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Mathematics-Based Methods in Artificial Intelligence, Pattern Recognition and Deep Learning, 2nd Edition

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

Deadline for manuscript submissions: 30 June 2025 | Viewed by 10966

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Special Issue Editors

Dr. Jie Wen

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School of Computer Science & Technology, Harbin Institute of Technology, Shenzhen 150001, China
Interests: machine learning; data mining; pattern recognition; computer vision
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Dr. Cai Xu

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School of Computer Science and Technology, Xidian University, Xi’an 710071, China
Interests: trustworthy machine learning; multi-modal learning; image retrieval
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Dr. Jinrong Cui

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College of Mathematics and Informatics, College of Software Engineering, South China Agricultural University, Guangzhou 510642, China
Interests: subspace learning; multi-view learning; biometric recognition

Special Issue Information

Dear Colleagues,

Artificial intelligence, pattern recognition, and deep learning have become hot topics in recent years. From basic necessities to aerospace, pattern recognition, deep learning, and artificial intelligence are everywhere. For example, face recognition, fingerprint recognition, and palmprint recognition are widely used for access control and attendance systems in daily life. We often enjoy smart product recommendations from many shopping platforms. Automatic driving cars, virtual reality, navigation and positioning, and beauty camera software in mobile phones are also representative applications of artificial intelligence, pattern recognition, and deep learning. In fact, all the artificial intelligence, pattern recognition, and deep learning algorithms have a high reliance on mathematical modeling and mathematical calculation. Good mathematical models and efficient calculation algorithms are crucial to success in these applications. For instance, it is very important to design a robust and efficient mathematical model for behavioral decisions in the application of multi-view information-based autonomous driving. The aim of this Special Issue is to highlight recent advances in mathematics-based methods in artificial intelligence, pattern recognition, and deep learning. Papers with interesting/significant new applications of artificial intelligence, pattern recognition, and deep learning are also welcome.

Topics of interest include, but are not limited to, the following:

Mathematics-based methods in artificial intelligence;
Mathematics-based methods in pattern recognition;
Biometric recognition algorithms and applications, such as face recognition, palmprint recognition, eye classification, fingerprint recognition;
Multi-view/-modal learning and fusion;
Dimensionality reduction;
Subspace learning and clustering;
Deep-learning-based methods and applications;
Image super-resolution/enhancing/restoration;
Mathematics-based methods in computer vision, such as object tracking and detection;
Sparse representation and application.

Dr. Jie Wen
Dr. Cai Xu
Dr. Jinrong Cui
Guest Editors

Chengliang Liu
Guest Editor Assistant

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

pattern recognition and application
deep learning
artificial intelligence
computer vision

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Published Papers (9 papers)

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Research

16 pages, 4756 KiB

Open AccessArticle

Hierarchical Feature Fusion and Enhanced Attention Mechanism for Robust GAN-Generated Image Detection

by Weinan Zhang, Sanshuai Cui, Qi Zhang, Biwei Chen, Hui Zeng and Qi Zhong

Mathematics 2025, 13(9), 1372; https://doi.org/10.3390/math13091372 - 23 Apr 2025

Viewed by 345

Abstract

In recent years, with the rapid advancement of deep learning technologies such as generative adversarial networks (GANs), deepfake technology has become increasingly sophisticated. As a result, the generated fake images are becoming more difficult to visually distinguish from real ones. Existing deepfake detection methods primarily rely on training models with specific datasets. However, these models often suffer from limited generalization when processing images of unknown origin or across domains, leading to a significant decrease in detection accuracy. To address this issue, this paper proposes a deepfake image-detection network based on feature aggregation and enhancement. The key innovation of the proposed method lies in the integration of two modules: the Feature Aggregation Module (FAM) and the Attention Enhancement Module (AEM). The FAM effectively aggregates both deep semantic information and shallow detail features through a multi-scale feature-fusion mechanism, overcoming the limitations of traditional methods that rely on a single-level feature. Meanwhile, the AEM enhances the network’s ability to capture subtle forgery traces by incorporating attention mechanisms and filtering techniques, significantly boosting the model’s efficiency in processing complex information. The experimental results demonstrate that the proposed method achieves significant improvements across all evaluation metrics. Specifically, on the StarGAN dataset, the model attained outstanding performance, with accuracy (Acc) and average precision (AP) both reaching 100%. In cross-dataset testing, the proposed method exhibited strong generalization ability, raising the overall average accuracy to 87.0% and average precision to 92.8%, representing improvements of 5.2% and 6.7%, respectively, compared to existing state-of-the-art methods. These results show that the proposed method can not only achieve optimal performance on data with the same distribution, but also demonstrate strong generalization ability in cross-domain detection tasks. Full article

(This article belongs to the Special Issue Mathematics-Based Methods in Artificial Intelligence, Pattern Recognition and Deep Learning, 2nd Edition)

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20 pages, 946 KiB

Open AccessArticle

Multi-Modal Temporal Dynamic Graph Construction for Stock Rank Prediction

by Ying Liu, Zengyu Wei, Long Chen, Cai Xu and Ziyu Guan

Mathematics 2025, 13(5), 845; https://doi.org/10.3390/math13050845 - 3 Mar 2025

Viewed by 882

Abstract

Stock rank prediction is an important and challenging task. Recently, graph-based prediction methods have emerged as a valuable approach for capturing the complex relationships between stocks. Existing works mainly construct static undirected relational graphs, leading to two main drawbacks: (1) overlooking the bidirectional asymmetric effects of stock data, i.e., financial messages affect each other differently when they occur at different nodes of the graph; and (2) failing to capture the dynamic relationships of stocks over time. In this paper, we propose a Multi-modal Temporal Dynamic Graph method (MTDGraph). MTDGraph comprehensively considers the bidirectional relationships from multi-modal stock data (price and texts) and models the time-varying relationships. In particular, we generate the textual relationship strength from the topic sensitivity and the text topic embeddings. Then, we inject a causality factor via the transfer entropy between the interrelated stock historical sequential embeddings as the historical relationship strength. Afterwards, we apply both the textual and historical relationship strengths to guide the multi-modal information propagation in the graph. The framework of the MTDGraph method consists of the stock-level sequential embedding layer, the inter-stock relation embedding layer based on temporal dynamic graph construction and the multi-model information fusion layer. Finally, the MTDGraph optimizes the point-wise regression loss and the ranking-aware loss to obtain the appropriate stock rank list. We empirically validate MTDGraph in the publicly available dataset, CMUN-US and compare it with state-of-the-art baselines. The proposed MTDGraph method outperforms the baseline methods in both accuracy and investment revenues. Full article

(This article belongs to the Special Issue Mathematics-Based Methods in Artificial Intelligence, Pattern Recognition and Deep Learning, 2nd Edition)

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18 pages, 575 KiB

Open AccessArticle

A Deep Learning Method of Credit Card Fraud Detection Based on Continuous-Coupled Neural Networks

by Yanxi Wu, Liping Wang, Hongyu Li and Jizhao Liu

Mathematics 2025, 13(5), 819; https://doi.org/10.3390/math13050819 - 28 Feb 2025

Cited by 1 | Viewed by 2141

Abstract

With the widespread use of credit cards in online and offline transactions, credit card fraud has become a significant challenge in the financial sector. The rapid advancement of payment technologies has led to increasingly sophisticated fraud techniques, necessitating more effective detection methods. While machine learning has been extensively applied in fraud detection, the application of deep learning methods remains relatively limited. Inspired by brain-like computing, this work employs the Continuous-Coupled Neural Network (CCNN) for credit card fraud detection. Unlike traditional neural networks, the CCNN enhances the representation of complex temporal and spatial patterns through continuous neuron activation and dynamic coupling mechanisms. Using the Kaggle Credit Card Fraud Detection (CCFD) dataset, we mitigate data imbalance via the Synthetic Minority Oversampling Technique (SMOTE) and transform sample feature vectors into matrices for training. Experimental results show that our method achieves an accuracy of 0.9998, precision of 0.9996, recall of 1.0000, and an F1-score of 0.9998, surpassing traditional machine learning models, which highlight CCNN’s potential to enhance the security and efficiency of fraud detection in the financial industry. Full article

(This article belongs to the Special Issue Mathematics-Based Methods in Artificial Intelligence, Pattern Recognition and Deep Learning, 2nd Edition)

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20 pages, 7330 KiB

Open AccessArticle

A Method for Predicting the Timing of Mine Earthquakes Based on Deformation Localization States

by Chenli Zhu, Linlin Ding, Yimin Song and Yuda Li

Mathematics 2025, 13(1), 40; https://doi.org/10.3390/math13010040 - 26 Dec 2024

Viewed by 583

Abstract

As a prevalent geological hazard in underground engineering, the accurate prediction of mine earthquakes is crucial for ensuring operational safety and enhancing mining efficiency. The deformation localization method effectively predicts the instability of disaster rocks, yet the timing of mine earthquakes remains understudied. This study established a correlation between rock deformation localization and seismic activity within mines through theoretical derivations. A predictive model algorithm for forecasting mine earthquake timing was developed based on Saito’s theory, integrating optics, acoustics, and mathematical modeling theories. The “quiet period” was identified as a significant precursor; thus, the model used the initiation of deformation localization to accurately predict rock failure. Using the model, a coal mine in Inner Mongolia was selected as a case study to predict a historical mining earthquake. The results indicated that the following: (1) Deformation localization and the “quiet period” of microseismic (MS) and acoustic emission (AE) activities were identified as two key pre-cursory indicators. The model utilized the initiation time of deformation localization and the inflection point of the “quiet period” in MS and AE activity as primary parameters. (2) For predicting rock failure times, the earliest prediction time deviates from the actual failure time by 143 s. The accuracy rate of predicted time points falling within a 90% confidence interval of the actual failure times is 100%. The model achieved 60% in forecasting the occurrence times of mine earthquakes. (3) The model’s prediction accuracy improved as the starting time parameter more closely approximated the actual initiation time of deformation localization, with the accuracy increasing from 0% to 100%. Full article

(This article belongs to the Special Issue Mathematics-Based Methods in Artificial Intelligence, Pattern Recognition and Deep Learning, 2nd Edition)

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16 pages, 610 KiB

Open AccessArticle

Research on Small-Sample Credit Card Fraud Identification Based on Temporal Attention-Boundary-Enhanced Prototype Network

by Boyu Liu, Longrui Wu and Shengdong Mu

Mathematics 2024, 12(24), 3894; https://doi.org/10.3390/math12243894 - 10 Dec 2024

Cited by 1 | Viewed by 911

Abstract

The Nielsen Report points out that credit card fraud caused business losses of USD 28.65 billion globally in 2019, with the US accounting for more than one-third of the high share, and that insufficient identification of credit card fraud has brought about a serious loss of financial institutions’ ability to do business. In small sample data environments, traditional fraud detection methods based on prototype network models struggle with the loss of time-series features and the challenge of identifying the uncorrected sample distribution in the metric space. In this paper, we propose a credit card fraud detection method called the Time-Series Attention-Boundary-Enhanced Prototype Network (TABEP), which strengthens the temporal feature dependency between channels by incorporating a time-series attention module to achieve channel temporal fusion feature acquisition. Additionally, nearest-neighbor boundary loss is introduced after the computation of the prototype-like network model to adjust the overall distribution of features in the metric space and to clarify the representation boundaries of the prototype-like model. Experimental results show that the TABEP model achieves higher accuracy in credit card fraud detection compared to five existing baseline prototype network methods, better fits the overall data distribution, and significantly improves fraud detection performance. This study highlights the effectiveness of open innovation methods in addressing complex financial security problems, which is of great significance for promoting technological advancement in the field of credit card security. Full article

(This article belongs to the Special Issue Mathematics-Based Methods in Artificial Intelligence, Pattern Recognition and Deep Learning, 2nd Edition)

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20 pages, 22039 KiB

Open AccessArticle

A Nonconvex Approach with Structural Priors for Restoring Underwater Images

by Hafiz Shakeel Ahmad Awan and Muhammad Tariq Mahmood

Mathematics 2024, 12(22), 3553; https://doi.org/10.3390/math12223553 - 13 Nov 2024

Viewed by 832

Abstract

Underwater image restoration is a crucial task in various computer vision applications, including underwater target detection and recognition, autonomous underwater vehicles, underwater rescue, marine organism monitoring, and marine geological survey. Among other categories, the physics-based methods restore underwater images by improving the transmission map through optimization or regularization techniques. Conventional optimization-based methods often do not consider the effect of structural differences between guidance and transmission maps. To address this issue, in this paper, we present a regularization-based method for restoring underwater images that uses coherent structures between the guidance map and the transmission map. The proposed approach models the optimization of transmission maps through a nonconvex energy function comprising data and smoothness terms. The smoothness term includes static and dynamic structural priors, and the optimization problem is solved using a majorize-minimize algorithm. We evaluate the proposed method on benchmark datasets, and the results demonstrate the superiority of the proposed method over state-of-the-art techniques in terms of improving transmission maps and producing high-quality restored images. Full article

(This article belongs to the Special Issue Mathematics-Based Methods in Artificial Intelligence, Pattern Recognition and Deep Learning, 2nd Edition)

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18 pages, 11050 KiB

Open AccessArticle

Mitigating Adversarial Attacks in Object Detection through Conditional Diffusion Models

by Xudong Ye, Qi Zhang, Sanshuai Cui, Zuobin Ying, Jingzhang Sun and Xia Du

Mathematics 2024, 12(19), 3093; https://doi.org/10.3390/math12193093 - 2 Oct 2024

Viewed by 2142

Abstract

The field of object detection has witnessed significant advancements in recent years, thanks to the remarkable progress in artificial intelligence and deep learning. These breakthroughs have significantly enhanced the accuracy and efficiency of detecting and categorizing objects in digital images. Nonetheless, contemporary object detection technologies have certain limitations, such as their inability to counter white-box attacks, insufficient denoising, suboptimal reconstruction, and gradient confusion. To overcome these hurdles, this study proposes an innovative approach that uses conditional diffusion models to perturb adversarial examples. The process begins with the application of a random chessboard mask to the adversarial example, followed by the addition of a slight noise to fill the masked area during the forward process. The adversarial image is then restored to its original form through a reverse generative process that only considers the masked pixels, not the entire image. Next, we use the complement of the initial mask as the mask for the second stage to reconstruct the image once more. This two-stage masking process allows for the complete removal of global disturbances and aids in image reconstruction. In particular, we employ a conditional diffusion model based on a class-conditional U-Net architecture, with the source image further conditioned through concatenation. Our method outperforms the recently introduced HARP method by 5% and 6.5% in mAP on the COCO2017 and PASCAL VOC datasets, respectively, under non-APT PGD attacks. Comprehensive experimental results confirm that our method can effectively restore adversarial examples, demonstrating its practical utility. Full article

(This article belongs to the Special Issue Mathematics-Based Methods in Artificial Intelligence, Pattern Recognition and Deep Learning, 2nd Edition)

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15 pages, 12772 KiB

Open AccessArticle

Learning Unsupervised Cross-Domain Model for TIR Target Tracking

by Xiu Shu, Feng Huang, Zhaobing Qiu, Xinming Zhang and Di Yuan

Mathematics 2024, 12(18), 2882; https://doi.org/10.3390/math12182882 - 15 Sep 2024

Viewed by 944

Abstract

The limited availability of thermal infrared (TIR) training samples leads to suboptimal target representation by convolutional feature extraction networks, which adversely impacts the accuracy of TIR target tracking methods. To address this issue, we propose an unsupervised cross-domain model (UCDT) for TIR tracking. Our approach leverages labeled training samples from the RGB domain (source domain) to train a general feature extraction network. We then employ a cross-domain model to adapt this network for effective target feature extraction in the TIR domain (target domain). This cross-domain strategy addresses the challenge of limited TIR training samples effectively. Additionally, we utilize an unsupervised learning technique to generate pseudo-labels for unlabeled training samples in the source domain, which helps overcome the limitations imposed by the scarcity of annotated training data. Extensive experiments demonstrate that our UCDT tracking method outperforms existing tracking approaches on the PTB-TIR and LSOTB-TIR benchmarks. Full article

(This article belongs to the Special Issue Mathematics-Based Methods in Artificial Intelligence, Pattern Recognition and Deep Learning, 2nd Edition)

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20 pages, 797 KiB

Open AccessArticle

Research on Stock Index Prediction Based on the Spatiotemporal Attention BiLSTM Model

by Shengdong Mu, Boyu Liu, Jijian Gu, Chaolung Lien and Nedjah Nadia

Mathematics 2024, 12(18), 2812; https://doi.org/10.3390/math12182812 - 11 Sep 2024

Cited by 2 | Viewed by 1099

Abstract

Stock index fluctuations are characterized by high noise and their accurate prediction is extremely challenging. To address this challenge, this study proposes a spatial–temporal–bidirectional long short-term memory (STBL) model, incorporating spatiotemporal attention mechanisms. The model enhances the analysis of temporal dependencies between data by introducing graph attention networks with multi-hop neighbor nodes while incorporating the temporal attention mechanism of long short-term memory (LSTM) to effectively address the potential interdependencies in the data structure. In addition, by assigning different learning weights to different neighbor nodes, the model can better integrate the correlation between node features. To verify the accuracy of the proposed model, this study utilized the closing prices of the Hong Kong Hang Seng Index (HSI) from 31 December 1986 to 31 December 2023 for analysis. By comparing it with nine other forecasting models, the experimental results show that the STBL model achieves more accurate predictions of the closing prices for short-term, medium-term, and long-term forecasts of the stock index. Full article

(This article belongs to the Special Issue Mathematics-Based Methods in Artificial Intelligence, Pattern Recognition and Deep Learning, 2nd Edition)

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