics 2018-03-26 Montacer Essid , Justin Solomon

Scalable addressing of high dimensional constrained combinatorial optimization problems is a challenge that arises in several science and engineering disciplines. Recent work introduced novel application of graph neural networks for solving…

Optimization and Control · Mathematics 2024-05-20 Nasimeh Heydaribeni , Xinrui Zhan , Ruisi Zhang , Tina Eliassi-Rad , Farinaz Koushanfar

Hypergraphs are a powerful abstraction for modeling high-order relations, which are ubiquitous in many fields. A hypergraph consists of nodes and hyperedges (i.e., subsets of nodes); and there have been a number of attempts to extend the…

Social and Information Networks · Computer Science 2023-08-24 Fanchen Bu , Geon Lee , Kijung Shin

In this paper we study fundamental connectivity properties of hypergraphs from a graph-theoretic perspective, with the emphasis on cut edges, cut vertices, and blocks. To prepare the ground, we define various types of subhypergraphs, as…

Combinatorics · Mathematics 2015-05-29 M. Amin Bahmanian , Mateja Šajna

Many existing transductive bounds rely on classical complexity measures that are computationally intractable and often misaligned with empirical behavior. In this work, we establish new representation-based generalization bounds in a…

Machine Learning · Computer Science 2026-03-11 MoonJeong Park , Seungbeom Lee , Kyungmin Kim , Jaeseung Heo , Seunghyuk Cho , Shouheng Li , Sangdon Park , Dongwoo Kim

We investigate the problem of efficiently computing optimal transport (OT) distances, which is equivalent to the node-capacitated minimum cost maximum flow problem in a bipartite graph. We compare runtimes in computing OT distances on data…

Data Structures and Algorithms · Computer Science 2020-07-07 Yihe Dong , Yu Gao , Richard Peng , Ilya Razenshteyn , Saurabh Sawlani

Urban mobility forecast and analysis can be addressed through grid-based and graph-based models. However, graph-based representations have the advantage of more realistically depicting the mobility networks and being more robust since they…

Discrete Mathematics · Computer Science 2023-10-11 Rafael Martínez Márquez , Giuseppe Patanè

Hypergraphs are generalisation of graphs in which a hyperedge can connect any number of vertices. It can describe n-ary relationships and high-order information among entities compared to conventional graphs. In this paper, we study the…

Databases · Computer Science 2023-02-21 Zhengyi Yang , Wenjie Zhang , Xuemin Lin , Ying Zhang , Shunyang Li

Encoding a driving scene into vector representations has been an essential task for autonomous driving that can benefit downstream tasks e.g. trajectory prediction. The driving scene often involves heterogeneous elements such as the…

Artificial Intelligence · Computer Science 2023-07-21 Xiaosong Jia , Penghao Wu , Li Chen , Yu Liu , Hongyang Li , Junchi Yan

A deluge of new data on social, technological and biological networked systems suggests that a large number of interactions among system units are not limited to pairs, but rather involve a higher number of nodes. To properly encode such…

Physics and Society · Physics 2023-11-08 Quintino Francesco Lotito , Federico Musciotto , Alberto Montresor , Federico Battiston

In this paper, we introduce a variant of optimal transport adapted to the causal structure given by an underlying directed graph $G$. Different graph structures lead to different specifications of the optimal transport problem. For…

Statistics Theory · Mathematics 2024-07-08 Patrick Cheridito , Stephan Eckstein

Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…

Data Structures and Algorithms · Computer Science 2018-06-21 Loukianos Spyrou , Javier Escudero

In this work, we propose a novel approach for subgraph matching, the problem of finding a given query graph in a large source graph, based on the fused Gromov-Wasserstein distance. We formulate the subgraph matching problem as a partial…

Information Theory · Computer Science 2024-07-01 Wen-Xin Pan , Isabel Haasler , Pascal Frossard

In this paper, we propose a simple and effective {geometric} model fitting method to fit and segment multi-structure data even in the presence of severe outliers. We cast the task of geometric model fitting as a representative mode-seeking…

Computer Vision and Pattern Recognition · Computer Science 2018-02-07 Hanzi Wang , Guobao Xiao , Yan Yan , David Suter