Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
5.3
2.2
Journals
Symmetry
Special Issues
Advances in Machine Learning and Symmetry/Asymmetry
share announcement

Advances in Machine Learning and Symmetry/Asymmetry

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer".

Deadline for manuscript submissions: 30 November 2026 | Viewed by 8613

Special Issue Editors

Dr. Jun Song

E-Mail Website
Guest Editor
College of Information Science and Technology & Artificial Intelligence, Nanjing Forestry University, Nanjing 210037, China
Interests: Internet of Things system design; machine learning and its application in agriculture and forestry; embedded instrumentation
Dr. Hongbin Liu

E-Mail Website
Guest Editor
Department of Food Science and Engineering, Nanjing Forestry University, Nanjing 210037, China
Interests: deep learning; machine learning; soft sensing modeling; process monitoring; fault diagnosis

Special Issue Information

Dear Colleagues,

As a critical concept in understanding the laws of nature, symmetry has been well-investigated in studies of mathematical optimizations. Over the past few decades, optimization has played a pivotal role in formulating and solving machine learning tasks, thus the connection between optimization and machine learning is becoming a popular research topic. It is no surprise that with the ever-increasing complexity of real-life tasks, both optimization and machine learning come with inherent facets of symmetry or asymmetry conveyed in different formal ways, which requires effective approaches to produce optimal solutions as well as efficient algorithms.

This Special Issue is focused on the methodologies and applications of coping with symmetry in optimization through the usage of concepts of machine learning. Research papers that employ theoretical analysis and/or practical applications in the related scope are welcomed. Papers devoted to improving the interpretability and the computational efficiency of the symmetry constrained optimization models are also welcomed.

Dr. Jun Song
Dr. Hongbin Liu
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 250 words) can be sent to the Editorial Office for assessment.

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. Symmetry is an international peer-reviewed open access monthly 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 2400 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
  • iIterative algorithm
  • heuristic method
  • efficiency
  • symmetry constrained optimization
  • process monitoring
  • fault diagnosis

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (6 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

22 pages, 660 KB  
Article
Symmetry-Aware Dynamic Graph Learning for One-Step Scenic-Spot Visitor Demand Forecasting
by Wenliang Cheng, Yiqiang Wang, Yulong Xiao and Yuxue Xiao
Symmetry 2026, 18(3), 449; https://doi.org/10.3390/sym18030449 - 6 Mar 2026
Viewed by 447
Abstract
Accurate one-step forecasting of scenic-spot visitor demand is challenging due to strong non-stationarity, holiday-induced peaks, and abrupt reputation-driven shocks. We propose a symmetry-aware dynamic graph learning framework that fuses social–physical sensing streams for robust demand prediction. Online reviews are treated as social sensing, [...] Read more.
Accurate one-step forecasting of scenic-spot visitor demand is challenging due to strong non-stationarity, holiday-induced peaks, and abrupt reputation-driven shocks. We propose a symmetry-aware dynamic graph learning framework that fuses social–physical sensing streams for robust demand prediction. Online reviews are treated as social sensing, transformed into daily sentiment indicators, and aligned with demand using a delay-aware aggregation scheme. To capture evolving inter-spot dependencies, we construct a time-varying adjacency matrix that is updated over time and integrated into a lightweight spatio-temporal forecasting model, Dynamic Spatio-temporal Graph Attention LSTM (DSGAT-LSTM). The model preserves the permutation-invariant property of graph learning while introducing sentiment-guided feature reweighting and sentiment-gated temporal updates to better track volatility. Experiments on multi-year daily data from multiple A-level scenic spots with holiday and weather context demonstrate consistent error reductions over representative temporal and graph-based baselines, together with improved stability under peak and shock conditions. We will release the processed feature-level dataset and implementation scripts to support reproducibility. Full article
(This article belongs to the Special Issue Advances in Machine Learning and Symmetry/Asymmetry)
►▼ Show Figures

Figure 1

29 pages, 3905 KB  
Article
CS-MLAkNN: A Cost-Sensitive Adaptive k-Nearest Neighbors Algorithm for Imbalanced Multi-Label Learning
by Zhengyao Shen, Jicong Duan, Ying Wang and Hualong Yu
Symmetry 2026, 18(3), 448; https://doi.org/10.3390/sym18030448 - 5 Mar 2026
Viewed by 403
Abstract
Multi-label data usually carries a complex structural class imbalance, which significantly affects the overall predictive performance of multi-label learning models. Although many studies have investigated this problem, most existing methods rely on resampling, static cost weighting, or ensemble learning. Few studies simultaneously consider [...] Read more.
Multi-label data usually carries a complex structural class imbalance, which significantly affects the overall predictive performance of multi-label learning models. Although many studies have investigated this problem, most existing methods rely on resampling, static cost weighting, or ensemble learning. Few studies simultaneously consider cost information and neighborhood size within the local statistical model of ML-kNN. To address this issue, this paper proposes a cost-sensitive adaptive k-nearest neighbors algorithm, named CS-MLAkNN, for imbalanced multi-label learning. The algorithm implements a dual cost-sensitive strategy at both the feature and label levels within the ML-kNN framework. Specifically, feature-level cost sensitivity is achieved through distance weighting during the training phase. In the prediction phase, label distribution information is incorporated into the posterior probability calculation to achieve label-level cost sensitivity. Moreover, the optimal number of neighbors (k) is determined adaptively through cross-validation. CS-MLAkNN maintains the simplicity and interpretability of the original ML-kNN, and meanwhile it explicitly introduces cost sensitivity and adaptiveness into three key steps: distance metric, posterior decision, and neighbor determination. Experimental results on 14 benchmark datasets demonstrate that the proposed method achieves optimal or near-optimal performance across various evaluation metrics. It also shows significant advantages over other state-of-the-art imbalanced multi-label learning algorithms. Full article
(This article belongs to the Special Issue Advances in Machine Learning and Symmetry/Asymmetry)
►▼ Show Figures

Figure 1

21 pages, 4855 KB  
Article
A Fair Ensemble Clustering Method
by Yanqing Li, Ruixin Feng and Caiming Zhong
Symmetry 2025, 17(12), 2184; https://doi.org/10.3390/sym17122184 - 18 Dec 2025
Viewed by 538
Abstract
Ensemble clustering has become a widely used technique for improving robustness and accuracy by combining multiple clustering results. However, traditional ensemble clustering methods often fail to provide fair treatment between groups defined by sensitive attributes. Central to many ensemble methods is the symmetric [...] Read more.
Ensemble clustering has become a widely used technique for improving robustness and accuracy by combining multiple clustering results. However, traditional ensemble clustering methods often fail to provide fair treatment between groups defined by sensitive attributes. Central to many ensemble methods is the symmetric co-association matrix, which captures pairwise similarity between data points based on their co-occurrence across base clusterings. This paper introduces a fair ensemble clustering method based on the symmetric co-association matrix. The proposed method integrates fairness constraints into the objective function of the ensemble process, using the results from base clusterings that lack fairness considerations as input. The optimization is performed iteratively, and the final clustering results are represented directly by a label matrix obtained efficiently using a coordinate descent approach. By integrating fairness into the clustering process, the method avoids the need for post-processing to achieve fair results. Comprehensive experiments on both real-world and synthetic datasets validate the effectiveness and practicality of the proposed method. Full article
(This article belongs to the Special Issue Advances in Machine Learning and Symmetry/Asymmetry)
►▼ Show Figures

Figure 1

20 pages, 3319 KB  
Article
Symmetric Versus Asymmetric Transformer Architectures for Spatio-Temporal Modeling in Effluent Wastewater Quality Prediction
by Tong Hu, Zikang Chen, Jun Song and Hongbin Liu
Symmetry 2025, 17(8), 1322; https://doi.org/10.3390/sym17081322 - 14 Aug 2025
Cited by 1 | Viewed by 960
Abstract
Accurate prediction of effluent quality indicators is essential for ensuring stable operation and regulatory compliance in wastewater treatment plants. However, the inherent spatial distribution and temporal fluctuations of wastewater processes present significant challenges for modeling. In this study, we propose a dynamic multi-scale [...] Read more.
Accurate prediction of effluent quality indicators is essential for ensuring stable operation and regulatory compliance in wastewater treatment plants. However, the inherent spatial distribution and temporal fluctuations of wastewater processes present significant challenges for modeling. In this study, we propose a dynamic multi-scale spatio-temporal Transformer (DMST-Transformer) with a symmetric architecture to enhance prediction accuracy in complex wastewater systems. Unlike conventional asymmetric designs, the DMST-Transformer extracts spatial and temporal features in parallel using a spatial graph convolutional network and a multi-scale self-attention mechanism coupled with a dynamic self-tuning module. The model is evaluated on a full-process dataset collected from a municipal wastewater treatment plant, with biochemical oxygen demand selected as the target indicator. Experimental results on test data show that the DMST-Transformer achieves a coefficient of determination of 0.93, root mean square error of 1.40 mg/L, and mean absolute percentage error of 6.61%, outperforming classical models such as linear regression, partial least squares, and graph convolutional networks, as well as advanced deep learning baselines including Transformer and ST-Transformer. Ablation studies confirm the complementary effectiveness of the spatial and temporal modules, and computational time comparisons demonstrate the model’s suitability for real-time applications. These results validate the practical potential of the DMST-Transformer for robust effluent quality monitoring in wastewater treatment plants. Future research will focus on scaling the model to larger and more diverse datasets, extending it to predict additional water quality indicators, and deploying it in real-time environmental monitoring systems to support intelligent water resource management. Full article
(This article belongs to the Special Issue Advances in Machine Learning and Symmetry/Asymmetry)
►▼ Show Figures

Figure 1

22 pages, 2531 KB  
Article
An Improved Self-Organizing Map (SOM) Based on Virtual Winning Neurons
by Xiaoliang Fan, Shaodong Zhang, Xuefeng Xue, Rui Jiang, Shuwen Fan and Hanliang Kou
Symmetry 2025, 17(3), 449; https://doi.org/10.3390/sym17030449 - 17 Mar 2025
Cited by 9 | Viewed by 4049
Abstract
Self-Organizing Map (SOM) neural networks can project complex, high-dimensional data onto a two-dimensional plane for data visualization, enabling an intuitive understanding of the distribution and symmetric structures of such data, thereby facilitating the clustering and anomaly detection of complex high-dimensional data. However, this [...] Read more.
Self-Organizing Map (SOM) neural networks can project complex, high-dimensional data onto a two-dimensional plane for data visualization, enabling an intuitive understanding of the distribution and symmetric structures of such data, thereby facilitating the clustering and anomaly detection of complex high-dimensional data. However, this algorithm is sensitive to the initial weight matrix and suffers from insufficient feature extraction. To address these issues, this paper proposes an improved SOM based on virtual winning neurons (virtual-winner SOMs, vwSOMs). In this method, the principal component analysis (PCA) is utilized to generate the initial weight matrix, allowing the weights to better capture the main features of the data and thereby enhance clustering performance. Subsequently, when new input sample data are mapped to the output layer, multiple neurons with a high similarity in the weight matrix are selected to calculate a virtual winning neuron, which is then used to update the weight matrix to comprehensively represent the input data features within a minimal error range, thus improving the algorithm’s robustness. Multiple datasets were used to analyze the clustering performance of vwSOM. On the Iris dataset, the S is 0.5262, the F1 value is 0.93, the ACC value is 0.9412, and the VA is 0.0012, and the experimental result with the Wine dataset shows that the S is 0.5255, the F1 value is 0.93, the ACC value is 0.9401, and the VA is 0.0014. Finally, to further demonstrate the performance of the algorithm, we use the more complex Waveform dataset; the S is 0.5101, the F1 value is 0.88, the ACC value is 0.8931, and the VA is 0.0033. All the experimental results show that the proposed algorithm can significantly improve clustering accuracy and have better stability, and its algorithm complexity can meet the requirements for real-time data processing. Full article
(This article belongs to the Special Issue Advances in Machine Learning and Symmetry/Asymmetry)
►▼ Show Figures

Figure 1

27 pages, 4905 KB  
Article
Robust Discriminative Non-Negative and Symmetric Low-Rank Projection Learning for Feature Extraction
by Wentao Zhang and Xiuhong Chen
Symmetry 2025, 17(2), 307; https://doi.org/10.3390/sym17020307 - 18 Feb 2025
Cited by 2 | Viewed by 1128
Abstract
Feature extraction plays a vital role in pattern recognition and computer vision. In recent years, low-rank representation (LRR) has been widely used in feature extraction, due to its robustness against noise. However, existing methods often overlook the impact of a well-constructed low-rank coefficient [...] Read more.
Feature extraction plays a vital role in pattern recognition and computer vision. In recent years, low-rank representation (LRR) has been widely used in feature extraction, due to its robustness against noise. However, existing methods often overlook the impact of a well-constructed low-rank coefficient matrix on projection learning. This paper introduces a novel feature extraction method, i.e., robust discriminative non-negative and symmetric low-rank projection learning (RDNSLRP), where a coefficient matrix with better properties, such as low-rank, non-negativity, symmetry and block-diagonal structure, is utilized as a graph matrix for learning the projection matrix. Additionally, a discriminant term is introduced to increase inter-class divergence while decreasing intra-class divergence, thereby extracting more discriminative features. An iterative algorithm for solving the proposed model was designed by using the augmented Lagrange multiplier method, and its convergence and computational complexity were analyzed. Our experimental results on multiple data sets demonstrate the effectiveness and superior image-recognition performance of the proposed method, particularly on data sets with complex intrinsic structures. Furthermore, by investigating the effects of noise corruption and feature dimension, the robustness against noise and the discrimination of the proposed model were further verified. Full article
(This article belongs to the Special Issue Advances in Machine Learning and Symmetry/Asymmetry)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-6
Back to TopTop