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A spectral graph convolution for signed directed graphs via magnetic Laplacian

NEURAL NETWORKS 2023年第1期164卷 562-574页

作者： Ko, Taewook Choi, Yoonhyuk Kim, Chong -Kwon Seoul Natl Univ Seoul South Korea Korea Inst Energy Technol Naju South Korea

signed directed graphs contain both sign and direction information on their edges, providing richer information about real-world phenomena compared to unsigned or undirected graphs. However, analyzing such graphs is more challenging due to their complexity, and the limited availability of existing methods. Consequently, despite their potential uses, signed directed graphs have received less research attention. In this paper, we propose a novel spectral graph convolution model that effectively captures the underlying patterns in signed directed graphs. To this end, we introduce a complex Hermitian adjacency matrix that can represent both sign and direction of edges using complex numbers. We then define a magnetic Laplacian matrix based on the adjacency matrix, which we use to perform spectral convolution. We demonstrate that the magnetic Laplacian matrix is positive semi-definite (PSD), which guarantees its applicability to spectral methods. Compared to traditional Laplacians, the magnetic Laplacian captures additional edge information, which makes it a more informative tool for graph analysis. By leveraging the information of signed directed edges, our method generates embeddings that are more representative of the underlying graph structure. Furthermore, we showed that the proposed method has wide applicability for various graph types and is the most generalized Laplacian form. We evaluate the effectiveness of the proposed model through extensive experiments on several real-world datasets. The results demonstrate that our method outperforms state-of-the-art techniques in signed directed graph embedding. (c) 2023 The Authors. Published by Elsevier Ltd.

关键词： Graph convolution Spectral convolution Magnetic Laplacian signed directed graphs Link sign prediction Link existence prediction

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Learning disentangled representations in signed directed graphs without social assumptions

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INFORMATION SCIENCES 2024年 665卷

作者： Ko, Geonwoo Jung, Jinhong Soongsil Univ Dept Software Seoul 07027 South Korea

signed graphs can represent complex systems of positive and negative relationships such as trust or preference in various domains. Learning node representations is indispensable because they serve as pivotal features for downstream tasks on signed graphs. However, most existing methods often oversimplify the modeling of signed relationships by relying on social theories, while real-world relationships can be influenced by multiple latent factors. This hinders those methods from effectively capturing the diverse factors, thereby limiting the expressiveness of node representations. In this paper, we propose DINES, a novel method for learning disentangled node representations in signed directed graphs without social assumptions. We adopt a disentangled framework that separates each embedding into distinct factors, allowing for capturing multiple latent factors, and uses signed directed graph convolutions that focus solely on sign and direction, without depending on social theories. Additionally, we propose a new decoder that effectively classifies an edge's sign by considering correlations between the factors. To further enhance disentanglement, we jointly train a self-supervised factor discriminator with our encoder and decoder. Throughout extensive experiments on real-world signed directed graphs, we show that DINES effectively learns disentangled node representations, and significantly outperforms its competitors in predicting link signs.

关键词： signed directed graphs Disentangled representation learning Graph neural networks Link sign prediction

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Adaptive Bipartite Leaderless Consensus of Multiagent Systems With Uncertain MIMO Dynamics Over a signed directed Graph

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2023年第8期70卷 2969-2973页

作者： Tian, Congcong Mei, Jie Harbin Inst Technol Sch Mech Engn & Automat Shenzhen 518055 Guangdong Peoples R China

This brief investigates the bipartite leaderless consensus problem for uncertain multi-input multi-output (MIMO) multi-agent systems (MASs) over a directed cooperation-competition network. An adaptive control protocol is proposed to achieve the bipartite consensus for agents in the presence of matching uncertainties. It is required that the signed directed graph should be structurally balanced and contain a directed spanning tree. A numerical example is performed to verify the effectiveness of the proposed algorithm.

关键词： Multi-agent systems signed directed graphs adaptive bipartite leaderless consensus uncertainties

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Data-driven consensus control for networked agents: an iterative learning control-motivated approach

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IET CONTROL THEORY AND APPLICATIONS 2015年第14期9卷 2084-2096页

作者： Meng, Deyuan Du, Wen Jia, Yingmin Beihang Univ BUAA Res Div 7 Beijing 100191 Peoples R China Beihang Univ BUAA Sch Automat Sci & Elect Engn Beijing 100191 Peoples R China Beihang Univ BUAA Sch Math & Syst Sci Beijing 100191 Peoples R China

This study considers an iterative learning control approach to achieve accurate coordination performances of the output data sequences for multiple plants that are involved in a networked environment. To realise such a desirable control objective, an update process of the input data sequence is needed to refine its output performance iteratively for each plant, which uses the local or nearest neighbour knowledge. The nominal multi-agent systems are employed as the plants' description, for which input-output data-driven consensus problems are addressed in a hybrid networked environment given by signed directed graphs with both cooperative and antagonistic interactions. It is proved that the output data can be guaranteed to achieve bipartite consensus or remain stable for the multi-agent networks under structurally balanced or structurally unbalanced signed graphs. Moreover, the convergence conditions are derived, which need less knowledge of the agents' plant, and the proposed consensus results can be developed to take into account the plant uncertainties and noises. Simulation tests are performed to verify the effectiveness of the learning approach in refining high input-output data-driven consensus performances of networked agents.

关键词： iterative learning control multi-agent systems networked control systems data-driven consensus control networked agents iterative learning control-motivated approach nominal multiagent systems input–output data-driven consensus problems signed directed graphs bipartite consensus plant uncertainties

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Assessing model structure uncertainty through an analysis of system feedback and Bayesian networks

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ECOLOGICAL APPLICATIONS 2008年第4期18卷 1070-1082页

作者： Hosack, Geoffrey R. Hayes, Keith R. Dambacher, Jeffrey M. Oregon State Univ Dept Fisheries & Wildlife Corvallis OR 97331 USA CSIRO Math & Informat Sci Hobart Tas 7001 Australia

Ecological predictions and management strategies are sensitive to variability in model parameters as well as uncertainty in model structure. Systematic analysis of the effect of alternative model structures, however, is often beyond the resources typically available to ecologists, ecological risk practitioners, and natural resource managers. Many of these practitioners are also using Bayesian belief networks based on expert opinion to fill gaps in empirical information. The practical application of this approach can be limited by the need to populate large conditional probability tables and the complexity associated with ecological feedback cycles. In this paper, we describe a modeling approach that helps solve these problems by embedding a qualitative analysis of sign directed graphs into the probabilistic framework of a Bayesian belief network. Our approach incorporates the effects of feedback on the model's response to a sustained change in one or more of its parameters, provides an efficient means to explore the effect of alternative model structures, mitigates the cognitive bias in expert opinion, and is amenable to stakeholder input. We demonstrate our approach by examining two published case studies: a host-parasitoid community centered on a nonnative, agricultural pest of citrus cultivars and the response of an experimental lake mesocosm to nutrient input. Observations drawn from these case studies are used to diagnose alternative model structures and to predict the system's response following management intervention.

关键词： Bayesian belief network expert opinion feedback model uncertainty risk assessment signed directed graphs

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Verifying signed directed graph models for process plants

Verifying signed directed graph models for process plants

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European Symposium on Computer Aided Process Engineering-9 (Escape-9)

作者： Palmer, C Chung, PWH Loughborough Univ Technol Dept Chem Engn Loughborough LE11 3TU Leics England

Qualitative modelling using signed directed graphs is briefly described. The need for verification is discussed and the verification techniques for signed directed graph models of process plants are detailed.

关键词： qualitative modelling signed directed graphs verification

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Verifying signed directed graph models for process plants

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COMPUTERS & CHEMICAL ENGINEERING 1999年 23卷 S391-S394页

作者： Palmer, C Chung, PWH Loughborough Univ Technol Dept Chem Engn Loughborough LE11 3TU Leics England

关键词： qualitative modelling signed directed graphs verification

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SDG Model-Based Structures for Fault Detection

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IFAC Proceedings Volumes 1998年第10期31卷 243-248页

作者： I.P. Gál K.M. Hangos Systems and Control Research Laboratory Computer and Automation Institute Hungarian Academy of Sciences 1518 Budapest POBox. 63 Hungary. Phone: 36 1 1667 483 Fax: 36 1 1667 503

A signed directed graph (SDG) model-based approach is given in this paper for fault diagnosis of process systems. The proposed method is modular, the model for fault propagation is built from the mini SDGs of the units driven by the process flowsheet. Thus the fault detection is decomposed into two steps: off-line generation of the SOG model and its rule set equivalent and the step of on-line fault detection.

关键词： Fault detection Process models Graph theoretic models Rules signed directed graphs Reasoning

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Eliminating ambiguities in qualitative causal feedback

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COMPUTERS & CHEMICAL ENGINEERING 1998年第sup1期22卷 S843-S846页

作者： Palmer, C Chung, PWH Loughborough Univ Technol Dept Chem Engn Loughborough LE11 3TU Leics England

After a brief description of qualitative modelling, current methods to resolve ambiguities within qualitative modelling are discussed. Examples are given showing how unit-based qualitative modelling can lead to incorrect or ambiguous inference. A new modular approach is presented which overcomes this type of problem. (C) 1998 Elsevier Science Ltd. All rights reserved.

关键词： qualitative modelling signed directed graphs ambiguities

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