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Mathematical and Computing Sciences for Artificial Intelligence
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Mathematical and Computing Sciences for Artificial Intelligence

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 July 2025 | Viewed by 7098

Special Issue Editor

Prof. Dr. Chong-zhi Gao

E-Mail Website
Guest Editor
School of Computer Science, Guangzhou University, Guangzhou, China
Interests: security and privacy in machine learning and artificial intelligence

Special Issue Information

Dear Colleagues,

​The field of artificial intelligence relies on a deep understanding of mathematics, statistics and computer science to create algorithms that can learn from data and make intelligent decisions. However, due to the lack of data and bias in data, as well as the complexity of real-world systems, there are still many challenges in this field, including mathematical foundations and modelling in artificial intelligence, better optimization algorithms, interpretability of artificial intelligence, and building AI algorithms to solve specific application problems. Since mathematics is the foundation of artificial intelligence, and the integration of mathematical and computing sciences plays a crucial role in advancing AI research, this Special Issue aims to explore the latest developments, methodologies, and applications that highlight the synergy between mathematics, computing, and AI. We welcome original research papers addressing various aspects of mathematical and computing sciences for artificial intelligence. Topics of interest include, but are not limited to:

  • Optimization algorithms and machine learning;
  • Probabilistic modeling and Bayesian inference in AI;
  • Reinforcement learning and control theory;
  • Adversarial attacks and defense in AI;
  • Game theory and AI decision;
  • Mathematical approaches to explainable AI;
  • Graph theory and network analysis for AI systems;
  • Natural language processing and computational linguistics;
  • Mathematical modeling for computer vision;
  • The applications of AI in the field of medical sciences.

Prof. Dr. Chong-zhi Gao
Guest Editor

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.

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Published Papers (5 papers)

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Research

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17 pages, 2383 KiB  
Article
A New Composite Dissimilarity Measure for Planar Curves Based on Higher-Order Derivatives
by Yupeng Wang, Jianghui Cai, Haifeng Yang, Jie Wang, Bo Liang and Xujun Zhao
Mathematics 2024, 12(19), 3083; https://doi.org/10.3390/math12193083 - 1 Oct 2024
Viewed by 919
Abstract
With the rapid development of information technology, the problem of curve matching has appeared in many application domains, including sequence analysis, signals processing, speech recognition, etc. Many similarity measures have been studied for matching curves based on Euclidean distance, which shows fragility in [...] Read more.
With the rapid development of information technology, the problem of curve matching has appeared in many application domains, including sequence analysis, signals processing, speech recognition, etc. Many similarity measures have been studied for matching curves based on Euclidean distance, which shows fragility in portraying the morphological information of curve data. In this paper, we propose a novel weighted composite curve dissimilarity metric (WCDM). First, the WCDM measures the dissimilarity based on the higher-order semantic difference between curve shapes and location difference. These two differences are calculated using the curvature difference and Euclidean distance between the curves, respectively. Second, a new dynamic weighting function is defined by employing the relationship between the trends of the curves. This function aims at adjusting the contributions of the curvature difference and the Euclidean distance to compose the dissimilarity measure WCDM. Finally, to ascertain the rationality of the WCDM, its metric properties are studied and proved theoretically. Comparison experiments on clustering and classification tasks are carried out on curve sets transformed from UCR time series datasets, and an application analysis of the WCDM is conducted on spectral data. The experimental results indicate the effectiveness of the WCDM. Specifically, clustering and classification based on the WCDM are superior to those based on ED, DTW, Hausdorff, Fréchet, and LCSS on at least 8 out of 14 datasets across all evaluation indices. In particular, the Purity and ARI on the Beetlefly dataset are improved by more than 7.5%, while accuracy on the Beef, Chinatown, and OliveOil datasets increases by 13.32%, 10.08%, and 12.83%, respectively. Full article
(This article belongs to the Special Issue Mathematical and Computing Sciences for Artificial Intelligence)
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9 pages, 236 KiB  
Article
Algorithms for Densest Subgraphs of Vertex-Weighted Graphs
by Zhongling Liu, Wenbin Chen, Fufang Li, Ke Qi and Jianxiong Wang
Mathematics 2024, 12(14), 2206; https://doi.org/10.3390/math12142206 - 14 Jul 2024
Viewed by 930
Abstract
Finding the densest subgraph has tremendous potential in computer vision and social network research, among other domains. In computer vision, it can demonstrate essential structures, and in social network research, it aids in identifying closely associated communities. The densest subgraph problem is finding [...] Read more.
Finding the densest subgraph has tremendous potential in computer vision and social network research, among other domains. In computer vision, it can demonstrate essential structures, and in social network research, it aids in identifying closely associated communities. The densest subgraph problem is finding a subgraph with maximum mean density. However, most densest subgraph-finding algorithms are based on edge-weighted graphs, where edge weights can only represent a single value dimension, whereas practical applications involve multiple dimensions. To resolve the challenge, we propose two algorithms for resolving the densest subgraph problem in a vertex-weighted graph. First, we present an exact algorithm that builds upon Goldberg’s original algorithm. Through theoretical exploration and analysis, we rigorously verify our proposed algorithm’s correctness and confirm that it can efficiently run in polynomial time O(n(n + m)log2n) is its temporal complexity. Our approach can be applied to identify closely related subgroups demonstrating the maximum average density in real-life situations. Additionally, we consistently offer an approximation algorithm that guarantees an accurate approximation ratio of 2. In conclusion, our contributions enrich theoretical foundations for addressing the densest subgraph problem. Full article
(This article belongs to the Special Issue Mathematical and Computing Sciences for Artificial Intelligence)
18 pages, 426 KiB  
Article
Optimizing Attribute Reduction in Multi-Granularity Data through a Hybrid Supervised–Unsupervised Model
by Zeyuan Fan, Jianjun Chen, Hongyang Cui, Jingjing Song and Taihua Xu
Mathematics 2024, 12(10), 1434; https://doi.org/10.3390/math12101434 - 7 May 2024
Viewed by 1123
Abstract
Attribute reduction is a core technique in the rough set domain and an important step in data preprocessing. Researchers have proposed numerous innovative methods to enhance the capability of attribute reduction, such as the emergence of multi-granularity rough set models, which can effectively [...] Read more.
Attribute reduction is a core technique in the rough set domain and an important step in data preprocessing. Researchers have proposed numerous innovative methods to enhance the capability of attribute reduction, such as the emergence of multi-granularity rough set models, which can effectively process distributed and multi-granularity data. However, these innovative methods still have numerous shortcomings, such as addressing complex constraints and conducting multi-angle effectiveness evaluations. Based on the multi-granularity model, this study proposes a new method of attribute reduction, namely using multi-granularity neighborhood information gain ratio as the measurement criterion. This method combines both supervised and unsupervised perspectives, and by integrating multi-granularity technology with neighborhood rough set theory, constructs a model that can adapt to multi-level data features. This novel method stands out by addressing complex constraints and facilitating multi-perspective effectiveness evaluations. It has several advantages: (1) it combines supervised and unsupervised learning methods, allowing for nuanced data interpretation and enhanced attribute selection; (2) by incorporating multi-granularity structures, the algorithm can analyze data at various levels of granularity. This allows for a more detailed understanding of data characteristics at each level, which can be crucial for complex datasets; and (3) by using neighborhood relations instead of indiscernibility relations, the method effectively handles uncertain and fuzzy data, making it suitable for real-world datasets that often contain imprecise or incomplete information. It not only selects the optimal granularity level or attribute set based on specific requirements, but also demonstrates its versatility and robustness through extensive experiments on 15 UCI datasets. Comparative analyses against six established attribute reduction algorithms confirms the superior reliability and consistency of our proposed method. This research not only enhances the understanding of attribute reduction mechanisms, but also sets a new benchmark for future explorations in the field. Full article
(This article belongs to the Special Issue Mathematical and Computing Sciences for Artificial Intelligence)
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17 pages, 1081 KiB  
Article
Malicious Traffic Classification via Edge Intelligence in IIoT
by Maoli Wang, Bowen Zhang, Xiaodong Zang, Kang Wang and Xu Ma
Mathematics 2023, 11(18), 3951; https://doi.org/10.3390/math11183951 - 17 Sep 2023
Cited by 3 | Viewed by 1739
Abstract
The proliferation of smart devices in the 5G era of industrial IoT (IIoT) produces significant traffic data, some of which is encrypted malicious traffic, creating a significant problem for malicious traffic detection. Malicious traffic classification is one of the most efficient techniques for [...] Read more.
The proliferation of smart devices in the 5G era of industrial IoT (IIoT) produces significant traffic data, some of which is encrypted malicious traffic, creating a significant problem for malicious traffic detection. Malicious traffic classification is one of the most efficient techniques for detecting malicious traffic. Although it is a labor-intensive and time-consuming process to gather large labeled datasets, the majority of prior studies on the classification of malicious traffic use supervised learning approaches and provide decent classification results when a substantial quantity of labeled data is available. This paper proposes a semi-supervised learning approach for classifying malicious IIoT traffic. The approach utilizes the encoder–decoder model framework to classify the traffic, even with a limited amount of labeled data available. We sample and normalize the data during the data-processing stage. In the semi-supervised model-building stage, we first pre-train a model on a large unlabeled dataset. Subsequently, we transfer the learned weights to a new model, which is then retrained using a small labeled dataset. We also offer an edge intelligence model that considers aspects such as computation latency, transmission latency, and privacy protection to improve the model’s performance. To achieve the lowest total latency and to reduce the risk of privacy leakage, we first create latency and privacy-protection models for each local, edge, and cloud. Then, we optimize the total latency and overall privacy level. In the study of IIoT malicious traffic classification, experimental results demonstrate that our method reduces the model training and classification time with 97.55% accuracy; moreover, our approach boosts the privacy-protection factor. Full article
(This article belongs to the Special Issue Mathematical and Computing Sciences for Artificial Intelligence)
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Review

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22 pages, 491 KiB  
Review
Domain Generalization Through Data Augmentation: A Survey of Methods, Applications, and Challenges
by Junjie Mai, Chongzhi Gao and Jun Bao
Mathematics 2025, 13(5), 824; https://doi.org/10.3390/math13050824 - 28 Feb 2025
Viewed by 1150
Abstract
Domain generalization (DG) has become a pivotal research area in machine learning, focusing on equipping models with the ability to generalize effectively to unseen test domains that differ from the training distribution. This capability is crucial, as real-world data frequently exhibit domain shifts [...] Read more.
Domain generalization (DG) has become a pivotal research area in machine learning, focusing on equipping models with the ability to generalize effectively to unseen test domains that differ from the training distribution. This capability is crucial, as real-world data frequently exhibit domain shifts that violate the assumption of independent and identically distributed (i.i.d.) data, resulting in significant declines in model performance. Among the various strategies to address domain generalization, data augmentation has garnered substantial attention as an effective approach for mitigating domain shifts and improving model robustness. In this survey, we examine the role of data augmentation in domain generalization, offering a comprehensive overview of its methods, applications, and challenges. We present a detailed taxonomy of data augmentation techniques, categorized along three dimensions: scope, nature, and training dependency. Additionally, we provide a comparative analysis of key methods, highlighting their strengths and limitations. Finally, we explore the domain-specific applications of data augmentation and analyze their effectiveness in enhancing generalization across various real-world tasks, including computer vision, NLP, speech, and robotics. We conclude by examining key challenges—such as computational cost and augmentation overfitting—and outline promising research directions, with a focus on advancing cross-modal augmentation techniques and developing standardized evaluation benchmarks. Full article
(This article belongs to the Special Issue Mathematical and Computing Sciences for Artificial Intelligence)
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