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Mathematics
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Mathematical Computation in Knowledge Graph: Theories, Techniques, and Applications
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Mathematical Computation in Knowledge Graph: Theories, Techniques, and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 31 May 2025 | Viewed by 19542

Special Issue Editors

Dr. Tianxing Wu

E-Mail Website
Guest Editor
School of Computer Science and Engineering, Southeast University, Nanjing 211189, China
Interests: knowledge graph; knowledge representation and reasoning; data mining
Special Issues, Collections and Topics in MDPI journals
Dr. Yuxiang Wang

E-Mail Website
Guest Editor
School of Computer Science, Hangzhou Dianzi University, Hangzhou 310018, China
Interests: knowledge graph; community search; graph neural network
Dr. Ningyu Zhang

E-Mail Website
Guest Editor
School of Software Technology, Zhejiang University, Hangzhou 310028, China
Interests: knowledge graph; natural language processing

Special Issue Information

Dear Colleagues,

As a representative technique of the new generation of knowledge engineering, Knowledge Graph (KG) has attracted extensive attention from both academia and industry. KG refers to any collection of knowledge represented in the form of graph, such as Semantic Web knowledge bases, RDF datasets, and formal ontologies. Nowadays, KG is widely applied in the research areas of artificial intelligence, natural language processing, machine learning, and data mining, since it can provide the capabilities of cognition, reasoning, and decision-making. However, a large number of KG-relevant real-world problems are still unsolved, such as high robust open-world KG construction, alignment, reasoning, update, querying, question answering, and etc. The most difficult key points are the mathematical computation and optimization in the above problems. Thus, this special issue aims to address these challenges by inviting scholarly contributions covering advanced theories, techniques, and applications of mathematical computation in KG. We are looking forward to receiving original research papers, experimental papers, and dataset papers related to the topic.

Dr. Tianxing Wu
Dr. Yuxiang Wang
Dr. Ningyu Zhang
Guest Editors

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Keywords

  • mathematics and knowledge graph
  • knowledge graph construction
  • knowledge graph alignment
  • knowledge graph reasoning
  • knowledge graph querying
  • knowledge graph embedding
  • multimodal knowledge graph
  • multilingual knowledge graph
  • nlp and knowledge graph
  • data mining and knowledge graph
  • machine learning on graphs
  • question answering on knowledge graph
  • semantic search
  • ontology engineering
  • linked open data
  • knowledge graph applications in medicine, law, security, and smart grid

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Published Papers (4 papers)

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Research

28 pages, 16776 KiB  
Article
Efficient Complex Aggregate Queries with Accuracy Guarantee Based on Execution Cost Model over Knowledge Graphs
by Shuzhan Ye, Xiaoliang Xu, Yuxiang Wang and Tao Fu
Mathematics 2023, 11(18), 3908; https://doi.org/10.3390/math11183908 - 14 Sep 2023
Cited by 1 | Viewed by 1423
Abstract
Knowledge graphs (KGs) have gained prominence for representing real-world facts, with queries of KGs being crucial for their application. Aggregate queries, as one of the most important parts of KG queries (e.g., “ What is the average price of cars produced in Germany?”), [...] Read more.
Knowledge graphs (KGs) have gained prominence for representing real-world facts, with queries of KGs being crucial for their application. Aggregate queries, as one of the most important parts of KG queries (e.g., “ What is the average price of cars produced in Germany?”), can provide users with valuable statistical insights. An efficient solution for KG aggregate queries is approximate aggregate queries with semantic-aware sampling (AQS). This balances the query time and result accuracy by estimating an approximate aggregate result based on random samples collected from a KG, ensuring that the relative error of the approximate aggregate result is bounded by a predefined error. However, AQS is tailored for simple aggregate queries and exhibits varying performance for complex aggregate queries. This is because a complex aggregate query usually consists of multiple simple aggregate queries, and each sub-query influences the overall processing time and result quality. Setting a large error bound for each sub-query yields quick results but with a lower quality, while aiming for high-quality results demands a smaller predefined error bound for each sub-query, leading to a longer processing time. Hence, devising efficient and effective methods for executing complex aggregate queries has emerged as a significant research challenge within contemporary KG querying. To tackle this challenge, we first introduced an execution cost model tailored for original AQS (i.e., supporting simple queries) and founded on Taylor’s theorem. This model aids in identifying the initial parameters that play a pivotal role in the efficiency and efficacy of AQS. Subsequently, we conducted an in-depth exploration of the intrinsic relationship of the error bounds between a complex aggregate query and its constituent simple queries (i.e., sub-queries), and then we formalized an execution cost model for complex aggregate queries, given the accuracy constraints on the error bounds of all sub-queries. Harnessing the multi-objective optimization genetic algorithm, we refined the error bounds of all sub-queries with moderate values, to achieve a balance of query time and result accuracy for the complex aggregate query. An extensive experimental study on real-world datasets demonstrated our solution’s superiority in effectiveness and efficiency. Full article
(This article belongs to the Special Issue Mathematical Computation in Knowledge Graph: Theories, Techniques, and Applications)
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27 pages, 8427 KiB  
Article
A Social Media Knowledge Retrieval Method Based on Knowledge Demands and Knowledge Supplies
by Runsheng Miao, Yuchen Huang and Zhenyu Zhang
Mathematics 2023, 11(14), 3154; https://doi.org/10.3390/math11143154 - 18 Jul 2023
Cited by 1 | Viewed by 1518
Abstract
In large social media knowledge retrieval systems, employing a keyword-based fuzzy matching method to obtain knowledge presents several challenges, such as irrelevant, inaccurate, disorganized, or non-systematic knowledge results. Therefore, this paper proposes a knowledge retrieval method capable of returning hierarchical, systematized knowledge results. [...] Read more.
In large social media knowledge retrieval systems, employing a keyword-based fuzzy matching method to obtain knowledge presents several challenges, such as irrelevant, inaccurate, disorganized, or non-systematic knowledge results. Therefore, this paper proposes a knowledge retrieval method capable of returning hierarchical, systematized knowledge results. The method can match the knowledge demands according to the keyword input by users and then present the knowledge supplies corresponding to the knowledge demands as results to the users. Firstly, a knowledge structure named Knowledge Demand is designed to represent the genuine needs of social media users. This knowledge structure measures the popularity of topic combinations in the Topic Map, so the topic combinations with high popularity are regarded as the main content of the Knowledge Demands. Secondly, the proposed method designs a hierarchical and systematic knowledge structure, named Knowledge Supply, which provides Knowledge Solutions matched with the Knowledge Demands. The Knowledge Supply is generated based on the Knowledge Element Repository, using the BLEU similarity matrix to retrieve Knowledge Elements with high similarity, and then clustering these Knowledge Elements into several knowledge schemes to extract the Knowledge Solutions. The organized Knowledge Elements and Knowledge Solutions are the presentation of each Knowledge Supply. Finally, this research crawls posts in the “Autohome Forum” and conducts an experiment by simulating the user’s actual knowledge search process. The experiment shows that the proposed method is an effective knowledge retrieval method, which can provide users with hierarchical and systematized knowledge. Full article
(This article belongs to the Special Issue Mathematical Computation in Knowledge Graph: Theories, Techniques, and Applications)
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27 pages, 2098 KiB  
Article
A Survey on Multimodal Knowledge Graphs: Construction, Completion and Applications
by Yong Chen, Xinkai Ge, Shengli Yang, Linmei Hu, Jie Li and Jinwen Zhang
Mathematics 2023, 11(8), 1815; https://doi.org/10.3390/math11081815 - 11 Apr 2023
Cited by 16 | Viewed by 10704
Abstract
As an essential part of artificial intelligence, a knowledge graph describes the real-world entities, concepts and their various semantic relationships in a structured way and has been gradually popularized in a variety practical scenarios. The majority of existing knowledge graphs mainly concentrate on [...] Read more.
As an essential part of artificial intelligence, a knowledge graph describes the real-world entities, concepts and their various semantic relationships in a structured way and has been gradually popularized in a variety practical scenarios. The majority of existing knowledge graphs mainly concentrate on organizing and managing textual knowledge in a structured representation, while paying little attention to the multimodal resources (e.g., pictures and videos), which can serve as the foundation for the machine perception of a real-world data scenario. To this end, in this survey, we comprehensively review the related advances of multimodal knowledge graphs, covering multimodal knowledge graph construction, completion and typical applications. For construction, we outline the methods of named entity recognition, relation extraction and event extraction. For completion, we discuss the multimodal knowledge graph representation learning and entity linking. Finally, the mainstream applications of multimodal knowledge graphs in miscellaneous domains are summarized. Full article
(This article belongs to the Special Issue Mathematical Computation in Knowledge Graph: Theories, Techniques, and Applications)
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12 pages, 1668 KiB  
Article
Generative Transformer with Knowledge-Guided Decoding for Academic Knowledge Graph Completion
by Xiangwen Liu, Shengyu Mao, Xiaohan Wang and Jiajun Bu
Mathematics 2023, 11(5), 1073; https://doi.org/10.3390/math11051073 - 21 Feb 2023
Cited by 1 | Viewed by 3630
Abstract
Academic knowledge graphs are essential resources and can be beneficial in widespread real-world applications. Most of the existing academic knowledge graphs are far from completion; thus, knowledge graph completion—the task of extending a knowledge graph with missing entities and relations—attracts many researchers. Most [...] Read more.
Academic knowledge graphs are essential resources and can be beneficial in widespread real-world applications. Most of the existing academic knowledge graphs are far from completion; thus, knowledge graph completion—the task of extending a knowledge graph with missing entities and relations—attracts many researchers. Most existing methods utilize low-dimensional embeddings to represent entities and relations and follow the discrimination paradigm for link prediction. However, discrimination approaches may suffer from the scaling issue during inference with large-scale academic knowledge graphs. In this paper, we propose a novel approach of a generative transformer with knowledge-guided decoding for academic knowledge graph completion. Specifically, we introduce generative academic knowledge graph pre-training with a transformer. Then, we propose knowledge-guided decoding, which leverages relevant knowledge in the training corpus as guidance for help. We conducted experiments on benchmark datasets for knowledge graph completion. The experimental results show that the proposed approach can achieve performance gains of 30 units of the MRR score over the baselines on the academic knowledge graph AIDA. Full article
(This article belongs to the Special Issue Mathematical Computation in Knowledge Graph: Theories, Techniques, and Applications)
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