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Mathematics
Special Issues
Machine Learning Methods and Mathematical Modeling with Applications
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Machine Learning Methods and Mathematical Modeling with Applications

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

Deadline for manuscript submissions: 31 March 2025 | Viewed by 1377

Special Issue Editors

Prof. Dr. Jian Luo

E-Mail Website
Guest Editor
International Business School, Hainan University, Haikou 570228, China
Interests: machine learning methods with applications to operations management; energy forecasting; financial risk assessment and other fields; forecasting theories and methods; nonlinear optimization; data mining and artificial intelligence
Dr. Zheming Gao

E-Mail Website
Guest Editor
College of Information Science and Engineering, Northeastern University, Shenyang 110819, China
Interests: machine learning; optimization theory; healthcare
Dr. Xin Yan

E-Mail Website
Guest Editor
School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China
Interests: machine learning; optimization methods with applications

Special Issue Information

Dear Colleagues,

Machine learning methods (including support vector machine, deep learning and ensemble learning) and mathematical modeling have attracted much attention in recent years. In particular, many machine learning models are formulated as nonlinear optimization models, and mathematical modeling methods have employed machine learning to gain outstanding results. For handling large-scaled real-world data, it is also necessary to develop optimization algorithms for implementing well-known and emerging machine learning methods. Moreover, machine learning methods and mathematical modeling exhibit impressive performances in various real-world applications, including demand and price forecasting, electric load forecasting, scheduling optimization for emergency materials, etc. To this end, this Special Issue focuses on the application of current advances in machine learning and optimization methods for real-world problems, especially for industrial engineering and management science. This Special Issue will provide a platform for researchers from academia and industry to present their novel and unpublished work in the domain of machine learning and mathematical modeling, allowing us to foster future interesting research in related emerging fields.

Prof. Dr. Jian Luo
Dr. Zheming Gao
Dr. Xin Yan
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

  • machine learning
  • mathematical modeling
  • industrial engineering
  • forecasting methods
  • management science

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Published Papers (3 papers)

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22 pages, 2752 KiB  
Article
A Noisy Sample Selection Framework Based on a Mixup Loss and Recalibration Strategy
by Qian Zhang, De Yu, Xinru Zhou, Hanmeng Gong, Zheng Li, Yiming Liu and Ruirui Shao
Mathematics 2024, 12(15), 2389; https://doi.org/10.3390/math12152389 - 31 Jul 2024
Viewed by 361
Abstract
Deep neural networks (DNNs) have achieved breakthrough progress in various fields, largely owing to the support of large-scale datasets with manually annotated labels. However, obtaining such datasets is costly and time-consuming, making high-quality annotation a challenging task. In this work, we propose an [...] Read more.
Deep neural networks (DNNs) have achieved breakthrough progress in various fields, largely owing to the support of large-scale datasets with manually annotated labels. However, obtaining such datasets is costly and time-consuming, making high-quality annotation a challenging task. In this work, we propose an improved noisy sample selection method, termed “sample selection framework”, based on a mixup loss and recalibration strategy (SMR). This framework enhances the robustness and generalization abilities of models. First, we introduce a robust mixup loss function to pre-train two models with identical structures separately. This approach avoids additional hyperparameter adjustments and reduces the need for prior knowledge of noise types. Additionally, we use a Gaussian Mixture Model (GMM) to divide the entire training set into labeled and unlabeled subsets, followed by robust training using semi-supervised learning (SSL) techniques. Furthermore, we propose a recalibration strategy based on cross-entropy (CE) loss to prevent the models from converging to local optima during the SSL process, thus further improving performance. Ablation experiments on CIFAR-10 with 50% symmetric noise and 40% asymmetric noise demonstrate that the two modules introduced in this paper improve the accuracy of the baseline (i.e., DivideMix) by 1.5% and 0.5%, respectively. Moreover, the experimental results on multiple benchmark datasets demonstrate that our proposed method effectively mitigates the impact of noisy labels and significantly enhances the performance of DNNs on noisy datasets. For instance, on the WebVision dataset, our method improves the top-1 accuracy by 0.7% and 2.4% compared to the baseline method. Full article
(This article belongs to the Special Issue Machine Learning Methods and Mathematical Modeling with Applications)
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17 pages, 287 KiB  
Article
Priority-Based Capacity Allocation for Hierarchical Distributors with Limited Production Capacity
by Jun Tong, Xiaotao Zhou and Lei Lei
Mathematics 2024, 12(14), 2237; https://doi.org/10.3390/math12142237 - 18 Jul 2024
Viewed by 341
Abstract
This paper studies the issue of capacity allocation in multi-rank distribution channel management, a topic that has been significantly overlooked in the existing literature. Departing from conventional approaches, hierarchical priority rules are introduced as constraints, and an innovative assignment integer programming model focusing [...] Read more.
This paper studies the issue of capacity allocation in multi-rank distribution channel management, a topic that has been significantly overlooked in the existing literature. Departing from conventional approaches, hierarchical priority rules are introduced as constraints, and an innovative assignment integer programming model focusing on capacity selection is formulated. This model goes beyond merely optimizing profit or cost, aiming instead to enhance the overall business orientation of the firm. We propose a greedy algorithm and a priority-based binary particle swarm optimization (PB-BPSO) algorithm. Our numerical results indicate that both algorithms exhibit strong optimization capabilities and rapid solution speeds, especially in large-scale scenarios. Moreover, the model is validated through empirical tests using real-world data. The results demonstrate that the proposed approaches can provide actionable strategies to operators, in practice. Full article
(This article belongs to the Special Issue Machine Learning Methods and Mathematical Modeling with Applications)
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20 pages, 784 KiB  
Article
Fractional Adaptive Resonance Theory (FRA-ART): An Extension for a Stream Clustering Method with Enhanced Data Representation
by Yingwen Zhu, Ping Li, Qian Zhang, Yi Zhu and Jun Yang
Mathematics 2024, 12(13), 2049; https://doi.org/10.3390/math12132049 - 30 Jun 2024
Viewed by 431
Abstract
Clustering data streams has become a hot topic and has been extensively applied to many real-world applications. Compared with traditional clustering, data stream clustering is more challenging. Adaptive Resonance Theory (ART) is a powerful (online) clustering method, it can automatically adjust to learn [...] Read more.
Clustering data streams has become a hot topic and has been extensively applied to many real-world applications. Compared with traditional clustering, data stream clustering is more challenging. Adaptive Resonance Theory (ART) is a powerful (online) clustering method, it can automatically adjust to learn both abstract and concrete information, and can respond to arbitrarily large non-stationary databases while having fewer parameters, low computational complexity, and less sensitivity to noise, but its limited feature representation hinders its application to complex data streams. In this paper, considering its advantages and disadvantages, we present its flexible extension for stream clustering, called fractional adaptive resonance theory (FRA-ART). FRA-ART enhances data representation by fractionally exponentiating input features using self-interactive basis functions (SIBFs) and incorporating feature interaction through cross-interactive basis functions (CIBFs) at the cost only of introducing an additionally adjustable fractional order. Both SIBFs and CIBFs can be precomputed using existing algorithms, making FRA-ART easily adaptable to any ART variant. Finally, comparative experiments on five data stream datasets, including artificial and real-world datasets, demonstrate FRA-ART’s superior robustness and comparable or improved performance in terms of accuracy, normalized mutual information, rand index, and cluster stability compared to ART and the state-of-the-art G-Stream algorithm. Full article
(This article belongs to the Special Issue Machine Learning Methods and Mathematical Modeling with Applications)
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