Learning the effective order of a hypergraph dynamical system

Science Advances, Journal Year: 2024, Volume and Issue: 10(19)

Published: May 8, 2024

Dynamical systems on hypergraphs can display a rich set of behaviors not observable for with pairwise interactions. Given distributed dynamical system putative hypergraph structure, an interesting question is thus how much this structure actually necessary to faithfully replicate the observed behavior. To answer question, we propose method determine minimum order approximate corresponding dynamics accurately. Specifically, develop mathematical framework that allows us when type known. We use these ideas in conjunction neural network directly learn itself and resulting from both synthetic real datasets consisting trajectories.

Language: Английский

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Filtering higher-order datasets

Journal of Physics Complexity, Journal Year: 2024, Volume and Issue: 5(1), P. 015006 - 015006

Published: Feb. 2, 2024

Abstract Many complex systems often contain interactions between more than two nodes, known as higher-order , which can change the structure of these in significant ways. Researchers assume that all paint a consistent picture dataset’s structure. In contrast, connection patterns individuals or entities empirical are stratified by interaction size. Ignoring this fact aggregate exist only at certain scales interaction. To isolate scale-dependent patterns, we present an approach for analyzing datasets filtering their We apply framework to several from three domains demonstrate data practitioners gain valuable information approach.

Language: Английский

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How choosing random-walk model and network representation matters for flow-based community detection in hypergraphs

Communications Physics, Journal Year: 2021, Volume and Issue: 4(1)

Published: June 11, 2021

Abstract Hypergraphs offer an explicit formalism to describe multibody interactions in complex systems. To connect dynamics and function systems with these higher-order interactions, network scientists have generalised random-walk models hypergraphs studied the effects on flow-based centrality measures. Mapping large-scale structure of those flows requires effective community detection methods applied cogent representations. For different hypergraph data research questions, which combination model representation is best? We define unipartite, bipartite, multilayer representations explore how they underlying change number, size, depth, overlap identified multilevel communities. These results help researchers choose appropriate modelling approach when mapping hypergraphs.

Language: Английский

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T-HyperGNNs: Hypergraph Neural Networks via Tensor Representations

IEEE Transactions on Neural Networks and Learning Systems, Journal Year: 2024, Volume and Issue: 36(3), P. 5044 - 5058

Published: March 7, 2024

Hypergraph neural networks (HyperGNNs) are a family of deep designed to perform inference on hypergraphs. HyperGNNs follow either spectral or spatial approach, in which convolution message-passing operation is conducted based hypergraph algebraic descriptor. While many have been proposed and achieved state-of-the-art performance broad applications, there limited attempts at exploring high-dimensional descriptors (tensors) joint node interactions carried by hyperedges. In this article, we depart from matrix representations present new tensor-HyperGNN (T-HyperGNN) framework with cross-node (CNIs). The T-HyperGNN consists T-spectral convolution, T-spatial T-message-passing (T-MPHN). HyperGNN defined under the t-product algebra that closely connects space. To improve computational efficiency for large hypergraphs, localize approach formulate further devise novel tensor-message-passing algorithm practical implementation studying compressed adjacency tensor representation. Compared approaches, our T-HyperGNNs preserve intrinsic high-order network structures without any reduction model effects nodes through CNI layer. These advantages demonstrated wide range real-world datasets. code available https://github.com/wangfuli/T-HyperGNNs.git.

Language: Английский

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An information-theoretic approach to build hypergraphs in psychometrics

Behavior Research Methods, Journal Year: 2024, Volume and Issue: 56(7), P. 8057 - 8079

Published: July 30, 2024

Language: Английский

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