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Keywords = t-SNE dimensionality reduction

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23 pages, 1852 KB  
Article
Research on Financial Early Warning Models of A-Share Listed Companies Based on EBWO-BP Neural Networks
by Yizhou Chu, Guiyang Liu, Qiuyu Yu and Chunyan Yang
Mathematics 2026, 14(13), 2261; https://doi.org/10.3390/math14132261 - 25 Jun 2026
Viewed by 241
Abstract
The financial early warning mechanism of listed companies has an important strategic value for maintaining the stability of the capital market and preventing systemic financial risks. This study proposes a hybrid model (EBWO-BP) based on the improved beluga optimisation algorithm (EBWO) and BP [...] Read more.
The financial early warning mechanism of listed companies has an important strategic value for maintaining the stability of the capital market and preventing systemic financial risks. This study proposes a hybrid model (EBWO-BP) based on the improved beluga optimisation algorithm (EBWO) and BP neural network for financial early warning research. Innovative T-SNE nonlinear dimensionality reduction technique is applied to the multidimensional evaluation system constructed by 23 financial and two non-financial indicators. The empirical evidence based on the data of A-share listed companies in 2022–2024 shows that the accuracy of the EBWO-BP test set reaches 86.51% (AUC = 0.83), which demonstrates a significant prediction advantage compared with the optimisation algorithm models such as GA-BP and PSO-BP, as well as the CNN and LSTM deep learning models; when the sample size is increased to 700 groups, the accuracy is improved to 89.05%, verifying the model robustness. The method achieves significant improvement of financial risk prediction through algorithm fusion innovation, and provides methodological innovation and practical reference for intelligent financial risk monitoring. Full article
(This article belongs to the Special Issue Quantitative Finance with Mathematical Modelling)
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21 pages, 2838 KB  
Article
Exploratory Image-Level Classification of a Public Chest Radiograph Dataset Using a Lightweight SqueezeNet-Based Pipeline
by Luis Ramalhete, Vitor Oliveira, Rui Quintas and Rúben Araújo
AI Med. 2026, 1(2), 15; https://doi.org/10.3390/aimed1020015 - 2 Jun 2026
Viewed by 310
Abstract
Background: Chest radiography is widely used in clinical workflows; however, exploratory image-level classification across multiple public-dataset categories remains less studied than single-disease classification tasks. We aimed to develop and internally evaluate a compact SqueezeNet-based pipeline for nine-class chest radiograph classification within a public [...] Read more.
Background: Chest radiography is widely used in clinical workflows; however, exploratory image-level classification across multiple public-dataset categories remains less studied than single-disease classification tasks. We aimed to develop and internally evaluate a compact SqueezeNet-based pipeline for nine-class chest radiograph classification within a public dataset. Low-computational-footprint approaches may be relevant for future research prototypes in resource-constrained settings, particularly when offline operation is desirable; however, no real-world clinical deployment or triage validation was assessed in the present study. Methods: Using a public dataset of 6743 frontal radiographs spanning normal anatomy and eight pathology categories, we extracted 512-dimensional embeddings from a pre-trained SqueezeNet-1.0 (features module with global average pooling) and trained a scikit-learn MLP with a single hidden layer. Performance was assessed with stratified 5-fold cross-validation using accuracy and class-wise precision, recall, and F1; interpretability was examined via confusion matrices and dimensionality reduction techniques (t-SNE, and MDS). Results: The model achieved a mean accuracy of 98.83% across folds, with per-class precision, recall, and F1 generally ≥0.96 and a weighted F1 of 0.99; confusion matrices showed minimal off-diagonal errors, and embedding visualizations revealed well-separated, class-consistent clusters. Conclusions: Compact CNN features coupled with a simple MLP demonstrated strong internal performance for multi-class CXR classification within the evaluated dataset. However, the absence of external validation, the use of synthetically augmented data, and the lack of patient-level provenance metadata substantially limit conclusions regarding generalizability and clinical applicability. Full article
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29 pages, 33655 KB  
Article
Research on Intelligent Fault Diagnosis of Reciprocating Compressor Valves Based on Multi-Source Information Fusion with Improved SWD
by Zheng Chao, Fengfeng Bie, Qianqian Li, Wensheng Su, Tiantian Wei and Han Dong
Appl. Sci. 2026, 16(11), 5401; https://doi.org/10.3390/app16115401 - 28 May 2026
Viewed by 188
Abstract
Aiming at solving the problems of the complex impact vibration characteristics of reciprocating compressor valves, the inability of a single signal to fully characterize state characteristics, and the difficulty of effectively extracting and fusing feature information from multi-source signals, this paper constructs a [...] Read more.
Aiming at solving the problems of the complex impact vibration characteristics of reciprocating compressor valves, the inability of a single signal to fully characterize state characteristics, and the difficulty of effectively extracting and fusing feature information from multi-source signals, this paper constructs a fault diagnosis and prediction model combining Improved Swarm Decomposition (ISWD) and t-SNE dimensionality reduction and fusion with a Multi-scale Convolutional Neural Network–Bidirectional Gated Recurrent Unit (MCNN-BiGRU) based on multi-source signals and applies it to the fault diagnosis and pattern recognition prediction of reciprocating compressor valves. Firstly, atom search optimization (ASO) is adopted to optimize the decomposition parameters of Swarm Decomposition (SWD) to obtain the ISWD algorithm, which is applied to decompose the multi-source signals of compressors to extract the oscillating components (OCs). Secondly, the correlation coefficient method is used to screen the OCs and conduct signal reconstruction, and various entropy feature values are extracted from the reconstructed signals to form an initial feature set. Then the t-SNE algorithm is employed to perform dimensionality reduction and fusion on the initial feature set, yielding a more concise and representative fused feature set. Finally, the fused feature set after dimensionality reduction and fusion is input into the MCNN-BiGRU model for training, so as to realize the pattern recognition and prediction of valve faults. The effectiveness and superiority of this method in the fault diagnosis of reciprocating compressor valves are verified through numerical simulation and experimental analysis. Full article
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27 pages, 3752 KB  
Article
Reliability Assessment of AC/DC Hybrid Distribution Networks with Large-Scale Renewable Energy Integration
by Chuanguang Fan, Nian Shi, Lu Zhao, Jie Cheng and Xiaozhu Liu
Energies 2026, 19(11), 2549; https://doi.org/10.3390/en19112549 - 25 May 2026
Viewed by 238
Abstract
With the advancement of carbon peaking and carbon neutrality goals, the increasing penetration of renewable energy sources such as wind and photovoltaic power poses severe challenges to the power supply reliability of AC/DC hybrid distribution networks due to their fluctuating, intermittent, and stochastic [...] Read more.
With the advancement of carbon peaking and carbon neutrality goals, the increasing penetration of renewable energy sources such as wind and photovoltaic power poses severe challenges to the power supply reliability of AC/DC hybrid distribution networks due to their fluctuating, intermittent, and stochastic outputs. This paper proposes a reliability assessment method for AC/DC hybrid distribution networks under large-scale renewable energy integration based on clustering of typical operating scenarios. The net load duration curve is adopted as the feature variable to characterize typical operating scenarios. An improved t-distributed Stochastic Neighbor Embedding (t-SNE) nonlinear dimensionality reduction method with Kullback–Leibler (KL) divergence elbow correction is proposed for effective reduction of high-dimensional time-series data. An adaptive Density-Based Spatial Clustering of Applications with Noise (DBSCAN) parameter optimization method based on the k-nearest-neighbor curve and a secondary K-means clustering method based on entropy-weighted multi-objective optimization are further developed, forming a hybrid t-SNE-DBSCAN–K-means clustering algorithm. The power supply reliability is then assessed based on the clustered typical operating scenarios. A typical AC/DC hybrid distribution network is used as the test system. Results show that the DB index of the proposed clustering method improves by at least 22% compared with conventional methods, the maximum relative error between the typical-day-based and full time-series simulation results is less than 6%, and the computational efficiency improves by about 8.8 times, achieving a good balance between accuracy and efficiency. Full article
(This article belongs to the Section F: Electrical Engineering)
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22 pages, 19098 KB  
Article
Symmetry Analysis of Aesthetic Features for Computational Support in Assessment of Art Learning Outcomes
by Yan Ruan and Xiaofei Li
Symmetry 2026, 18(5), 811; https://doi.org/10.3390/sym18050811 - 9 May 2026
Viewed by 304
Abstract
The assessment of art learning outcomes has long relied on teachers’ subjective judgment, facing challenges such as inconsistent evaluation criteria and difficulty in multi-dimensional quantitative analysis. To address these issues, this study proposes a framework for the automatic assessment of art learning outcomes [...] Read more.
The assessment of art learning outcomes has long relied on teachers’ subjective judgment, facing challenges such as inconsistent evaluation criteria and difficulty in multi-dimensional quantitative analysis. To address these issues, this study proposes a framework for the automatic assessment of art learning outcomes based on symmetry analysis of multi-dimensional aesthetic features. The model quantifies the symmetry between student works and instructional exemplars across three aesthetic dimensions: color distribution features (HSV color space histograms and dominant color composition), compositional features (visual center distribution and structural symmetry), and art movement style features (multi-layer Gram matrices from VGG-19 with PCA dimensionality reduction). Using publicly available artwork datasets, this study constructed Temporal Evolution Pairs (early and late works by the same artist) and Stylistic Inheritance Pairs (works by different artists within the same movement) to validate the model’s effectiveness. The experimental results demonstrate that the proposed multi-dimensional feature fusion strategy achieves 87.6% accuracy in artist style evolution trajectory recognition and 82.3% accuracy in art movement style inheritance quantification, significantly outperforming baseline methods including SSIM (52.3%), VGG-fc features (68.9%), and single style loss (76.4%). Two in-depth case studies further validate the model’s quantitative capability: in analyzing Picasso’s stylistic evolution, the Mastery Index and the Creativity Divergence Index successfully captured the stylistic continuity of adjacent periods (Blue Period to Rose Period: the Mastery Index = 73.6) and the breakthrough innovation of cross-period transformations (Rose Period to Cubism: the Creativity Divergence Index = 82.7). t-SNE visualization of the feature space further revealed that deep style features can clearly distinguish different art movements and individual artists, with spatial distances between artists closely corresponding to stylistic affinities. This research provides new perspectives and tools for a computational framework with the potential for art education assessment practice. It is important to emphasize that the reported performance demonstrates the model’s ability to quantify stylistic relationships between artworks but does not yet demonstrate its validity for assessing student learning outcomes in real classroom settings. As noted, the current validation is based on art-historical consensus, and direct application to educational contexts will require further validation with actual student works and expert evaluation, which we plan to address in future work. Full article
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19 pages, 2896 KB  
Article
Exploring the Effectiveness of Dimensionality Reduction Methods for High-Dimensional Turbofan Engine Sensor Data
by Mehmet Şamil Güneş
Appl. Sci. 2026, 16(10), 4610; https://doi.org/10.3390/app16104610 - 7 May 2026
Viewed by 395
Abstract
This study presents a systematic comparison of three dimensionality reduction methods namely Principal Component Analysis (PCA), t-Distributed Stochastic Neighbor Embedding (t-SNE), and uniform manifold approximation and projection (UMAP) applied to multivariate turbofan engine sensor data from the NASA C-MAPSS benchmark. The analysis was [...] Read more.
This study presents a systematic comparison of three dimensionality reduction methods namely Principal Component Analysis (PCA), t-Distributed Stochastic Neighbor Embedding (t-SNE), and uniform manifold approximation and projection (UMAP) applied to multivariate turbofan engine sensor data from the NASA C-MAPSS benchmark. The analysis was conducted across three subsets of increasing complexity: FD001 (single operating condition, single-fault mode), FD002 (six operating conditions, single-fault mode), and FD004 (six operating conditions, two fault modes), comprising 20,631, 53,759, and 61,249 observations respectively. For multi-condition subsets, within-condition z-score normalization was applied to prevent inter-condition offsets from masking the degradation signal. Fourteen informative sensor variables were retained following the exclusion of near-constant sensors. Embedding quality was assessed using four complementary metrics: silhouette score (with bootstrap 95% confidence intervals), trustworthiness, continuity, and PCA reconstruction RMSE. A downstream remaining useful life (RUL) prediction task and a hyperparameter sensitivity analysis were also conducted. PCA achieved the best silhouette scores on FD001 (0.4608; 95% CI = [0.447, 0.475]; and FD002) and demonstrated RUL predictive capabilities similar to those of a 14-Dimensional Baseline Model, which supports the ability of PCA to be used as an interpretable tool for analyzing data globally. t-SNE maintained the highest levels of trustworthiness and continuity in preserving local neighborhood relationships among the models tested across each subset. UMAP had the best silhouette score on FD004 (0.4818; 95% CI = [0.463, 0.495]); UMAP also produced confidence intervals that did not overlap with either PCA or t-SNE, thus showing significant statistical differences when compared to these two methods under conditions involving multiple faults. The PCA ranking was consistent across the range of hyperparameter combinations tested (n = 36). The results provide a quantitative, generalizable framework for dimensionality reduction method selection in prognostic health management applications. Full article
(This article belongs to the Special Issue Exploring AI: Methods and Applications for Data Mining: 2nd Edition)
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29 pages, 3194 KB  
Article
Integrated Chemometric and Machine Learning Analysis Identifies Peripheral Biosignatures Distinguishing Major Depressive Disorder from Bipolar Disorder: A Translational Cross-Sectional Study
by Donatella Coradduzza, Stefania Sedda, Andrea Sanna, Alessandra Matilde Nivoli, Maria Rosaria De Miglio, Ciriaco Carru, Massimiliano Grosso and Serenella Medici
Medicina 2026, 62(5), 806; https://doi.org/10.3390/medicina62050806 - 23 Apr 2026
Viewed by 654
Abstract
Background and Objectives: Major Depressive Disorder (MDD) and Bipolar Disorder (BD) lack objective molecular stratification despite partial clinical overlap, particularly during depressive phases. This cross-sectional study explored whether coordinated peripheral biomarker patterns could be identified using an integrated multivariate analytical framework. Materials [...] Read more.
Background and Objectives: Major Depressive Disorder (MDD) and Bipolar Disorder (BD) lack objective molecular stratification despite partial clinical overlap, particularly during depressive phases. This cross-sectional study explored whether coordinated peripheral biomarker patterns could be identified using an integrated multivariate analytical framework. Materials and Methods: A total of 151 participants (MDD n = 41; BD n = 40; HC (healthy controls) n = 70) were profiled for 42 blood-derived parameters including composite inflammatory indices, hematological markers, trace elements measured by ICP-MS, and circulating BDNF and NLRP3 quantified by ELISA. Data were analyzed using univariate testing, unsupervised dimensionality reduction (PCA, t-SNE), and supervised classification (PLS-DA with cross-validation and permutation testing). Results: Thirty-seven of 42 parameters showed significant inter-group differences (p < 0.05). Circulating NLRP3 concentrations were markedly reduced in both psychiatric groups compared with HC. Composite inflammatory indices (NLR, SIRI, SII) were elevated in MDD. Zinc levels were modestly reduced, while manganese levels were increased in psychiatric cohorts. BDNF showed lower concentrations in MDD and higher concentrations in BD relative to HC. Cross-validated PLS-DA classification for psychiatric disorder vs. controls yielded an accuracy of 89.4% (AUC-ROC 0.947), with permutation testing indicating performance above chance. However, the sample-to-variable ratio and exploratory design warrant cautious interpretation. Conclusions: Multidomain peripheral biomarker profiling identified coordinated biochemical differences across diagnostic groups. These findings suggest the presence of multidimensional peripheral signatures associated with mood disorders within an exploratory framework. Full article
(This article belongs to the Section Psychiatry)
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19 pages, 1748 KB  
Article
Evaluating Embedding Representations for Multiclass Code Smell Detection: A Comparative Study of CodeBERT and General-Purpose Embeddings
by Marcela Mosquera and Rodolfo Bojorque
Appl. Sci. 2026, 16(8), 3622; https://doi.org/10.3390/app16083622 - 8 Apr 2026
Viewed by 475
Abstract
Code smells are indicators of potential design problems in software systems and are commonly used to guide refactoring activities. Recent advances in representation learning have enabled the use of embedding-based models for analyzing source code, offering an alternative to traditional approaches based on [...] Read more.
Code smells are indicators of potential design problems in software systems and are commonly used to guide refactoring activities. Recent advances in representation learning have enabled the use of embedding-based models for analyzing source code, offering an alternative to traditional approaches based on manually engineered metrics. However, the effectiveness of different embedding representations for multiclass code smell detection remains insufficiently explored. This study presents an empirical comparison of embedding models for the automatic detection of three widely studied code smells: Long Method, God Class, and Feature Envy. Using the Crowdsmelling dataset as an empirical basis, source code fragments were extracted from the original projects and transformed into vector representations using two embedding approaches: a general-purpose embedding model and the code-specialized CodeBERT model. The resulting representations were evaluated using several machine learning classifiers under a stratified group-based validation protocol. The results show that CodeBERT consistently outperforms the general-purpose embeddings across multiple evaluation metrics, including balanced accuracy, macro F1-score, and Matthews correlation coefficient. Dimensionality reduction analyses using PCA and t-SNE further indicate that CodeBERT organizes code smell instances in a more structured latent representation space, which facilitates the separation of smell categories. In particular, CodeBERT achieved a macro F1-score of 0.8619, outperforming general-purpose embeddings (0.7622) and substantially surpassing a classical TF-IDF baseline (0.4555). These findings highlight the value of this study as a controlled multiclass evaluation of embedding representations and demonstrate the practical value of domain-specific representations for improving automated code smell detection and class separability in real-world software engineering scenarios. Full article
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20 pages, 1516 KB  
Article
Fast NOx Emission Factor Accounting for Hybrid Electric Vehicles with Dictionary Learning-Based Incremental Dimensionality Reduction
by Hao Chen, Jianan Chen, Feiyang Zhao and Wenbin Yu
Energies 2026, 19(3), 680; https://doi.org/10.3390/en19030680 - 28 Jan 2026
Cited by 1 | Viewed by 369
Abstract
Amid the growing global environmental challenges, precise and efficient vehicle emission management plays a critical role in achieving energy-saving and emission reduction goals. At the same time, the rapid development of connected vehicles and autonomous driving technologies has generated a large amount of [...] Read more.
Amid the growing global environmental challenges, precise and efficient vehicle emission management plays a critical role in achieving energy-saving and emission reduction goals. At the same time, the rapid development of connected vehicles and autonomous driving technologies has generated a large amount of high-dimensional vehicle operation data. This not only provides a rich data foundation for refined emission accounting but also raises higher demands for the construction of accounting models. Therefore, this study aims to develop an accurate and efficient emission accounting model to contribute to the precise nitrogen oxide (NOx) emission accounting for hybrid electric vehicles (HEVs). A systematic approach is proposed that combines incremental dimensionality reduction with advanced regression algorithms to achieve refined and efficient emission accounting based on multiple variables. Specifically, the dimensionality of the real driving emission (RDE) data is first reduced using the feature selection and t-distributed stochastic neighbor embedding (t-SNE) feature extraction method to capture key parameter information and reduce subsequent computational complexity. Next, an incremental dimensionality reduction method based on dictionary learning is employed to efficiently embed new data into a low-dimensional space through straightforward matrix operations. Given the computational cost of the dictionary learning training process, this study introduces the FISTA (Fast Iterative Shrinkage-Thresholding Algorithm) for accelerated iterative optimization and enhances the computational efficiency through parameter optimization, while maintaining the accuracy of dictionary learning. Subsequently, an NOx emission factor correction factor prediction model is trained using the low-dimensional data obtained from t-SNE embeddings, enabling direct computation of the corresponding correction factor when presented with new incremental low-dimensional embeddings. Finally, validation on independent HEV datasets shows that parameter K improves to 1 ± 0.05 and R2 increases up to 0.990, laying a foundation for constructing an emission accounting model with broad applicability based on multiple variables. Full article
(This article belongs to the Collection State of the Art Electric Vehicle Technology in China)
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30 pages, 8381 KB  
Article
The Landscape of Ferroptosis-Related Gene Signatures as Molecular Stratification in Triple-Negative Breast Cancer
by Marko Buta, Nikola Jeftic, Irina Besu, Jovan Raketic, Ivan Markovic, Ana Djuric, Nina Petrovic and Tatjana Srdic-Rajic
Diagnostics 2026, 16(3), 379; https://doi.org/10.3390/diagnostics16030379 - 23 Jan 2026
Cited by 1 | Viewed by 1297
Abstract
Background: Triple-negative breast cancer (TNBC) represents the most aggressive breast cancer subtype, characterized by high genomic instability, metabolic stress, and limited therapeutic options. Ferroptosis, an iron-dependent form of regulated cell death, has emerged as a promising vulnerability in TNBC, yet its subtype-specific regulatory [...] Read more.
Background: Triple-negative breast cancer (TNBC) represents the most aggressive breast cancer subtype, characterized by high genomic instability, metabolic stress, and limited therapeutic options. Ferroptosis, an iron-dependent form of regulated cell death, has emerged as a promising vulnerability in TNBC, yet its subtype-specific regulatory landscape remains insufficiently defined. Methods: Using transcriptomic (METABRIC, TCGA, GEO) and proteomic (CPTAC) datasets, ferroptosis-related genes were profiled across PAM50 breast cancer subtypes. Differential expression, univariate Cox regression, LASSO modeling, survival analyses, GSEA, and dimensionality reduction (PCA, t-SNE) were applied. A Ferroptosis Index (FI) was calculated using β-coefficients from the Cox/LASSO regression model. Single-cell RNA-seq data was used to map ferroptosis-associated signature across tumor and microenvironmental compartments. Results: Basal-like tumors exhibited the strongest ferroptosis-associated transcriptional shift, characterized by upregulation of ACSL4 and EZH2 and downregulation of AR, GPX4, and CIRBP. Sixteen ferroptosis-related genes were associated with overall survival, forming a ferroptosis-associated signature. The FI was significantly higher in Basal-like tumors, indicating elevated ferroptosis-associated transcriptional state. GSEA revealed enrichment of cell cycle, mitotic, cytoskeletal, and metabolic stress pathways. Single-cell analysis demonstrated expression of ferroptosis markers across cancer epithelial, stromal, and myeloid populations. Conclusions: Basal-like tumors harbor a distinct ferroptosis-associated transcriptional state linked to tumor aggressiveness and poor prognosis. These findings provide a biologically grounded framework for ferroptosis-related stratification and support future functional and translational studies targeting ferroptosis vulnerabilities in aggressive breast cancer. Full article
(This article belongs to the Special Issue Diagnosis, Treatment, and Prognosis of Breast Cancer)
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17 pages, 2171 KB  
Article
Performance Analysis of Printed Circuit Board Defect Detection with Hybrid CNN Module Image Feature Extraction and Clustering
by Fan Jiang, Huaching Chen, Songlin Wei and Chengying Chen
Eng 2026, 7(1), 41; https://doi.org/10.3390/eng7010041 - 12 Jan 2026
Viewed by 1010
Abstract
Accurate and efficient defect detection in printed circuit boards (PCBs) is critical for manufacturing quality control. Existing methods predominantly rely on manually extracted features such as surface texture, color, and shape for defect recognition and classification within small-dimensional feature datasets. A convolutional neural [...] Read more.
Accurate and efficient defect detection in printed circuit boards (PCBs) is critical for manufacturing quality control. Existing methods predominantly rely on manually extracted features such as surface texture, color, and shape for defect recognition and classification within small-dimensional feature datasets. A convolutional neural network (CNN) model was developed via transfer learning. Feature extraction involves diverse operations across different CNN layers. Essential features were selected, and dimensionality was reduced via either t-distributed stochastic neighbor embedding (t-SNE) or principal component analysis (PCA). Defect classification was subsequently performed by clustering the reduced features with either the K-means or K-nearest neighbors (KNN) algorithm. Compared with alternative model feature learning classifiers, the proposed small-dimensional CNN model performs significantly better. A defect recognition accuracy of 97.33% was achieved, with processing completed in approximately 60 s. This approach, which integrates transfer learning-based CNN feature extraction with dimensionality reduction and clustering techniques, provides a fast and effective method for high-precision defect detection and classification in PCBs. Full article
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25 pages, 6319 KB  
Article
Uncovering Structure–Conductivity Relationships in Anion Exchange Membranes (AEMs) Using Interpretable Machine Learning
by Pegah Naghshnejad, Debojyoti Das, Jose A. Romagnoli, Revati Kumar and Jianhua Chen
Membranes 2026, 16(1), 12; https://doi.org/10.3390/membranes16010012 - 31 Dec 2025
Viewed by 1653
Abstract
Anion exchange membranes (AEMs) play a vital role in the performance of water electrolyzers and fuel cells, yet their discovery and optimization remain challenging due to the complexity of structure–property relationships. In this study, we introduce a machine learning framework that leverages conditional [...] Read more.
Anion exchange membranes (AEMs) play a vital role in the performance of water electrolyzers and fuel cells, yet their discovery and optimization remain challenging due to the complexity of structure–property relationships. In this study, we introduce a machine learning framework that leverages conditional graph neural networks (cGNNs) and descriptor-based models and a hybrid graph neural network (HGARE) to predict and interpret ionic conductivity. The descriptor-based pipeline employs principal component analysis (PCA), ablation, and SHAP analysis to identify factors governing anion conductivity, revealing electronic, topological, and compositional descriptors as key contributors. Beyond prediction, dimensionality reduction and clustering are performed by employing t-SNE and KMeans as well as SOM, which reveal distinct membranes clusters, some of which were enriched with high anion conductivity. Among graph-based approaches, the graph convolutional (GCN) achieved strong predictive performance, while the Hybrid Graph Autoencoder-Regressor Ensemble (HGARE) achieved the highest accuracy. Additionally, atom-level saliency maps from GCN provide spatial explanations for conductive behavior, revealing the importance of polarizable and flexible regions. This work contributes to the accelerated and data-driven design of high-performance AEMs. Full article
(This article belongs to the Special Issue Design, Synthesis and Applications of Ion Exchange Membranes)
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25 pages, 2486 KB  
Article
A Preliminary Mechanics-Informed Machine Learning Framework for Objective Assessment of Parkinson’s Disease and Rehabilitation Outcomes
by Amirali Hanifi, Roozbeh Abedini-Nassab and Mohammed N. Ashtiani
Diagnostics 2025, 15(22), 2855; https://doi.org/10.3390/diagnostics15222855 - 12 Nov 2025
Cited by 1 | Viewed by 902
Abstract
Background/Objectives: Non-invasive methods for evaluating rehabilitation outcomes in Parkinson’s disease (PD) remain limited. This preliminary study proposes a mechanics-informed machine learning (ML) framework integrating force-plate data with dimensionality reduction, clustering, and statistical analysis to objectively assess motor control and the effects of a [...] Read more.
Background/Objectives: Non-invasive methods for evaluating rehabilitation outcomes in Parkinson’s disease (PD) remain limited. This preliminary study proposes a mechanics-informed machine learning (ML) framework integrating force-plate data with dimensionality reduction, clustering, and statistical analysis to objectively assess motor control and the effects of a targeted intervention. Methods: Twelve PD patients were randomly assigned to a PD control group performing standard exercises or an intervention group incorporating additional transverse-plane trunk motion exercises for 10 weeks. Ground reaction forces and center of pressure (COP) signals were recorded pre- and post-intervention using a force plate, alongside data from six healthy individuals as a benchmark. Features related to postural sway and COP dynamics were extracted and refined using Forward Feature Selection. Dimensionality reduction (t-SNE) and unsupervised clustering (K-means) identified group-level patterns. SHAP values and Cohen’s d quantified feature importance and effect size. Clustering robustness was assessed with bootstrapping, nested cross-validation, and permutation testing. Results: K-means clustering revealed clear pre/post-intervention separation in five of six intervention patients, with post-intervention states shifting toward the control cluster. Clustering showed strong performance (Silhouette 0.77–0.79; Calinski–Harabasz 100.8–184.9; Davies–Bouldin 0.29–0.45). The most predictive features (RMS-SML and PL-SAP) showed large effect sizes (Cohen’s d = –12.1 and –4.53, respectively) distinguishing PD patients from healthy controls. Traditional statistical tests (e.g., ANOVA) failed to detect within-group changes (p > 0.05), but ML-based methods captured subtle, nonlinear postural adaptations. Conclusions: This preliminary mechanics-informed ML framework detects PD-related motor deficits and rehabilitation-induced improvements using force-plate data, warranting validation in larger cohorts. Full article
(This article belongs to the Section Machine Learning and Artificial Intelligence in Diagnostics)
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52 pages, 10804 KB  
Article
Silhouette-Based Evaluation of PCA, Isomap, and t-SNE on Linear and Nonlinear Data Structures
by Mostafa Zahed and Maryam Skafyan
Stats 2025, 8(4), 105; https://doi.org/10.3390/stats8040105 - 3 Nov 2025
Cited by 6 | Viewed by 2860
Abstract
Dimensionality reduction is fundamental for analyzing high-dimensional data, supporting visualization, denoising, and structure discovery. We present a systematic, large-scale benchmark of three widely used methods—Principal Component Analysis (PCA), Isometric Mapping (Isomap), and t-Distributed Stochastic Neighbor Embedding (t-SNE)—evaluated by average silhouette scores to quantify [...] Read more.
Dimensionality reduction is fundamental for analyzing high-dimensional data, supporting visualization, denoising, and structure discovery. We present a systematic, large-scale benchmark of three widely used methods—Principal Component Analysis (PCA), Isometric Mapping (Isomap), and t-Distributed Stochastic Neighbor Embedding (t-SNE)—evaluated by average silhouette scores to quantify cluster preservation after embedding. Our full factorial simulation varies sample size n{100,200,300,400,500}, noise variance σ2{0.25,0.5,0.75,1,1.5,2}, and feature count p{20,50,100,200,300,400} under four generative regimes: (1) a linear Gaussian mixture, (2) a linear Student-t mixture with heavy tails, (3) a nonlinear Swiss-roll manifold, and (4) a nonlinear concentric-spheres manifold, each replicated 1000 times per condition. Beyond empirical comparisons, we provide mathematical results that explain the observed rankings: under standard separation and sampling assumptions, PCA maximizes silhouettes for linear, low-rank structure, whereas Isomap dominates on smooth curved manifolds; t-SNE prioritizes local neighborhoods, yielding strong local separation but less reliable global geometry. Empirically, PCA consistently achieves the highest silhouettes for linear structure (Isomap second, t-SNE third); on manifolds the ordering reverses (Isomap > t-SNE > PCA). Increasing σ2 and adding uninformative dimensions (larger p) degrade all methods, while larger n improves levels and stability. To our knowledge, this is the first integrated study combining a comprehensive factorial simulation across linear and nonlinear regimes with distribution-based summaries (density and violin plots) and supporting theory that predicts method orderings. The results offer clear, practice-oriented guidance: prefer PCA when structure is approximately linear; favor manifold learning—especially Isomap—when curvature is present; and use t-SNE for the exploratory visualization of local neighborhoods. Complete tables and replication materials are provided to facilitate method selection and reproducibility. Full article
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20 pages, 569 KB  
Article
Symmetry-Preserving Optimization of Differentially Private Machine Learning Based on Feature Importance
by Nan-I Wu, Jing-Ting Wu and Min-Shiang Hwang
Symmetry 2025, 17(10), 1747; https://doi.org/10.3390/sym17101747 - 16 Oct 2025
Cited by 1 | Viewed by 940
Abstract
Symmetry plays a critical role in preserving the structural balance and statistical integrity of datasets, particularly in privacy-preserving machine learning. Differential privacy introduces random noise to individual data points to ensure privacy while maintaining the overall symmetry of statistical distributions. However, excessive noise [...] Read more.
Symmetry plays a critical role in preserving the structural balance and statistical integrity of datasets, particularly in privacy-preserving machine learning. Differential privacy introduces random noise to individual data points to ensure privacy while maintaining the overall symmetry of statistical distributions. However, excessive noise can reduce the utility of data, model accuracy, and computational efficiency. This study proposes a symmetry-preserving optimization framework for differentially private machine learning by integrating feature importance and t-SNE (t-distributed Stochastic Neighbor Embedding), UMAP (Uniform Manifold Approximation and Projection), and PCA (Principal Component Analysis), respectively. Feature importance derived from a random forest selects high-value features to improve data relevance. At the same time, t-SNE preserves geometric symmetry by retaining local and global structures more effectively than PCA or UMAP. Therefore, t-SNE is the best feature extraction method for dimensionality reduction in the proposed scheme. Experimental results demonstrate that the t-SNE method significantly enhances model performance under differential privacy, showing improved accuracy and reduced computational time compared to PCA and UMAP while preserving the underlying symmetry of the data distributions. Full article
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