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Symmetry
Special Issues
Advances in Machine Learning and Symmetry/Asymmetry
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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: 31 May 2025 | Viewed by 950

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 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. 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

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

Published Papers (2 papers)

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Research

22 pages, 2531 KiB  
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
Viewed by 251
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)
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27 pages, 4905 KiB  
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
Viewed by 402
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)
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