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Symmetry
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Symmetry and Asymmetry in Data Analysis
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Symmetry and Asymmetry in Data Analysis

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

Deadline for manuscript submissions: 15 August 2026 | Viewed by 7322

Special Issue Editors

Prof. Dr. Song Deng

E-Mail Website
Guest Editor
Institute of Advanced Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
Interests: data security; privacy preservation;cyber-physical system;data mining; big data
Prof. Dr. Xiong Fu

E-Mail Website
Guest Editor
School of Computer, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
Interests: data analysis; cloud computing
Prof. Dr. Di Wu

E-Mail Website
Guest Editor
College of Computer and Information Science, Southwest University, Chongqing, China
Interests: big data; recommender systems; environmental protection
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In the realm of data analysis, symmetry and asymmetry are pivotal concepts that offer profound insights into the structure and distribution of data. Symmetry in data often implies a balance or uniformity, which can be indicative of a stable or predictable system. It is frequently observed in well-behaved datasets, where the distribution of data points is even across different categories or variables. This property can simplify analysis by allowing analysts to apply symmetrical models, such as the normal distribution, to make predictions or inferences with a high degree of confidence.

Conversely, asymmetry in data introduces complexity and variability, which can be challenging to model but also rich in information. Asymmetric data distributions, such as skewed or bimodal patterns, suggest underlying processes that may not conform to simple assumptions of symmetry. Analyzing asymmetry requires more nuanced approaches, such as using non-parametric tests or transforming data to better fit symmetrical models. The presence of asymmetry can reveal hidden patterns, outliers, or the influence of confounding variables that might be overlooked in a symmetrical analysis.

Prof. Dr. Song Deng
Prof. Dr. Xiong Fu
Prof. Dr. Di Wu
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

  • data mining
  • machine learning
  • artificial intelligence
  • data analysis for industrial information
  • outlier identification
  • data distribution

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Published Papers (6 papers)

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Research

20 pages, 1369 KB  
Article
Symmetry-Aware Interpretable Anomaly Alarm Optimization Method for Power Monitoring Systems Based on Hierarchical Attention Deep Reinforcement Learning
by Zepeng Hou, Qiang Fu, Weixun Li, Yao Wang, Zhengkun Dong, Xianlin Ye, Xiaoyu Chen and Fangyu Zhang
Symmetry 2026, 18(2), 216; https://doi.org/10.3390/sym18020216 - 23 Jan 2026
Viewed by 621
Abstract
With the rapid advancement of smart grids driven by renewable energy integration and the extensive deployment of supervisory control and data acquisition (SCADA) and phasor measurement units (PMUs), addressing the escalating alarm flooding via intelligent analysis of large-scale alarm data is pivotal to [...] Read more.
With the rapid advancement of smart grids driven by renewable energy integration and the extensive deployment of supervisory control and data acquisition (SCADA) and phasor measurement units (PMUs), addressing the escalating alarm flooding via intelligent analysis of large-scale alarm data is pivotal to safeguarding the safe and stable operation of power grids. To tackle these challenges, this study introduces a pioneering alarm optimization framework based on symmetry-driven crowdsourced active learning and interpretable deep reinforcement learning (DRL). Firstly, an anomaly alarm annotation method integrating differentiated crowdsourcing and active learning is proposed to mitigate the inherent asymmetry in data distribution. Secondly, a symmetrically structured DRL-based hierarchical attention deep Q-network is designed with a dual-path encoder to balance the processing of multi-scale alarm features. Finally, a SHAP-driven interpretability framework is established, providing global and local attribution to enhance decision transparency. Experimental results on a real-world power alarm dataset demonstrate that the proposed method achieves a Fleiss’ Kappa of 0.82 in annotation consistency and an F1-Score of 0.95 in detection performance, significantly outperforming state-of-the-art baselines. Additionally, the false positive rate is reduced to 0.04, verifying the framework’s effectiveness in suppressing alarm flooding while maintaining high recall. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Data Analysis)
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19 pages, 1666 KB  
Article
Improved Trust Evaluation Model Based on PBFT and Zero Trust Integrated Power Network Security Defense Method
by Xiaoyun Liao, Sen Yang, Jun Xu, Li Liu, Wei Liang, Shengjie Yu, Yimu Ji and Shangdong Liu
Symmetry 2025, 17(11), 1982; https://doi.org/10.3390/sym17111982 - 16 Nov 2025
Cited by 2 | Viewed by 647
Abstract
In traditional power networks, security protection models primarily rely on perimeter-based defenses, utilizing firewalls, virtual private networks (VPNs), and identity authentication to block external threats. However, once a node within the power system is compromised, attackers can exploit it as a pivot to [...] Read more.
In traditional power networks, security protection models primarily rely on perimeter-based defenses, utilizing firewalls, virtual private networks (VPNs), and identity authentication to block external threats. However, once a node within the power system is compromised, attackers can exploit it as a pivot to launch lateral movement attacks from within the system, posing serious threats to the core operations of the power grid. To address the increasingly complex cybersecurity landscape, this paper proposes a security defense approach that integrates an improved trust evaluation model based on the Practical Byzantine Fault Tolerance (PBFT) algorithm with a zero-trust architecture, leveraging the structural and functional symmetry among network nodes. The PBFT algorithm’s fault tolerance and consensus mechanisms are leveraged to ensure dynamic trust scoring across multiple nodes. This approach guarantees that each node has an equal role in the system’s operations, maintaining fairness and security across the network. Furthermore, the primary node in the PBFT consensus process is redefined as the arbitration node in the zero-trust framework, and faulty nodes can be automatically replaced through the view change protocol, thereby mitigating the centralization risk inherent in traditional zero-trust models. Experimental results demonstrate that the proposed approach achieves high accuracy and robustness in defending against both internal and external attacks in power network scenarios, highlighting the role of symmetry in enhancing secure and balanced system operations. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Data Analysis)
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27 pages, 5317 KB  
Article
DRLMDS: A Deep Reinforcement Learning-Based Scheduling Algorithm for Mimic Defense Servers
by Xiaoyun Liao, Sen Yang, Lijian Ouyang, Rong Wu, Xin Huang, Shengjie Yu, Jinzhou Mao, Shangdong Liu and Yimu Ji
Symmetry 2025, 17(11), 1960; https://doi.org/10.3390/sym17111960 - 14 Nov 2025
Cited by 2 | Viewed by 1062
Abstract
Mimic defense, as an emerging active defense architecture, enhances the resilience of critical systems against unknown attacks through diversified redundant executors and dynamic switching mechanisms. However, the structural heterogeneity and dynamic behaviors of such systems pose great challenges for efficient and secure task [...] Read more.
Mimic defense, as an emerging active defense architecture, enhances the resilience of critical systems against unknown attacks through diversified redundant executors and dynamic switching mechanisms. However, the structural heterogeneity and dynamic behaviors of such systems pose great challenges for efficient and secure task scheduling, which traditional algorithms fail to address effectively. To overcome these limitations, this paper proposes a deep reinforcement learning-based scheduling algorithm for mimic defense servers, termed DRLMDS, which integrates an improved particle swarm optimization strategy to construct an environment-adaptive scheduling model capable of perceiving system state changes and optimizing task-resource allocation among heterogeneous executors. The algorithm is validated on mimic defense server datasets containing multiple heterogeneous nodes, where symmetric resource distribution and adjudication mechanisms are explicitly modeled to ensure balanced load distribution and robustness. Experimental results demonstrate that DRLMDS not only effectively defends against malicious attacks but also achieves approximately 30% reduction in task response time, 25% improvement in resource utilization, and nearly 40% enhancement in system stability compared with traditional swarm intelligence algorithms. These findings confirm the superior efficiency, robustness, and security advantages of the proposed approach in complex edge computing environments. This study provides a novel approach for intelligent and adaptive task scheduling in mimic defense architectures, offering theoretical support for active defense research and practical guidance for secure system deployment. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Data Analysis)
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15 pages, 5150 KB  
Article
Insulator Defect Detection Algorithm Based on Improved YOLO11s in Snowy Weather Environment
by Ziwei Ding, Song Deng and Qingsheng Liu
Symmetry 2025, 17(10), 1763; https://doi.org/10.3390/sym17101763 - 19 Oct 2025
Cited by 1 | Viewed by 909
Abstract
The intelligent transformation of power systems necessitates robust insulator condition detection to ensure grid safety. Existing methods, primarily reliant on manual inspection or conventional image processing, suffer significantly degraded target identification and detection efficiency under extreme weather conditions such as heavy snowfall. To [...] Read more.
The intelligent transformation of power systems necessitates robust insulator condition detection to ensure grid safety. Existing methods, primarily reliant on manual inspection or conventional image processing, suffer significantly degraded target identification and detection efficiency under extreme weather conditions such as heavy snowfall. To address this challenge, this paper proposes an enhanced YOLO11s detection framework integrated with image restoration technology, specifically targeting insulator defect identification in snowy environments. First, data augmentation and a FocalNet-based snow removal algorithm effectively enhance image resolution under snow conditions, enabling the construction of a high-quality training dataset. Next, the model architecture incorporates a dynamic snake convolution module to strengthen the perception of tubular structural features, while the MPDIoU loss function optimizes bounding box localization accuracy and recall. Comparative experiments demonstrate that the optimized framework significantly improves overall detection performance under complex weather compared to the baseline model. Furthermore, it exhibits clear advantages over current mainstream detection models. This approach provides a novel technical solution for monitoring power equipment conditions in extreme weather, offering significant practical value for ensuring reliable grid operation. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Data Analysis)
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20 pages, 1956 KB  
Article
Recommendation Model Based on Global Intention Learning and Sequence Augmentation
by Minghui Li, Wei Lu and Xiaodong Cai
Symmetry 2025, 17(4), 586; https://doi.org/10.3390/sym17040586 - 11 Apr 2025
Viewed by 1341
Abstract
User interaction behavior is influenced by various intentions, which are often asymmetric. Incorporating intention information into sequential recommendation can significantly improve recommendation performance. However, most existing intention modeling methods rely on auxiliary information or random data augmentation to capture user intentions, which cannot [...] Read more.
User interaction behavior is influenced by various intentions, which are often asymmetric. Incorporating intention information into sequential recommendation can significantly improve recommendation performance. However, most existing intention modeling methods rely on auxiliary information or random data augmentation to capture user intentions, which cannot effectively capture the potential correlations between different user intentions, especially when dealing with asymmetric intentions. Furthermore, using random data augmentation methods may amplify the noise in the original sequence, leading to a decline in the model’s recommendation performance. To address these issues, this paper proposes a recommendation model based on Global Intention Learning and Sequence Augmentation. Firstly, a novel sequence information extraction module is designed, which efficiently integrates the refined global item association graph into item representations through a self-supervised approach, thereby capturing global collaborative sequence information. Secondly, an improved sequence augmentation strategy is adopted to reduce the disruption of the original item correlations, making the intention representation more accurate. Finally, intention information is integrated into the sequential recommendation model through a contrastive learning method, further enhancing the accuracy of the model’s recommendations. Experimental results show that compared to several state-of-the-art methods, the proposed model exhibits significant improvements on the Sports, Toys and LastFM datasets. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Data Analysis)
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18 pages, 1412 KB  
Article
Photovoltaic Power Prediction Technology Based on Multi-Source Feature Fusion
by Xia Zhou, Xize Zhang, Jianfeng Dai and Tengfei Zhang
Symmetry 2025, 17(3), 414; https://doi.org/10.3390/sym17030414 - 10 Mar 2025
Cited by 3 | Viewed by 1543
Abstract
With the increase in photovoltaic installed capacity year by year, accurate photovoltaic power prediction is of great significance for photovoltaic grid-connected operation and scheduling planning. In order to improve the prediction accuracy, this paper proposes a photovoltaic power prediction combination model based on [...] Read more.
With the increase in photovoltaic installed capacity year by year, accurate photovoltaic power prediction is of great significance for photovoltaic grid-connected operation and scheduling planning. In order to improve the prediction accuracy, this paper proposes a photovoltaic power prediction combination model based on Pearson Correlation Coefficient (PCC), Complete Ensemble Empirical Mode Decomposition (CEEMDAN), K-means clustering, Variational Mode Decomposition (VMD), Convolutional Neural Network (CNN), and Bidirectional Long Short-Term Memory (BiLSTM). By making full use of the symmetric structure of the BiLSTM algorithm, one part is used to process the data sequence in order, and the other part is used to process the data sequence in reverse order. It captures the characteristics of sequence data by simultaneously processing a ‘symmetric’ information. Firstly, the historical photovoltaic data are preprocessed, and the correlation analysis of meteorological factors is carried out by PCC, and the high correlation factors are extracted to obtain the multivariate time series feature matrix of meteorological factors. Then, the historical photovoltaic power data are decomposed into multiple intrinsic modes and a residual component at one time by CEEMDAN. The high-frequency components are clustered by K-means combined with sample entropy, and the high-frequency components are decomposed and refined by VMD to form a multi-scale characteristic mode matrix. Finally, the obtained features are input into the CNN–BiLSTM model for the final photovoltaic power prediction results. After experimental verification, compared with the traditional single-mode decomposition algorithm (such as CEEMDAN–BiLSTM, VMD–BiLSTM), the combined prediction method proposed reduces MAE by more than 0.016 and RMSE by more than 0.017, which shows excellent accuracy and stability. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Data Analysis)
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