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Mathematics
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Mathematics-Based Methods in Graph Machine Learning
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Mathematics-Based Methods in Graph Machine Learning

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 6700

Special Issue Editors

Dr. Di Jin

E-Mail Website
Guest Editor
School of Computer Science and Technology, Tianjin University, Tianjin 300072, China
Interests: community detection; social network analysis; machine learning
Prof. Dr. Liang Yang

E-Mail Website
Guest Editor
School of Artificial Intelligence, Hebei University of Technology, Tianjin 300401, China
Interests: graph neural networks; pattern recognition; network embedding and data mining

Special Issue Information

Dear Colleagues,

Graphs are ubiquitous in the real world. The analysis of graphs has a long history, and fruitful theoretical results are obtained in many fields of mathematics ranging from graph theory, algebra, and topology to combinatorial mathematics. With the development of information technology and the Internet, graph data are now widely collected for research. In the age of big data, graph analysis is an emerging field in machine learning. In classic machine learning, spectral clustering based on graph cuts and graph-based semi-supervised learning have had a significant impact on many fields, such as image segmentation in computer vision. In the period of representation learning, graph embedding has received widespread attention, and many mathematics-based methods, such as matrix factorization, dominate this field. Recently, graph neural networks, which originate from spectral graph theory, generalize neural networks and deep learning to the graph. A broad class of models, which leverage results from mathematics, such as computational topology and wavelet analysis, are proposed. These models achieve new state-of-the-art performances in practical scenarios, including recommendation, traffic forecasting, medicine development, healthcare, and natural language processing. The aim of this Special Issue is to highlight the recent advances in the development of mathematics-based graph machine learning, including theories, models, algorithms, and applications in the real world.

The topics of interest include, but are not limited to:

  • Mathematics-based graph machine learning theories;
  • Mathematics-based graph machine learning models;
  • Mathematics-based graph machine learning algorithms;
  • Graph embedding/representation methods;
  • Graph neural networks/graph convolutional networks;
  • Graph-based unsupervised learning, spectral clustering and community detection algorithms;
  • Graph-based semi-supervised algorithms;
  • Graph machine learning applications in natural language processing, information retrieval, computer vision, intelligent traffic, recommendation system, biology, chemistry, safety, medicine design and industry.

Prof. Dr. Di Jin
Prof. Dr. Liang Yang
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • graph learning
  • graph neural networks
  • network embedding

Published Papers (4 papers)

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Research

14 pages, 7912 KiB  
Article
Biomedical Interaction Prediction with Adaptive Line Graph Contrastive Learning
by Shilin Sun, Hua Tian, Runze Wang and Zehua Zhang
Mathematics 2023, 11(3), 732; https://doi.org/10.3390/math11030732 - 01 Feb 2023
Cited by 1 | Viewed by 1410
Abstract
Biomedical interaction prediction is essential for the exploration of relationships between biomedical entities. Predicted biomedical interactions can help researchers with drug discovery, disease treatment, and more. In recent years, graph neural networks have taken advantage of their natural structure to achieve great progress [...] Read more.
Biomedical interaction prediction is essential for the exploration of relationships between biomedical entities. Predicted biomedical interactions can help researchers with drug discovery, disease treatment, and more. In recent years, graph neural networks have taken advantage of their natural structure to achieve great progress in biomedical interaction prediction. However, most of them use node embedding instead of directly using edge embedding, resulting in information loss. Moreover, they predict links based on node similarity correlation assumptions, which have poor generalization. In addition, they do not consider the difference in topological information between negative and positive sample links, which limits their performance. Therefore, in this paper, we propose an adaptive line graph contrastive (ALGC) method to convert negative and positive sample links into two kinds of line graph nodes. By adjusting the number of intra-class line graph edges and inter-class line graph edges, an augmented line graph is generated and, finally, the information of the two views is balanced by contrastive learning. Through experiments on four public datasets, it is proved that the ALGC model outperforms the state-of-the-art methods. Full article
(This article belongs to the Special Issue Mathematics-Based Methods in Graph Machine Learning)
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16 pages, 2460 KiB  
Article
Hyperbolic Directed Hypergraph-Based Reasoning for Multi-Hop KBQA
by Guanchen Xiao, Jinzhi Liao, Zhen Tan, Yiqi Yu and Bin Ge
Mathematics 2022, 10(20), 3905; https://doi.org/10.3390/math10203905 - 21 Oct 2022
Cited by 1 | Viewed by 1439
Abstract
The target of the multi-hop knowledge base question-answering task is to find answers of some factoid questions by reasoning across multiple knowledge triples in the knowledge base. Most of the existing methods for multi-hop knowledge base question answering based on a general knowledge [...] Read more.
The target of the multi-hop knowledge base question-answering task is to find answers of some factoid questions by reasoning across multiple knowledge triples in the knowledge base. Most of the existing methods for multi-hop knowledge base question answering based on a general knowledge graph ignore the semantic relationship between each hop. However, modeling the knowledge base as a directed hypergraph has the problems of sparse incidence matrices and asymmetric Laplacian matrices. To make up for the deficiency, we propose a directed hypergraph convolutional network modeled on hyperbolic space, which can better deal with the sparse structure, and effectively adapt to the problem of an asymmetric incidence matrix of directed hypergraphs modeled on a knowledge base. We propose an interpretable KBQA model based on the hyperbolic directed hypergraph convolutional neural network named HDH-GCN which can update relation semantic information hop-by-hop and pays attention to different relations at different hops. The model can improve the accuracy of the multi-hop knowledge base question-answering task, and has application value in text question answering, human–computer interactions and other fields. Extensive experiments on benchmarks—PQL, MetaQA—demonstrate the effectiveness and universality of our HDH-GCN model, leading to state-of-the-art performance. Full article
(This article belongs to the Special Issue Mathematics-Based Methods in Graph Machine Learning)
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18 pages, 597 KiB  
Article
Identification of Nonlinear State-Space Systems via Sparse Bayesian and Stein Approximation Approach
by Limin Zhang, Junpeng Li, Wenting Zhang and Junzi Yang
Mathematics 2022, 10(19), 3667; https://doi.org/10.3390/math10193667 - 06 Oct 2022
Viewed by 1326
Abstract
This paper is concerned with the parameter estimation of non-linear discrete-time systems from noisy state measurements in the state-space form. A novel sparse Bayesian convex optimisation algorithm is proposed for the parameter estimation and prediction. The method fully considers the approximation method, parameter [...] Read more.
This paper is concerned with the parameter estimation of non-linear discrete-time systems from noisy state measurements in the state-space form. A novel sparse Bayesian convex optimisation algorithm is proposed for the parameter estimation and prediction. The method fully considers the approximation method, parameter prior and posterior, and adds Bayesian sparse learning and optimization for explicit modeling. Different from the previous identification methods, the main identification challenge resides in two aspects: first, a new objective function is obtained by our improved Stein approximation method in the convex optimization problem, so as to capture more information of particle approximation and convergence; second, another objective function is developed with L1-regularization, which is sparse method based on recursive least squares estimation. Compared with the previous study, the new objective function contains more information and can easily mine more important information from the raw data. Three simulation examples are given to demonstrate the proposed algorithm’s effectiveness. Furthermore, the performances of these approaches are analyzed, including parameter estimation of root mean squared error (RMSE), parameter sparsity and prediction of state and output result. Full article
(This article belongs to the Special Issue Mathematics-Based Methods in Graph Machine Learning)
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16 pages, 3135 KiB  
Article
Wind Speed Prediction via Collaborative Filtering on Virtual Edge Expanding Graphs
by Xiang Ying, Keke Zhao, Zhiqiang Liu, Jie Gao, Dongxiao He, Xuewei Li and Wei Xiong
Mathematics 2022, 10(11), 1943; https://doi.org/10.3390/math10111943 - 06 Jun 2022
Cited by 3 | Viewed by 1532
Abstract
Accurate and stable wind speed prediction is crucial for the safe operation of large-scale wind power grid connections. Existing methods are typically limited to a certain fixed area when learning the information of the wind speed sequence, which cannot make full use of [...] Read more.
Accurate and stable wind speed prediction is crucial for the safe operation of large-scale wind power grid connections. Existing methods are typically limited to a certain fixed area when learning the information of the wind speed sequence, which cannot make full use of the spatiotemporal correlation of the wind speed sequence. To address this problem, in this paper we propose a new wind speed prediction method based on collaborative filtering against a virtual edge expansion graph structure in which virtual edges enrich the semantics that the graph can express. It is an effective extension of the dataset, connecting wind turbines of different wind farms through virtual edges to ensure that the spatial correlation of wind speed sequences can be effectively learned and utilized. The new collaborative filtering on the graph is reflected in the processing of the wind speed sequence. The wind speed is preprocessed from the perspective of pattern mining to effectively integrate various information, and the k-d tree is used to match the wind speed sequence to achieve the purpose of collaborative filtering. Finally, a model with long short-term memory (LSTM) as the main body is constructed for wind speed prediction. By taking the wind speed of the actual wind farm as the research object, we compare the new approach with four typical wind speed prediction methods. The mean square error is reduced by 16.40%, 11.78%, 9.57%, and 18.36%, respectively, which demonstrates the superiority of the proposed new method. Full article
(This article belongs to the Special Issue Mathematics-Based Methods in Graph Machine Learning)
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