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Graph matching is one of the most important problems in graph theory and combinatorial optimization, with many applications in various domains. Although meta-heuristic algorithms have had good performance on many NP-Hard and NP-Complete…

Neural and Evolutionary Computing · Computer Science 2019-04-01 Hashem Ezzati , Mahmood Amintoosi , Hashem Tabasi

Recent studies on Graph Neural Networks(GNNs) provide both empirical and theoretical evidence supporting their effectiveness in capturing structural patterns on both homophilic and certain heterophilic graphs. Notably, most real-world…

Machine Learning · Computer Science 2023-10-17 Haitao Mao , Zhikai Chen , Wei Jin , Haoyu Han , Yao Ma , Tong Zhao , Neil Shah , Jiliang Tang

Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…

Data Structures and Algorithms · Computer Science 2023-08-30 Rachit Nimavat

We introduce and study the problem \mpd, which asks for two planar graphs $G_1$ and $G_2$ whether $G_1$ can be embedded such that its dual is isomorphic to $G_2$. Our algorithmic main result is an NP-completeness proof for the general case…

Data Structures and Algorithms · Computer Science 2013-03-08 Patrizio Angelini , Thomas Bläsius , Ignaz Rutter

We propose a nonparametric two-sample test procedure based on Maximum Mean Discrepancy (MMD) for testing the hypothesis that two samples of functions have the same underlying distribution, using kernels defined on function spaces. This…

Statistics Theory · Mathematics 2020-10-20 George Wynne , Andrew B. Duncan

Functional Magnetic Resonance Imaging (fMRI) provides useful insights into the brain function both during task or rest. Representing fMRI data using correlation matrices is found to be a reliable method of analyzing the inherent…

Machine Learning · Computer Science 2025-01-29 Yicheng Leng , Syed Muhammad Anwar , Islem Rekik , Sen He , Eung-Joo Lee

While numerous methods have been proposed for computing distances between probability distributions in Euclidean space, relatively little attention has been given to computing such distances for distributions on graphs. However, there has…

Machine Learning · Computer Science 2023-06-06 Samuel Leone , Aarthi Venkat , Guillaume Huguet , Alexander Tong , Guy Wolf , Smita Krishnaswamy

In this paper, we consider the hypothesis testing of correlation between two $m$-uniform hypergraphs on $n$ unlabelled nodes. Under the null hypothesis, the hypergraphs are independent, while under the alternative hypothesis, the hyperdges…

Statistics Theory · Mathematics 2022-02-15 Mingao Yuan , Zuofeng Shang

Resting-state functional MRI (rs-fMRI) in functional neuroimaging techniques have improved in brain disorders, dysfunction studies via mapping the topology of the brain connections, i.e. connectopic mapping. Since, there are the slight…

Image and Video Processing · Electrical Eng. & Systems 2019-07-18 Jalal Mirakhorli , Hamidreza Amindavar , Mojgan Mirakhorli

The $\boldsymbol{\beta}$-model for random graphs is commonly used for representing pairwise interactions in a network with degree heterogeneity. Going beyond pairwise interactions, Stasi et al. (2014) introduced the hypergraph…

Statistics Theory · Mathematics 2024-06-07 Sagnik Nandy , Bhaswar B. Bhattacharya

Graph embeddings, a class of dimensionality reduction techniques designed for relational data, have proven useful in exploring and modeling network structure. Most dimensionality reduction methods allow out-of-sample extensions, by which an…

Machine Learning · Statistics 2019-10-02 Keith Levin , Fred Roosta , Minh Tang , Michael W. Mahoney , Carey E. Priebe

Distribution testing can be described as follows: $q$ samples are being drawn from some unknown distribution $P$ over a known domain $[n]$. After the sampling process, a decision must be made about whether $P$ holds some property, or is far…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-12-04 Uri Meir

We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test…

Methodology · Statistics 2008-02-06 E. Ceyhan , C. E. Priebe , D. J. Marchette

In this paper, we investigate three fundamental problems in the Massively Parallel Computation (MPC) model: (i) grid graph connectivity, (ii) approximate Euclidean Minimum Spanning Tree (EMST), and (iii) approximate DBSCAN. Our first result…

Data Structures and Algorithms · Computer Science 2025-01-22 Junhao Gan , Anthony Wirth , Zhuo Zhang

Theoretical studies on the representation power of GNNs have been centered around understanding the equivalence of GNNs, using WL-Tests for detecting graph isomorphism. In this paper, we argue that such equivalence ignores the accompanying…

Machine Learning · Computer Science 2024-08-26 P. Krishna Kumar a , Harish G. Ramaswamy

Many important results in extremal graph theory can be roughly summarised as "if a triangle-free graph $G$ has certain properties, then it has a homomorphism to a triangle-free graph $\Gamma$ of bounded size". For example, bounds on…

Combinatorics · Mathematics 2025-04-16 Lior Gishboliner , Eoin Hurley , Yuval Wigderson

Directional tests to compare incomplete undirected graphs are developed in the general context of covariance selection for Gaussian graphical models. The exactness of the underlying saddlepoint approximation is proved for chordal graphs and…

Methodology · Statistics 2023-05-16 Claudia Di Caterina , Nancy Reid , Nicola Sartori

We consider non-trivial homomorphisms to reflexive oriented graphs in which some pair of adjacent vertices have the same image. Using a notion of convexity for oriented graphs, we study those oriented graphs that do not admit such…

Discrete Mathematics · Computer Science 2023-06-22 Christopher Duffy , Sonja Linghui Shan

Graph theory has drawn a lot of attention in the field of Neuroscience during the last decade, mainly due to the abundance of tools that it provides to explore the interactions of elements in a complex network like the brain. The local and…

Neurons and Cognition · Quantitative Biology 2016-11-16 Sofia Ira Ktena , Sarah Parisot , Jonathan Passerat-Palmbach , Daniel Rueckert

The two-sample test is a fundamental problem in statistics with a wide range of applications. In the realm of high-dimensional data, nonparametric methods have gained prominence due to their flexibility and minimal distributional…

Methodology · Statistics 2024-12-24 Zexi Cai , Wenbo Fei , Doudou Zhou