Article
Automation & Control Systems
William E. Gilbraith, Caelin P. Celani, Karl S. Booksh
Summary: This article demonstrates the use of network analysis to visualize misclassified elements in a confusion matrix and presents the potential to use network graphs as a guide for developing hierarchical classification models. It provides a brief overview of graph theory and explains how these networks can be used to visualize confusion matrices with code examples. The article also discusses the use of network graphs to gain insight into different model performance.
JOURNAL OF CHEMOMETRICS
(2023)
Article
Computer Science, Software Engineering
Tim A. Hartmann, Stefan Lendl, Gerhard J. Woeginger
Summary: The study focuses on a continuous facility location problem on undirected graphs, aiming to cover the entire graph with a minimum number of facilities. The problem is proven to be polynomially solvable when delta is a unit fraction. However, it becomes NP-hard for all non unit fractions delta. Moreover, the parametrized complexity is analyzed, showing that the problem is fixed parameter tractable for delta < 3/2 and W[2]-hard for delta >= 3/2.
MATHEMATICAL PROGRAMMING
(2022)
Article
Mathematics
Valentin E. Brimkov, Reneta P. Barneva
Summary: This paper defines a class of Fibonacci graphs and studies their properties. The results show that these graphs are close in size to Turan graphs and their size-stability tradeoff is close to the maximum possible value. Additionally, a combinatorial game based on sequential vertex deletions is considered, and it is found that Fibonacci graphs are extreme in terms of the number of rounds in which the game can terminate.
Article
Mathematics, Applied
John Stewart Fabila-Carrasco, Fernando Lledo, Olaf Post
Summary: This article explores the spectrum of the discrete magnetic Laplacian on a finite simple graph in relation to the structural properties of the graph, introducing a family of spectral obstructions parametrised by the magnetic potential to determine the graph's matchability and the existence of a Hamiltonian cycle.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2022)
Review
Automation & Control Systems
Resul Das, Mucahit Soylu
Summary: This comprehensive review provides an in-depth analysis of the role of graph theory and graph visualization in scientific studies. It explores different graph types, special graphs, and the challenges and advancements in graph visualization techniques. The review serves as a valuable resource for researchers to understand the principles and applications of graphs in diverse scientific disciplines.
CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS
(2023)
Article
Computer Science, Information Systems
Shengwen Li, Chenpeng Sun, Renyao Chen, Xinchuan Li, Qingzhong Liang, Junfang Gong, Hong Yao
Summary: This paper proposes a location-aware neural graph collaborative filtering model (LA-NGCF) that incorporates location information of items to improve personalized recommendation performance.
INTERNATIONAL JOURNAL OF GEOGRAPHICAL INFORMATION SCIENCE
(2022)
Article
Computer Science, Software Engineering
Bo Jiao, Xin Lu, Jingbo Xia, Brij Bhooshan Gupta, Lei Bao, Qingshan Zhou
Summary: This paper proposes a hierarchical structure model and a corresponding hierarchical structure sampling algorithm for sampling large-scale scale-free graphs in visualization. The algorithm can preserve the core community structure, important minority structures, and the connection relationship between low-degree nodes in the graph.
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
(2023)
Article
Computer Science, Artificial Intelligence
Hao Li, Xin Gao
Summary: This paper discusses the contributions of edges to connectivity and proposes concepts about the significance of edges in an uncertain random graph. It also presents algorithms for calculating the connectivity index and significance of edges, with examples provided for illustration.
Article
Computer Science, Software Engineering
Tom Horak, Philip Berger, Heidrun Schumann, Raimund Dachselt, Christian Tominski
Summary: Responsive matrix cells are local zoomable regions in a matrix that offer auxiliary facilities for data exploration and editing for multivariate graphs, adapting their visual contents based on cell location, available display space, and user tasks.
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
(2021)
Article
Geosciences, Multidisciplinary
Yukun Guo, Jun Zhu, Jigang You, Saied Pirasteh, Weilian Li, Jianlin Wu, Jianbo Lai, Pei Dang
Summary: In order to enhance individuals' capacity and awareness in disaster prevention and mitigation, a novel strategy utilizing conceptual graphs to organize and guide the visual representation of flood disaster knowledge is proposed. A prototype system was developed to visualize disaster data obtained from flood-affected areas, and its visualization output was compared to expert-based reports using a questionnaire. The results demonstrated the superiority of the approach in attractiveness and comprehensibility.
Article
Mathematics
Gi-Sang Cheon, Jang Soo Kim, Seyed Ahmad Mojallal, Meesue Yoo
Summary: The paper examines the spectral properties of the symmetric Pascal matrix and binomial graph, including eigenvalues, eigenvectors, algebraic connectivity, and inertia indices. The determinant of the Pascal matrix modulo 3 is also computed in the study.
LINEAR & MULTILINEAR ALGEBRA
(2022)
Article
Mathematics, Applied
Zhuang Xiong, Yaoping Hou
Summary: This paper investigates the distribution of eigenvalues for Seidel matrices of threshold graphs. The research shows that there are no eigenvalues of Seidel matrices of threshold graphs in the interval (-√2, √2) except for -1 and 1. The inertia of the Seidel matrix of a threshold graph is also determined based on its binary string.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Computer Science, Artificial Intelligence
Ya Chen, Samuel Mensah, Fei Ma, Hao Wang, Zhongan Jiang
Summary: Matrix Factorization (MF) is an effective collaborative filtering technique for modeling user-item interactions in recommender systems, but its effectiveness is limited by sparse data. To address this, leveraging knowledge graphs as supplementary information has shown to improve performance in extremely sparse settings.
PATTERN RECOGNITION LETTERS
(2021)
Article
Computer Science, Artificial Intelligence
Amirhosein Bodaghi, Jonice Oliveira
Summary: The study found that tweeters of truth have the highest value of page rank centrality on Twitter, while fake news retweeters excel in rate of modularity and ratio of intra- to inter-links. Additionally, reciprocal relationships serve as channels for diffusion into the network, but users with lower ratio of following to follower perform better in sparking the spreading process itself.
EXPERT SYSTEMS WITH APPLICATIONS
(2022)
Article
Computer Science, Artificial Intelligence
Aanchal Mongia, Angshul Majumdar
Summary: This study proposes an alternative method for collaborative filtering by addressing the issue of inaccurate representation of true similarities when computing graph, showing improved performance on benchmarking against fixed graph techniques and state-of-the-art collaborative filtering algorithms.
EXPERT SYSTEMS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
W. Erb, A. Weinmann, M. Ahlborg, C. Brandt, G. Bringout, T. M. Buzug, J. Frikel, C. Kaethner, T. Knopp, T. Maerz, M. Moeddel, M. Storath, A. Weber
Article
Mathematics, Applied
Gael Bringout, Wolfgang Erb, Juergen Frikel
Article
Mathematics, Applied
Roberto Cavoretto, Alessandra De Rossi, Wolfgang Erb
Summary: Partition of unity methods (PUMs) on graphs are simple and highly adaptive auxiliary tools for graph signal processing. By combining PUMs with local graph basis function (GBF) approximation methods, low-cost global interpolation or classification schemes can be achieved. Theoretical prerequisites for PUMs and their global error estimates have been studied, while properties like cost-efficiency and approximation accuracy have been investigated numerically.
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Wolfgang Erb
Summary: This paper introduces the concept of positive definite functions on graphs for the interpolation of graph signals with generalized shifts of a graph basis function (GBF). By describing and analyzing positive definite functions, we design GBFs and study the interpolation error and numerical stability. Finally, we demonstrate the application of using GBF interpolation to derive quadrature formulas on graphs.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2022)
Article
Computer Science, Artificial Intelligence
Luca Pasa, Nicolo Navarin, Wolfgang Erb, Alessandro Sperduti
Summary: Many neural networks for graphs are based on the graph convolution operator proposed more than a decade ago. Recently, a simplified version called simple graph convolution has been proposed, which aims to remove nonlinearities. In this article, the authors propose, analyze, and compare different simple graph convolution operators that can be implemented in single-layer graph convolutional networks, showing competitive predictive performance on node classification benchmark datasets.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Mathematics, Applied
S. De Marchi, W. Erb, F. Marchetti, E. Perracchione, M. Rossini
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2020)
