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Search Results (2,630)

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29 pages, 4030 KiB  
Article
Compact DINO-ViT: Feature Reduction for Visual Transformer
by Didih Rizki Chandranegara, Przemysław Niedziela and Bogusław Cyganek
Electronics 2024, 13(23), 4694; https://doi.org/10.3390/electronics13234694 - 27 Nov 2024
Abstract
Research has been ongoing for years to discover image features that enable their best classification. One of the latest developments in this area is the Self-Distillation with No Labels Vision Transformer—DINO-ViT features. However, even for a single image, their volume is significant. Therefore, [...] Read more.
Research has been ongoing for years to discover image features that enable their best classification. One of the latest developments in this area is the Self-Distillation with No Labels Vision Transformer—DINO-ViT features. However, even for a single image, their volume is significant. Therefore, for this article we proposed to substantially reduce their size, using two methods: Principal Component Analysis and Neighborhood Component Analysis. Our developed methods, PCA-DINO and NCA-DINO, showed a significant reduction in the volume of the features, often exceeding an order of magnitude while maintaining or slightly reducing the classification accuracy, which was confirmed by numerous experiments. Additionally, we evaluated the Uniform Manifold Approximation and Projection (UMAP) method, showing the superiority of the PCA and NCA approaches. Our experiments involving modifications to patch size, attention heads, and noise insertion in DINO-ViT demonstrated that both PCA-DINO and NCA-DINO exhibited reliable accuracy. While NCA-DINO is optimal for high-performance applications despite its higher computational cost, PCA-DINO offers a faster, more resource-efficient solution, depending on the application-specific requirements. The code for our method is available on GitHub. Full article
56 pages, 12429 KiB  
Article
Mitigating Algorithmic Bias in AI-Driven Cardiovascular Imaging for Fairer Diagnostics
by Md Abu Sufian, Lujain Alsadder, Wahiba Hamzi, Sadia Zaman, A. S. M. Sharifuzzaman Sagar and Boumediene Hamzi
Diagnostics 2024, 14(23), 2675; https://doi.org/10.3390/diagnostics14232675 - 27 Nov 2024
Abstract
Background/Objectives: The research addresses algorithmic bias in deep learning models for cardiovascular risk prediction, focusing on fairness across demographic and socioeconomic groups to mitigate health disparities. It integrates fairness-aware algorithms, susceptible carrier-infected-recovered (SCIR) models, and interpretability frameworks to combine fairness with actionable AI [...] Read more.
Background/Objectives: The research addresses algorithmic bias in deep learning models for cardiovascular risk prediction, focusing on fairness across demographic and socioeconomic groups to mitigate health disparities. It integrates fairness-aware algorithms, susceptible carrier-infected-recovered (SCIR) models, and interpretability frameworks to combine fairness with actionable AI insights supported by robust segmentation and classification metrics. Methods: The research utilised quantitative 3D/4D heart magnetic resonance imaging and tabular datasets from the Cardiac Atlas Project’s (CAP) open challenges to explore AI-driven methodologies for mitigating algorithmic bias in cardiac imaging. The SCIR model, known for its robustness, was adapted with the Capuchin algorithm, adversarial debiasing, Fairlearn, and post-processing with equalised odds. The robustness of the SCIR model was further demonstrated in the fairness evaluation metrics, which included demographic parity, equal opportunity difference (0.037), equalised odds difference (0.026), disparate impact (1.081), and Theil Index (0.249). For interpretability, YOLOv5, Mask R-CNN, and ResNet18 were implemented with LIME and SHAP. Bias mitigation improved disparate impact (0.80 to 0.95), reduced equal opportunity difference (0.20 to 0.05), and decreased false favourable rates for males (0.0059 to 0.0033) and females (0.0096 to 0.0064) through balanced probability adjustment. Results: The SCIR model outperformed the SIR model (recovery rate: 1.38 vs 0.83) with a 10% transmission bias impact. Parameters (β=0.5, δ=0.2, γ=0.15) reduced susceptible counts to 2.53×1012 and increased recovered counts to 9.98 by t=50. YOLOv5 achieved high Intersection over Union (IoU) scores (94.8%, 93.7%, 80.6% for normal, severe, and abnormal cases). Mask R-CNN showed 82.5% peak confidence, while ResNet demonstrated a 10.4% accuracy drop under noise. Performance metrics (IoU: 0.910.96, Dice: 0.9410.980, Kappa: 0.95) highlighted strong predictive accuracy and reliability. Conclusions: The findings validate the effectiveness of fairness-aware algorithms in addressing cardiovascular predictive model biases. The integration of fairness and explainable AI not only promotes equitable diagnostic precision but also significantly reduces diagnostic disparities across vulnerable populations. This reduction in disparities is a key outcome of the research, enhancing clinical trust in AI-driven systems. The promising results of this study pave the way for future work that will explore scalability in real-world clinical settings and address limitations such as computational complexity in large-scale data processing. Full article
(This article belongs to the Special Issue Artificial Intelligence in Cardiology Diagnosis )
13 pages, 3195 KiB  
Article
Application and Optimization of a Fast Non-Local Means Noise Reduction Algorithm in Pediatric Abdominal Virtual Monoenergetic Images
by Hajin Kim, Juho Park, Jina Shim and Youngjin Lee
Electronics 2024, 13(23), 4684; https://doi.org/10.3390/electronics13234684 - 27 Nov 2024
Viewed by 65
Abstract
In this study, we applied and optimized a fast non-local means (FNLM) algorithm to reduce noise in pediatric abdominal virtual monoenergetic images (VMIs). To analyze various contrast agent concentrations, we produced contrast agent concentration samples (20, 40, 60, 80, and 100%) and inserted [...] Read more.
In this study, we applied and optimized a fast non-local means (FNLM) algorithm to reduce noise in pediatric abdominal virtual monoenergetic images (VMIs). To analyze various contrast agent concentrations, we produced contrast agent concentration samples (20, 40, 60, 80, and 100%) and inserted them into a phantom model of a one-year-old pediatric patient. Single-energy computed tomography (SECT) and dual-energy computed tomography (DECT) images were acquired from the phantom, and 40 kilo-electron-volt (keV) VMI was acquired based on the DECT images. For the 40 keV VMI, the smoothing factor of the FNLM algorithm was applied from 0.01 to 1.00 in increments of 0.01. We derived the optimized value of the FNLM algorithm based on quantitative evaluation and performed a comparative assessment with SECT, DECT, and a total variation (TV) algorithm. As a result of the analysis, we found that the average contrast to noise ratio (CNR) and coefficient of variation (COV) of each concentration were most improved at a smoothing factor of 0.02. Based on these results, we derived the optimized smoothing factor value of 0.02. Comparative evaluation shows that the optimized FNLM algorithm improves the CNR and COV results by approximately 3.14 and 2.45 times, respectively, compared with the DECT image, and the normalized noise power spectrum result shows a 101 mm2 improvement. The main contribution of this study is to demonstrate the effectiveness of an optimized FNLM algorithm in reducing noise in pediatric abdominal VMI, allowing high-quality images to be acquired while reducing contrast dose. This advancement has significant implications for minimizing the risk of contrast-induced toxicity, especially in pediatric patients. Our approach addresses the problem of limited datasets in pediatric imaging by providing a computationally efficient noise reduction technique and highlights the clinical applicability of the FNLM algorithm. In addition, effective noise reduction enables high-contrast imaging with minimal radiation and contrast exposure, which is expected to be suitable for repeat CT examinations of pediatric liver cancer patients and other abdominal diseases. Full article
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<p>ATOM phantom images for CT image acquisition: (<b>a</b>) ATOM phantom with iodine contrast agents of various concentrations (100, 80, 60, 40, and 20%) and (<b>b</b>) set up phantom positions.</p>
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<p>Computed tomography scans acquired ATOM phantom images: (<b>a</b>) region of interest for quantitative and visual evaluation, (<b>b</b>) single-energy computed tomography image, and (<b>c</b>) dual -energy computed tomography image.</p>
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<p>Quantitative evaluation results according to the smoothing factor of the fast non-local means algorithm in a virtual monoenergetic image: (<b>a</b>) contrast to noise ratio and (<b>b</b>) coefficient of variation.</p>
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<p>Comparative evaluation results of single-energy computed tomography, dual-energy computed tomography, the total variation noise reduction algorithm, and the optimized fast non-local means: (<b>a</b>) contrast to noise ratio and (<b>b</b>) coefficient of variation.</p>
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<p>Comparative evaluation result of normalized noise power spectrum evaluation with single -energy computed tomography, dual-energy computed tomography, the total variation noise reduction algorithm, and the optimized fast non-local means.</p>
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<p>A magnified image of a contrast agent sample at 100% concentration for comparative visual evaluation: (<b>a</b>) single-energy computed tomography image, (<b>b</b>) dual-energy computed tomography image, (<b>c</b>) the total variation noise reduction algorithm, and (<b>d</b>) the optimized fast non-local means noise reduction algorithm.</p>
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17 pages, 554 KiB  
Article
The Quality Urban Label and the 4Q City Model: Levers for Urban Adaptation and Climate Change Mitigation in Mediterranean Cities
by Jordi Mazon
Urban Sci. 2024, 8(4), 228; https://doi.org/10.3390/urbansci8040228 - 27 Nov 2024
Viewed by 107
Abstract
Simple indicators are often used to summarize the complexity of systems or products, commonly through color-coded labels paired with letters. These labels, like those indicating energy efficiency or nutritional ratings, help users quickly understand essential characteristics. Building on this approach, the Quality Urban [...] Read more.
Simple indicators are often used to summarize the complexity of systems or products, commonly through color-coded labels paired with letters. These labels, like those indicating energy efficiency or nutritional ratings, help users quickly understand essential characteristics. Building on this approach, the Quality Urban Label (QUL) has been developed to assess public space adaptation to urban climate change. The QUL utilizes four key indicators, called quality components: air quality (pollutants), noise pollution, thermal comfort, and visual comfort. It ranges from 0 to 25 and is represented by a color and letter code (green, A, ranging from 0 to 2; blue, B, ranging from 6 to 11; orange, C, ranging from 15 to 19; and red, D, ranging from 22 to 25), with green representing better quality and red poorer quality. The QUL aims to evaluate public spaces based on energy consumption reduction, greenhouse gas emissions reduction, and progress toward carbon neutrality. This article explores some ecological and climate benefits of the QUL, especially in warm Mediterranean cities. An objective label that quantifies the alignment of urban public space with climate neutrality has numerous advantages, which are discussed in the article. In addition, it is a key tool for urban project planning, focused on reducing urban social inequalities and promoting a just energy transition of urban public space. Full article
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<p>Classification approach for the Q factors and the general QUL visualization.</p>
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27 pages, 3158 KiB  
Article
Development of HTC-DBSCAN: A Hierarchical Trajectory Clustering Algorithm with Automated Parameter Tuning
by Dae-Han Lee and Joo-Sung Kim
Appl. Sci. 2024, 14(23), 10995; https://doi.org/10.3390/app142310995 - 26 Nov 2024
Viewed by 210
Abstract
Existing route-clustering methods often fail to identify abnormal sections or similarities between routes, mainly when working with large or long datasets. While sub-route clustering can detect regional patterns, it struggles to accurately capture the overall route structure. The present study proposes a new [...] Read more.
Existing route-clustering methods often fail to identify abnormal sections or similarities between routes, mainly when working with large or long datasets. While sub-route clustering can detect regional patterns, it struggles to accurately capture the overall route structure. The present study proposes a new ship route-clustering method that enhances computational efficiency and noise recognition while addressing these limitations. We refined Automatic Identification System data via four data-cleaning processes and applied a statistical distance measurement to assess ship trajectory similarity. Dimensionality reduction was then used to facilitate clustering. The clustering of ship route similarities is non-parametric and can be applied to datasets not separated based on density to find clusters of various densities. Density-Based Spatial Clustering of Applications (DBSCA) applies to many research fields; using the DBSCA with Noise (DBSCAN) algorithm, we propose an improved DBSCAN algorithm that automatically determines the parameters Epsilon and MinPts. In this study, as a core ship route-clustering process, we propose a sub-route clustering process by setting the distance and density of data points to clear standards for re-analysis and completion. The proposed approach demonstrates markedly enhanced clustering performance, offering a more sophisticated and efficient basis for ship route decision-making. Full article
(This article belongs to the Special Issue Advances in Intelligent Maritime Navigation and Ship Safety)
16 pages, 4014 KiB  
Article
Radio Front-End for Frequency Agile Microwave Photonic Radars
by Aljaž Blatnik, Luka Zmrzlak and Boštjan Batagelj
Electronics 2024, 13(23), 4662; https://doi.org/10.3390/electronics13234662 - 26 Nov 2024
Viewed by 217
Abstract
Recent advancements in photonic integrated circuits (PICs) have paved the way for a new era of frequency-agile coherent radar systems. Unlike traditional all-electronic RF radar techniques, fully photonic systems offer superior performance, overcoming bandwidth limitations and noise degradation when operating across S (2–4 [...] Read more.
Recent advancements in photonic integrated circuits (PICs) have paved the way for a new era of frequency-agile coherent radar systems. Unlike traditional all-electronic RF radar techniques, fully photonic systems offer superior performance, overcoming bandwidth limitations and noise degradation when operating across S (2–4 GHz), X (8–12 GHz), and K-band (12–40 GHz) frequencies. They also exhibit excellent phase noise performance, even at frequencies exceeding 20 GHz. However, current state-of-the-art PICs still suffer from high processing losses in the optical domain, necessitating careful design of the electrical RF domain. This study delves into the critical challenges of designing RF front-ends for microwave photonic radars, including stability, noise minimization, and intermodulation distortion reduction. To demonstrate the feasibility of the proposed design, a functional prototype is constructed, achieving a total power gain of 107 dB (radar system at 10 GHz) while minimizing signal noise degradation. Furthermore, a comprehensive demonstration of the RF front-end, encompassing both optical RF signal generation and experimental measurements of a rotor blade’s Doppler fingerprint with 0.5 Hz resolution, validates the proposed system’s performance. Full article
(This article belongs to the Special Issue Radar System and Radar Signal Processing)
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<p>(<b>a</b>) The optical and electrical domains in signal production in a simplified dual-band radar configuration [<a href="#B15-electronics-13-04662" class="html-bibr">15</a>]; DDS: Direct digital synthesis, MLL: Mode-locked laser, ADC: Analog-to-digital converter, MZM: Mach–Zehnder modulator. (<b>b</b>) Signal generation in different stages: (A)—MLL spectrum, (B)—modulated optical spectrum, (C)—PD output RF spectrum.</p>
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<p>Radar and lidar architecture on a single integrated photonic circuit; DAC: Digital-to-analog converter, TX: Transmitter, RX: Receiver, ADC: Analog-to-digital converter.</p>
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<p>Schematic diagram of the output and input RF chains. The values indicated on the transmitting and receiving stages represent worst-case scenarios. The transmitter power is set to enable measurements within a range of several hundred meters, adhering to ISM band limitations. The receiver power is the maximum input power that the amplifier chain can tolerate without incurring significant intermodulation distortion, which would degrade radar measurement performance.</p>
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<p>Experimental setup for generating stable X-band RF signals using optical heterodyne mixing.</p>
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<p>Schematic diagram of the RF front-end architecture.</p>
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<p>(<b>a</b>) S-parameters of a transmitter amplifier chain; (<b>b</b>) S-parameters of the directional couples; (<b>c</b>) S-parameters of the circulator; (<b>d</b>) 1-dB compression point of output amplifiers.</p>
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<p>Experimental setup for RF front-end evaluation.</p>
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<p>Antenna visualization: (<b>a</b>) simulated model; (<b>b</b>) experimental prototype.</p>
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<p>Schematic of a half-patch antenna group, with dimensions in millimeters.</p>
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<p>Comparison of simulated and measured antenna reflection coefficient (S11 parameter).</p>
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<p>Comparison of simulated and measured radiation patterns. (<b>a</b>) Horizontal plane, Directivity: 18.18 dBi; (<b>b</b>) Vertical plane, Directivity: 8.71 dBi.</p>
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<p>(<b>a</b>) Servo motor with a rectangular rotor blade attached to its shaft, serving as a known radar cross-section target. (<b>b</b>) Frequency domain reflection of the target at a constant speed of 26 revolutions per second.</p>
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<p>(<b>a</b>) FFT waterfall illustrating the response as rotor speed increases; (<b>b</b>) A detailed view of the primary frequency response used for UAV classification.</p>
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<p>RF front-end amplifier block diagram. The complex impedance is denoted in the figure by <math display="inline"><semantics> <mrow> <msub> <mi>Z</mi> <mi>x</mi> </msub> </mrow> </semantics></math> (<a href="#electronics-13-04662-t0A1" class="html-table">Table A1</a>).</p>
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<p>(<b>a</b>) Manufactured circuit board without enclosure. (<b>b</b>) PCB layout.</p>
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19 pages, 19517 KiB  
Article
Design and Implementation of the Python-Driven Digital Horn System: A Novel Approach for Electric Vehicle Sound Systems
by Hakan Tekin, Hikmet Karşıyaka and Davut Ertekin
Appl. Sci. 2024, 14(23), 10977; https://doi.org/10.3390/app142310977 - 26 Nov 2024
Viewed by 245
Abstract
Electric and hybrid vehicles are known for their significant reduction in road noise. However, concerns have emerged regarding their silent operation, potentially increasing risks for other road users. To mitigate this, the Acoustic Vehicle Alert System (AVAS) has been mandated by regulations such [...] Read more.
Electric and hybrid vehicles are known for their significant reduction in road noise. However, concerns have emerged regarding their silent operation, potentially increasing risks for other road users. To mitigate this, the Acoustic Vehicle Alert System (AVAS) has been mandated by regulations such as R138 by UNECE in the USA and Europe. This regulation dictates the generation of sound in electric vehicles of categories M and N1 during normal, reverse, and forward motion without the internal combustion engine engaged. Compliance involves meeting specific sound requirements based on vehicle mode and condition. This paper introduces a Python-based approach to designing digital horn sounds, leveraging music theory and signal processing techniques to replace traditional mechanical horns in electric vehicles equipped with AVAS devices. The aim is to offer a practical and efficient means of generating digital horn sounds using this software. The software includes an application capable of producing and customizing horn sounds, with the HornSoundGeneratorGUI class providing a user-friendly interface built with the Tkinter library. To validate the digital horn produced sounds by the software and ensure compliance with AVAS regulations, comprehensive electrical and acoustic tests were conducted in a fully equipped quality laboratory. The results demonstrated that the sound levels achieved met the required 105–107 dB/2 m standard specified by the regulation. Full article
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<p>The harmonic series in musical notation.</p>
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<p>(<b>a</b>) Schematic depiction of the proposed horn generator code and (<b>b</b>) suggested Python code.</p>
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<p>(<b>a</b>) Schematic depiction of the proposed horn generator code and (<b>b</b>) suggested Python code.</p>
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<p>(<b>a</b>) Schematic depiction of the proposed horn generator code and (<b>b</b>) suggested Python code.</p>
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<p>Flow diagram of the horn sound generator.</p>
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<p>Sound design interface.</p>
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<p>Horn sound generator unit.</p>
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<p>A horn sound that has been created and displayed within the graphical interface of the unit.</p>
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<p>dB organization menu.</p>
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<p>EQ Apply Unit main interface.</p>
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<p>The AVAS Sound Flash Unit interface.</p>
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<p>The stage of producing sounds for the Sound Unit through the program: (<b>a</b>) creation of 400 Hz horn sound; (<b>b</b>) creation of 500 Hz horn sound.</p>
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<p>The stage of producing sounds for the Sound Unit through the program: (<b>a</b>) creation of 400 Hz horn sound; (<b>b</b>) creation of 500 Hz horn sound.</p>
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<p>The 400–500 Merge signal, which is created by combining two signals without editing and Downmixing. This merge signal has undergone various mixing processes, including the Downmixing process.</p>
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<p>Block diagram of the Downmixing Method [<a href="#B23-applsci-14-10977" class="html-bibr">23</a>].</p>
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<p>Performing Downmixing editing on the audio file using Vectorscope.</p>
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<p>(<b>a</b>) Notch filter applications; (<b>b</b>) simulated result of the notch filter application.</p>
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<p>(<b>a</b>) Notch filter applications; (<b>b</b>) simulated result of the notch filter application.</p>
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<p>Using the compression technique to adjust dynamic range.</p>
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<p>“Downmixing Merge” file represents the audio signal after arranging operations, and the “400–500 Merge” file represents the audio signal converted to a single channel without arranging.</p>
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<p>Computer-based simulation of the audio file.</p>
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<p>(<b>a</b>) The proposed AVAS test setup, (<b>b</b>) the acoustic room test environment (<b>b</b>), and (<b>c</b>) the real-time FFT graph of the designed sound obtained during experimentation.</p>
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<p>(<b>a</b>) FFT output of the digital horn sound signal of the proposed AVAS device; (<b>b</b>) FFT output of the digital horn sound signal of the AVAS device used in one of the other suppliers.</p>
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21 pages, 3912 KiB  
Article
Advancing Healthcare: Intelligent Speech Technology for Transcription, Disease Diagnosis, and Interactive Control of Medical Equipment in Smart Hospitals
by Ahmed Elhadad, Safwat Hamad, Noha Elfiky, Fulayjan Alanazi, Ahmed I. Taloba and Rasha M. Abd El-Aziz
AI 2024, 5(4), 2497-2517; https://doi.org/10.3390/ai5040121 - 26 Nov 2024
Viewed by 366
Abstract
Intelligent Speech Technology (IST) is revolutionizing healthcare by enhancing transcription accuracy, disease diagnosis, and medical equipment control in smart hospital environments. This study introduces an innovative approach employing federated learning with Multi-Layer Perceptron (MLP) and Gated Recurrent Unit (GRU) neural networks to improve [...] Read more.
Intelligent Speech Technology (IST) is revolutionizing healthcare by enhancing transcription accuracy, disease diagnosis, and medical equipment control in smart hospital environments. This study introduces an innovative approach employing federated learning with Multi-Layer Perceptron (MLP) and Gated Recurrent Unit (GRU) neural networks to improve IST performance. Leveraging the “Medical Speech, Transcription, and Intent” dataset from Kaggle, comprising a variety of speech recordings and corresponding medical symptom labels, noise reduction was applied using a Wiener filter to improve audio quality. Feature extraction through MLP and sequence classification with GRU highlighted the model’s robustness and capacity for detailed medical understanding. The federated learning framework enabled collaborative model training across multiple hospital sites, preserving patient privacy by avoiding raw data exchange. This distributed approach allowed the model to learn from diverse, real-world data while ensuring compliance with strict data protection standards. Through rigorous five-fold cross-validation, the proposed Fed MLP-GRU model demonstrated an accuracy of 98.6%, with consistently high sensitivity and specificity, highlighting its reliable generalization across multiple test conditions. In real-time applications, the model effectively performed medical transcription, provided symptom-based diagnostic insights, and facilitated hands-free control of healthcare equipment, reducing contamination risks and enhancing workflow efficiency. These findings indicate that IST, powered by federated neural networks, can significantly improve healthcare delivery, accuracy in patient diagnosis, and operational efficiency in clinical settings. This research underscores the transformative potential of federated learning and advanced neural networks for addressing pressing challenges in modern healthcare and setting the stage for future innovations in intelligent medical technology. Full article
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<p>Proposed Fed MLP GRU Methodology for Intelligent Speech Technology in Smart Hospitals.</p>
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<p>Architecture of MLP.</p>
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<p>Architecture of GRU.</p>
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<p>Architecture of Federated Learning.</p>
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<p>Comparison of Training and Validation Accuracies Across Different Neural Network Models.</p>
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<p>Training and Testing Loss Curves. (<b>A</b>) Scenario A. (<b>B</b>) Scenario B. (<b>C</b>) Scenario C. (<b>D</b>) Federated: The federated model’s performance.</p>
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<p>ROC Curves for FED LSTM Model across Different Sample Sizes.</p>
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<p>Model Performance Convergence across Different Datasets and Thresholds.</p>
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<p>Performance Evaluation for Different Methods.</p>
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19 pages, 5451 KiB  
Article
Joint Battery State of Charge Estimation Method Based on a Fractional-Order Model with an Improved Unscented Kalman Filter and Extended Kalman Filter for Full Parameter Updating
by Jingjin Wu, Yuhao Li, Qian Sun, Yu Zhu, Jiejie Xing and Lina Zhang
Fractal Fract. 2024, 8(12), 695; https://doi.org/10.3390/fractalfract8120695 - 26 Nov 2024
Viewed by 232
Abstract
State estimation of batteries is crucial in battery management systems (BMSs), particularly for accurately predicting the state of charge (SOC), which ensures safe and efficient battery operation. This paper proposes a joint SOC estimation method based on a fractional-order model, utilizing a multi-innovation [...] Read more.
State estimation of batteries is crucial in battery management systems (BMSs), particularly for accurately predicting the state of charge (SOC), which ensures safe and efficient battery operation. This paper proposes a joint SOC estimation method based on a fractional-order model, utilizing a multi-innovation full-tracking adaptive unscented Kalman filter (FOMIST-AUKF-EKF) combined with an extended Kalman filter (EKF) for online parameter updates. The fractional-order model more effectively represents the battery’s dynamic characteristics compared to traditional integer-order models, providing a more precise depiction of electrochemical processes and nonlinear behaviors. It offers superior modeling for long-memory effects, complex dynamics, and aging processes, enhancing adaptability to aging and nonlinear characteristics. Comparative results indicate a maximum end-voltage error reduction of 0.002 V with the fractional-order model compared to the integer-order model. The multi-innovation technology increases filter robustness against noise by incorporating multiple historical observations, while the full-tracking adaptive strategy dynamically adjusts the noise covariance matrix based on real-time data, thus enhancing estimation accuracy. Furthermore, EKF updates battery parameters (e.g., resistance and capacitance) in real time, correcting model errors and improving SOC prediction accuracy. Simulation and experimental validation show that the proposed method significantly outperforms traditional UKF-based SOC estimation techniques in accuracy, stability, and adaptability. Specifically, under varying conditions such as NEDC and DST, the method demonstrates excellent robustness and practicality, with maximum SOC estimation errors of 0.27% and 0.67%, respectively. Full article
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<p>Fractional-order second-order RC model.</p>
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<p>HPPC impulse test current test. (<b>a</b>) Current curve; (<b>b</b>) SOC curve.</p>
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<p>Model identification results. (<b>a</b>) End voltage comparison; (<b>b</b>) end voltage error comparison.</p>
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<p>FOMIST-AUKF-EKF process.</p>
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<p>Battery experiment platform.</p>
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<p>(<b>a</b>) Current map of NEDC working condition; (<b>b</b>) current map of DST working end.</p>
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<p>NEDC operating conditions. (<b>a</b>) SOC comparison; (<b>b</b>) SOC error comparison; (<b>c</b>) end voltage comparison; (<b>d</b>) end voltage error.</p>
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<p>(<b>a</b>) SOC comparison; (<b>b</b>) SOC error comparison; (<b>c</b>) terminal voltage comparison; (<b>d</b>) terminal voltage error under DST operating conditions.</p>
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<p>Change in ohmic resistance <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Parameter identification and update results of second-order RC network. (<b>a</b>) Change in ohmic resistance <span class="html-italic">R</span><sub>1</sub> (<b>b</b>) Change in ohmic resistance <span class="html-italic">R</span><sub>2</sub> (<b>c</b>) Change in ohmic resistance C<sub>1</sub> (<b>d</b>) Change in ohmic resistance C<sub>2</sub>.</p>
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<p>(<b>a</b>) Fractional-order parameters <math display="inline"><semantics> <mrow> <mi>α</mi> </mrow> </semantics></math> and (<b>b</b>) identification results <math display="inline"><semantics> <mrow> <mi>β</mi> </mrow> </semantics></math>.</p>
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8 pages, 3626 KiB  
Communication
Analysis and Design of Low-Noise Radio-Frequency Power Amplifier Supply Modulator for Frequency Division Duplex Cellular Systems
by Ji-Seon Paek
Electronics 2024, 13(23), 4635; https://doi.org/10.3390/electronics13234635 - 25 Nov 2024
Viewed by 323
Abstract
This paper describes an analysis of power supply rejection and noise improvement techniques for an envelope-tracking power amplifier. Although the envelope-tracking technique improves efficiency, its power supply rejection ratio is much lower than that of average power tracking or a fixed-supply power amplifier. [...] Read more.
This paper describes an analysis of power supply rejection and noise improvement techniques for an envelope-tracking power amplifier. Although the envelope-tracking technique improves efficiency, its power supply rejection ratio is much lower than that of average power tracking or a fixed-supply power amplifier. In FDD systems with the envelope-tracking technique, the low power supply rejection ratio generates much output noise in the RX band and degrades the receiver’s sensitivity. An SM is designed by using a 130 nm CMOS process, and the chip die area is 2 × 2 mm2 with a 25-pin wafer-level chip-scale package. The designed SM achieved peak efficiencies of 78–83% for LTE signals with a 5.8 dB PAPR and various channel bandwidths. For the low-output-noise-supply modulator, noise reduction techniques using resonant-frequency tuning and a notch filter are employed, and the measured results show maximum 1.8/5/5.3/3.8/3 dB noise reduction in LTE bands B17/B5/B2/B3/B7, respectively. Full article
(This article belongs to the Special Issue Millimeter-Wave/Terahertz Integrated Circuit Design)
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<p>RX-band noise transfer from ET PA in FDD system.</p>
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<p>PSRR of PA in linear and saturated regions near P1dB.</p>
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<p>Simulated gain and PSRRSSB curves of APT and ET.</p>
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<p>Simulated PAE, gain, and calculated PSRRSSB curves of PA at each supply voltage (1 V to 3.5 V with 0.5 V step).</p>
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<p>Average PAE, gain, output power, and PSRRSSB according to saturation level in ET operation.</p>
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<p>Block diagram of the hybrid switching supply modulator.</p>
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<p>SM output open-loop noise model and noise contribution depending on frequency offset.</p>
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<p>Proposed noise reduction techniques: (<b>a</b>) resonant-frequency tuning (RFT); (<b>b</b>) notch filter.</p>
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<p>PSRR measurement setup and chip photograph.</p>
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<p>Measured output noise of the designed supply modulator in the cases of reference sensitivity QPSK PREFSENS (Table 7.3.1-1 in [<a href="#B5-electronics-13-04635" class="html-bibr">5</a>]) for each LTE band.</p>
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15 pages, 7377 KiB  
Article
Application of Adaptive Search Window-Based Nonlocal Total Variation Filter in Low-Dose Computed Tomography Images: A Phantom Study
by Hajin Kim, Bo Kyung Cha, Kyuseok Kim and Youngjin Lee
Appl. Sci. 2024, 14(23), 10886; https://doi.org/10.3390/app142310886 - 24 Nov 2024
Viewed by 394
Abstract
Computed tomography (CT) imaging using low-dose radiation effectively reduces radiation exposure; however, it introduces noise amplification in the resulting image. This study models an adaptive nonlocal total variation (NL-TV) algorithm that efficiently reduces noise in X-ray-based images and applies it to low-dose CT [...] Read more.
Computed tomography (CT) imaging using low-dose radiation effectively reduces radiation exposure; however, it introduces noise amplification in the resulting image. This study models an adaptive nonlocal total variation (NL-TV) algorithm that efficiently reduces noise in X-ray-based images and applies it to low-dose CT images. In this study, an AAPM CT performance phantom is used, and the resulting image is obtained by applying an annotation filter and a high-pitch protocol. The adaptive NL-TV filter was designed by applying the optimal window value calculated by confirming the difference between Gaussian filtering and the basic NL-TV approach. For quantitative image quality evaluation parameters, contrast-to-noise ratio (CNR), coefficient of variation (COV), and sigma value were used to confirm the noise reduction effectiveness and spatial resolution value. The CNR and COV values in low-dose CT images using the adaptive NL-TV filter, which performed an optimization process, improved by approximately 1.29 and 1.45 times, respectively, compared with conventional NL-TV. In addition, the adaptive NL-TV filter was able to acquire spatial resolution data that were similar to a CT image without applying noise reduction. In conclusion, the proposed NL-TV filter is feasible and effective in improving the quality of low-dose CT images. Full article
(This article belongs to the Special Issue Advances and Applications of Medical Imaging Physics)
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<p>Simplified scheme of adaptive search window NL-TV filter using the gray-level difference (GLD) in low-dose CT.</p>
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<p>(<b>a</b>) Low-dose CT image acquired by marking ROIs for CNR and COV evaluation. Resulting images obtained by applying (<b>b</b>) TV, (<b>c</b>) NL-TV, and (<b>d</b>) adaptive NL-TV filters to the low-dose CT image in (<b>a</b>). The proposed adaptive NL-TV filter was effectively applied in the red arrow area (smallest diameter hole).</p>
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<p>(<b>a</b>) CNR and (<b>b</b>) COV graphs measured from the resulting image after the application of each filtering method to the acquired low-dose CT image. In both the CNR and COV result graphs, the excellent value was derived from the adaptive NL-TV filter regardless of the hole diameter.</p>
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<p>Images obtained by applying low-dose CT and filters to evaluate spatial resolution. In the acquired low-dose CT image (<b>a</b>), the boundaries of the holes are clearly observed, but the overall noise level appears to have increased (the AB line indicates the position for measuring the spread function.). As a result of applying (<b>b</b>) TV, (<b>c</b>) NL-TV, and (<b>d</b>) adaptive NL-TV filters to (<b>a</b>) image, it was confirmed that the overall noise level was reduced in the images. As a result of applying TV and NL-TV filters in the area indicated by the red arrow in (<b>d</b>), we were able to observe that the boundary surface was more clearly distinguished than in the image.</p>
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<p>(<b>a</b>) ESF and (<b>b</b>) normalized LSF graph results measured at the AB line marked in red in <a href="#applsci-14-10886-f004" class="html-fig">Figure 4</a>a. ESF and LSF graphs of almost similar shapes were observed in the unprocessed low-dose CT image and the image processed using the NL-TV filter.</p>
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<p>Sigma value results graph according to each filtering method. The sigma value calculated from LSF was derived from the best value in the unprocessed low-dose CT image and the image processed using the adaptive NL-TV filter method.</p>
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20 pages, 5551 KiB  
Article
Multi-Level Decomposition and Interpretability-Enhanced Air Conditioning Load Forecasting Study
by Xinting Yang, Ling Zhang, Hong Zhao, Wenhua Zhang, Chuan Long, Gang Wu, Junhao Zhao and Xiaodong Shen
Energies 2024, 17(23), 5881; https://doi.org/10.3390/en17235881 - 23 Nov 2024
Viewed by 245
Abstract
This study seeks to improve the accuracy of air conditioning load forecasting to address the challenges of load management in power systems during high-temperature periods in the summer. Given the limitations of traditional forecasting models in capturing different frequency components and noise within [...] Read more.
This study seeks to improve the accuracy of air conditioning load forecasting to address the challenges of load management in power systems during high-temperature periods in the summer. Given the limitations of traditional forecasting models in capturing different frequency components and noise within complex load sequences, this paper proposes a multi-level decomposition forecasting model using complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), sample entropy (SE), variational mode decomposition (VMD), and long short-term memory (LSTM). First, CEEMDAN is used for the preliminary decomposition of the raw air-conditioning load series, with modal components aggregated by sample entropy to generate high-, medium-, and low-frequency subsequences. VMD then performs a secondary decomposition on the high-frequency subsequence to reduce its complexity, while LSTM is applied to each subsequence for prediction. The final prediction result of the air-conditioning load is obtained through reconstruction. To validate model performance, this paper uses air-conditioning load data from Nanchong City and Sichuan Province, for experimental analysis. Results show that the proposed method significantly outperforms the LSTM model without decomposition and other benchmark models in prediction accuracy, with the Root Mean Square Error (RMSE) reductions ranging from 40.26% to 74.18% and the Modified Mean Absolute Percentage Error (MMAPE) reductions from 37.75% to 73.41%. By employing the SHAP (Shapley additive explanations) method for both global and local interpretability, the model reveals the influence of key factors, such as historical load and temperature, on load forecasting. The decomposition and aggregation approach introduced in this paper substantially enhances forecasting accuracy, providing a scientific foundation for power system load management and dispatch. Full article
(This article belongs to the Topic Short-Term Load Forecasting)
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<p>Overall prediction framework.</p>
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<p>LSTM structure diagram.</p>
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<p>Air conditioning load curve.</p>
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<p>CEEMDAN decomposition results.</p>
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<p>Sample entropy results.</p>
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<p>Sample entropy integration results.</p>
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<p>VMD secondary decomposition results of Co-IMF1.</p>
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<p>Comparison of prediction results.</p>
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<p>Prediction results on the test set.</p>
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<p>Global interpretability of features.</p>
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<p>Local interpretability of features.</p>
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13 pages, 9768 KiB  
Communication
Reduced Gaussian Kernel Filtered-x LMS Algorithm with Historical Error Correction for Nonlinear Active Noise Control
by Jinhua Ku, Hongyu Han, Weixi Zhou, Hong Wang and Sheng Zhang
Entropy 2024, 26(12), 1010; https://doi.org/10.3390/e26121010 - 22 Nov 2024
Viewed by 283
Abstract
This paper introduces a reduced Gaussian kernel filtered-x least mean square (RGKxLMS) algorithm for a nonlinear active noise control (NANC) system. This algorithm addresses the computational and storage challenges posed by the traditional kernel (i.e., KFxLMS) algorithm. Then, we analyze the mean weight [...] Read more.
This paper introduces a reduced Gaussian kernel filtered-x least mean square (RGKxLMS) algorithm for a nonlinear active noise control (NANC) system. This algorithm addresses the computational and storage challenges posed by the traditional kernel (i.e., KFxLMS) algorithm. Then, we analyze the mean weight behavior and computational complexity of the RGKxLMS, demonstrating its reduced complexity compared to existing kernel filtering methods and its mean stable performance. To further enhance noise reduction, we also develop the historical error correction RGKxLMS (HECRGKxLMS) algorithm, incorporating historical error information. Finally, the effectiveness of the proposed algorithms is validated, using Lorenz chaotic noise, non-stationary noise environments, and factory noise. Full article
(This article belongs to the Section Multidisciplinary Applications)
32 pages, 6565 KiB  
Article
Sparse Feature-Weighted Double Laplacian Rank Constraint Non-Negative Matrix Factorization for Image Clustering
by Hu Ma, Ziping Ma, Huirong Li and Jingyu Wang
Mathematics 2024, 12(23), 3656; https://doi.org/10.3390/math12233656 - 22 Nov 2024
Viewed by 257
Abstract
As an extension of non-negative matrix factorization (NMF), graph-regularized non-negative matrix factorization (GNMF) has been widely applied in data mining and machine learning, particularly for tasks such as clustering and feature selection. Traditional GNMF methods typically rely on predefined graph structures to guide [...] Read more.
As an extension of non-negative matrix factorization (NMF), graph-regularized non-negative matrix factorization (GNMF) has been widely applied in data mining and machine learning, particularly for tasks such as clustering and feature selection. Traditional GNMF methods typically rely on predefined graph structures to guide the decomposition process, using fixed data graphs and feature graphs to capture relationships between data points and features. However, these fixed graphs may limit the model’s expressiveness. Additionally, many NMF variants face challenges when dealing with complex data distributions and are vulnerable to noise and outliers. To overcome these challenges, we propose a novel method called sparse feature-weighted double Laplacian rank constraint non-negative matrix factorization (SFLRNMF), along with its extended version, SFLRNMTF. These methods adaptively construct more accurate data similarity and feature similarity graphs, while imposing rank constraints on the Laplacian matrices of these graphs. This rank constraint ensures that the resulting matrix ranks reflect the true number of clusters, thereby improving clustering performance. Moreover, we introduce a feature weighting matrix into the original data matrix to reduce the influence of irrelevant features and apply an L2,1/2 norm sparsity constraint in the basis matrix to encourage sparse representations. An orthogonal constraint is also enforced on the coefficient matrix to ensure interpretability of the dimensionality reduction results. In the extended model (SFLRNMTF), we introduce a double orthogonal constraint on the basis matrix and coefficient matrix to enhance the uniqueness and interpretability of the decomposition, thereby facilitating clearer clustering results for both rows and columns. However, enforcing double orthogonal constraints can reduce approximation accuracy, especially with low-rank matrices, as it restricts the model’s flexibility. To address this limitation, we introduce an additional factor matrix R, which acts as an adaptive component that balances the trade-off between constraint enforcement and approximation accuracy. This adjustment allows the model to achieve greater representational flexibility, improving reconstruction accuracy while preserving the interpretability and clustering clarity provided by the double orthogonality constraints. Consequently, the SFLRNMTF approach becomes more robust in capturing data patterns and achieving high-quality clustering results in complex datasets. We also propose an efficient alternating iterative update algorithm to optimize the proposed model and provide a theoretical analysis of its performance. Clustering results on four benchmark datasets demonstrate that our method outperforms competing approaches. Full article
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<p>Construction of optimal graph.</p>
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<p>Clustering ACC on the dataset JAFFE.</p>
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<p>Clustering NMI on the dataset JAFFE.</p>
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<p>Clustering ACC on the dataset COIL20.</p>
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<p>Clustering NMI on the dataset COIL20.</p>
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<p>Clustering ACC on the dataset UMIST.</p>
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<p>Clustering NMI on the dataset UMIST.</p>
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<p>Clustering ACC on the dataset YaleB.</p>
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<p>Clustering NMI on the dataset YaleB.</p>
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<p>Two-dimensional representations of UMIST dataset using t-SNE on the results of different methods.</p>
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<p>Two-dimensional representations of UMIST dataset using t-SNE on the results of different methods.</p>
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<p>Two-dimensional representations of COIL20 dataset using t-SNE on the results of different methods.</p>
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<p>Two-dimensional representations of COIL20 dataset using t-SNE on the results of different methods.</p>
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<p>The ACC and NMI of SFLRNMF with different <span class="html-italic">α</span> and <span class="html-italic">β</span> on JAFFE.</p>
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<p>The ACC and NMI of SFLRNMF with different <span class="html-italic">α</span> and θ on JAFFE.</p>
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<p>The ACC and NMI of SFLRNMF with different <math display="inline"><semantics> <mrow> <mi>θ</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>β</mi> </mrow> </semantics></math> on JAFFE.</p>
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<p>The ACC and NMI of SFLRNMTF with different <math display="inline"><semantics> <mrow> <mi>θ</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>β</mi> </mrow> </semantics></math> on JAFFE.</p>
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<p>The ACC and NMI of SFLRNMTF with different <math display="inline"><semantics> <mrow> <mi>θ</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>α</mi> </mrow> </semantics></math> on JAFFE.</p>
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<p>The ACC and NMI of SFLRNMTF with different <math display="inline"><semantics> <mrow> <mi>β</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>α</mi> </mrow> </semantics></math> on JAFFE.</p>
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<p>Convergence curves of the SFLRNMF algorithm on four datasets.</p>
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<p>Convergence curves of the SFLRNMTF algorithm on four datasets.</p>
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34 pages, 7354 KiB  
Article
Analysis of High-Frequency Sea-State Variability Using SWOT Nadir Measurements and Application to Altimeter Sea State Bias Modelling
by Estelle Mazaleyrat, Ngan Tran, Laïba Amarouche, Douglas Vandemark, Hui Feng, Gérald Dibarboure and François Bignalet-Cazalet
Remote Sens. 2024, 16(23), 4361; https://doi.org/10.3390/rs16234361 - 22 Nov 2024
Viewed by 339
Abstract
The 1-day fast-sampling orbit phase of the Surface Water Ocean Topography (SWOT) satellite mission provides a unique opportunity to analyze high-frequency sea-state variability and its implications for altimeter sea state bias (SSB) model development. Time series with 1-day repeat sampling of sea-level anomaly [...] Read more.
The 1-day fast-sampling orbit phase of the Surface Water Ocean Topography (SWOT) satellite mission provides a unique opportunity to analyze high-frequency sea-state variability and its implications for altimeter sea state bias (SSB) model development. Time series with 1-day repeat sampling of sea-level anomaly (SLA) and SSB input parameters—comprising the significant wave height (SWH), wind speed (WS), and mean wave period (MWP)—are constructed using SWOT’s nadir altimeter data. The analyses corroborate the following key SSB modelling assumption central to empirical developments: the SLA noise due to all factors, aside from sea state change, is zero-mean. Global variance reduction tests on the SSB model’s performance using corrected SLA differences show that correction skill estimation using a specific (1D, 2D, or 3D) SSB model is unstable when using short time difference intervals ranging from 1 to 5 days, reaching a stable asymptotic limit after 5 days. It is proposed that this result is related to the temporal auto- and cross-correlations associated with the SSB model’s input parameters; the present study shows that SSB wind-wave input measurements take time (typically 1–4 days) to decorrelate in any given region. The latter finding, obtained using unprecedented high-frequency satellite data from multiple ocean basins, is shown to be consistent with estimates from an ocean wave model. The results also imply that optimal time-differencing (i.e., >4 days) should be considered when building SSB model data training sets. The SWOT altimeter data analysis of the temporal cross-correlations also permits an evaluation of the relationships between the SSB input parameters (SWH, WS, and MWP), where distinct behaviors are found in the swell- and wind-sea-dominated areas, and associated time scales are less than or on the order of 1 day. Finally, it is demonstrated that computing cross-correlations between the SLA (with and without SSB correction) and the SSB input parameters offers an additional tool for evaluating the relevance of candidate SSB input parameters, as well as for assessing the performance of SSB correction models, which, so far, mainly rely on the reduction in the variance of the differences in the SLA at crossover points. Full article
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<p>(<b>a</b>) Global means of the SWOT nadir SLA collinear differences as a function of the time interval considered for the SLA differences. The examined SLA types are SLA_uncorr (no SSB applied), SLA_corr1D (application of SSB = −3.2% SWH), SLA_corr2D (with J3 GDR-F 2D SSB table), and SLA_corr3D (with J3 GDR-F 3D SSB table); (<b>b</b>) same as in (<b>a</b>) but for the global variance; (<b>c</b>) global variance reduction as a function of the considered time interval obtained when one computes var(∆SLA_corr) minus var(∆SLA_uncorr). Negative values indicate an improvement in the SLA precision resulting from the application of the SSB correction. Higher reduction magnitudes indicate greater model skill.</p>
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<p>(<b>a</b>) Map showing the two locations from SWOT nadir pass 28 (40°S and 20°N) associated with the ACFs shown in (<b>b</b>,<b>c</b>); (<b>b</b>) autocorrelation functions (with associated 95% confidence intervals as dotted lines) of the five considered SSB input-related parameters at the 40°S location; (<b>c</b>) same as in (<b>b</b>) but for the 20°N location.</p>
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<p>Maps of the decorrelation time scales: (<b>a</b>) SWH_alti; (<b>b</b>) WS_alti; (<b>c</b>) MWP_model.</p>
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<p>Decorrelation time scales of SWH_alti with respect to the mean sea-state conditions covered by the SWOT fast-sampling nadir dataset: (<b>a</b>–<b>c</b>) density plots of the decorrelation time scales with respect to (<b>a</b>) (mean SWH_alti and mean WS_alti); (<b>b</b>) (mean_SWH_alti and mean MWP_model); (<b>c</b>) (mean MWP_model and mean WS_alti). The 3D space associated with the mean sea-state conditions (SWH, WS, and MWP) was binned, and the number of occurrences (i.e., count) pertaining to a specific bin is color-coded. (<b>d</b>–<b>f</b>) Same as in (<b>a</b>–<b>c</b>), except the decorrelation time scale values (rather than the number of their occurrences) are color-coded.</p>
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<p>Average latitudinal variations (in red) and associated dispersions (in blue) of the decorrelation time scales of the five considered SSB input-related parameters. The zonal averages were computed using 3° latitudinal bands, and the displayed dispersions correspond to <math display="inline"><semantics> <mrow> <mo>±</mo> </mrow> </semantics></math> one standard deviation.</p>
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<p>Average latitudinal variations (in red) and associated dispersions (in blue) of the mean values of the five considered SSB input-related parameters. The zonal averages were computed using 3° latitudinal bands, and the displayed dispersions correspond to <math display="inline"><semantics> <mrow> <mo>±</mo> </mrow> </semantics></math> one standard deviation.</p>
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<p>Cross-correlation functions (with the associated 95% confidence intervals as dotted lines) of the three considered SSB input-related parameters combinations at the (<b>a</b>) 40°S and (<b>b</b>) 20°N locations from SWOT nadir pass 28, as shown in <a href="#remotesensing-16-04361-f002" class="html-fig">Figure 2</a>a. For each of the three (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math>) combinations, the correlations associated with positive time delays inform on whether <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> is a predictor of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math>, whereas the correlations at negative lags indicate whether <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> is a predictor of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Maps of cross-correlation values for the three SSB input-related combinations mentioned in <a href="#remotesensing-16-04361-t002" class="html-table">Table 2</a> at time delays equal to (<b>a</b>–<b>c</b>) 0 day and (<b>d</b>–<b>f</b>) +1 day. Non-significant correlations (i.e., falling within the 95% confidence interval) were removed from all maps, leaving an empty [−0.2, 0.2] range.</p>
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<p>Maps of the cross-correlation values for the six (SSB input-related parameter, SLA) combinations mentioned in <a href="#remotesensing-16-04361-t003" class="html-table">Table 3</a> at 0 day. The maps shown in (<b>a</b>–<b>c</b>) (resp., (<b>d</b>–<b>f</b>)) are associated with combinations involving SLA_uncorr (resp., SLA_corr2D). Non-significant correlations (i.e., falling within the 95% confidence interval) were removed from all maps, leaving an empty [−0.2, 0.2] range.</p>
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<p>Comparison of the matching between the DTs of SWH_alti and SWH_model determined using the (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>L</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>L</mi> </mrow> <mrow> <mi>h</mi> <mi>a</mi> <mi>l</mi> <mi>f</mi> </mrow> </msub> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>L</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>, and (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>L</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> definitions. For each plot, a linear regression is shown in red (with the associated fitted linear relationship and the Pearson correlation coefficient indicated in the top left corner) and the bisector in blue.</p>
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<p>Maps of decorrelation time scales for SWH_alti computed using the (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>L</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>L</mi> </mrow> <mrow> <mi>h</mi> <mi>a</mi> <mi>l</mi> <mi>f</mi> </mrow> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>L</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>L</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> definitions.</p>
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<p>Autocorrelation maps of WS_alti: (<b>a</b>) +1 day; (<b>b</b>) +2 days; (<b>c</b>) +3 days.</p>
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