Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (155)

Search Parameters:
Keywords = coordinate descent

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
24 pages, 3484 KB  
Article
A Method for Maximizing UAV Deployment and Reducing Energy Consumption Based on Strong Weiszfeld and Steepest Descent with Goldstein Algorithms
by Qian Zeng, Ziyao Chen, Chuanqi Li, Dong Chen, Shengbang Zhou, Geng Wei and Thioanh Bui
Appl. Sci. 2025, 15(17), 9798; https://doi.org/10.3390/app15179798 - 6 Sep 2025
Viewed by 309
Abstract
Unmanned Aerial Vehicles (UAVs) play a crucial role in the continuous monitoring and coordination of disaster relief operations, providing real-time information that aids in decision-making and resource allocation. However, optimizing the deployment of multi-UAV systems in disaster-stricken areas presents a significant challenge. This [...] Read more.
Unmanned Aerial Vehicles (UAVs) play a crucial role in the continuous monitoring and coordination of disaster relief operations, providing real-time information that aids in decision-making and resource allocation. However, optimizing the deployment of multi-UAV systems in disaster-stricken areas presents a significant challenge. This challenge arises due to conflicting objectives, such as maximizing coverage while minimizing energy consumption, critical to ensuring prolonged operational capability in dynamic and unpredictable environments. To address these challenges, this paper proposes a novel successive deployment method specifically designed for optimizing UAV placements in complex disaster relief scenarios. The overall optimization problem is decomposed into two NP-hard subproblems: the coverage problem and the Energy Consumption (EC) problem. To achieve maximum coverage of the affected area, we employ the Strong Weiszfeld (SW) algorithm to determine optimal UAV placement. Simultaneously, to minimize energy consumption while maintaining optimal coverage performance, we utilize the Steepest Descent with Goldstein (SDG) algorithm. This dual-algorithmic approach is tailored to balance the trade-offs between wide-area coverage and energy efficiency. We validate the effectiveness of the proposed SW + SDG method by comparing its performance against traditional deployment strategies across multiple scenarios. Experimental results demonstrate that our approach significantly reduces energy consumption while maintaining extensive coverage, and outperforms conventional algorithms. This not only ensures a more sustainable and long-lasting operational network but also enhances deployment efficiency and stability. These findings suggest that the SW + SDG algorithm is a robust and versatile solution for optimizing multi-UAV deployments in dynamic, resource-constrained environments, providing a balanced approach to coverage and energy efficiency. Full article
Show Figures

Figure 1

18 pages, 2138 KB  
Article
Weighted STAP Algorithm Based on the Greedy Block Coordinate Descent Method
by Zhiqi Gao, Na Yang, Zhixia Wu, Wei Xu and Weixian Tan
Electronics 2025, 14(17), 3432; https://doi.org/10.3390/electronics14173432 - 28 Aug 2025
Viewed by 297
Abstract
Space–time adaptive processing (STAP) based on sparse recovery (SR-STAP) has demonstrated remarkable clutter suppression performance under insufficient sample conditions. However, the main aim of sparse recovery is to solve the norm minimization problem. To this end, this study proposes a weighted STAP algorithm [...] Read more.
Space–time adaptive processing (STAP) based on sparse recovery (SR-STAP) has demonstrated remarkable clutter suppression performance under insufficient sample conditions. However, the main aim of sparse recovery is to solve the norm minimization problem. To this end, this study proposes a weighted STAP algorithm based on a greedy block coordinate descent method to address the problems of slow convergence speed and insufficient estimation accuracy in the existing l2,1-norm minimization methods. First, the weights are estimated using the multiple signal classification (MUSIC) algorithm. Then, a greedy block selection rule that favors sparsity is used, prioritizing the update of the weighted block that has the greatest impact on sparsity. Although the proposed algorithm in this paper is greedy in nature, it is globally convergent. Finally, the accuracy of clutter covariance matrix estimation and the convergence speed of the SR-STAP algorithm are enhanced by reasonably estimating the noise power and selecting appropriate regularization parameters. The results of simulation experiments indicate that the proposed algorithm can effectively suppress clutter ridge expansion, achieving excellent clutter suppression and target detection performance compared with the existing methods, as well as satisfactory convergence properties. Full article
Show Figures

Figure 1

42 pages, 5531 KB  
Article
Preliminary Analysis and Proof-of-Concept Validation of a Neuronally Controlled Visual Assistive Device Integrating Computer Vision with EEG-Based Binary Control
by Preetam Kumar Khuntia, Prajwal Sanjay Bhide and Pudureddiyur Venkataraman Manivannan
Sensors 2025, 25(16), 5187; https://doi.org/10.3390/s25165187 - 21 Aug 2025
Viewed by 741
Abstract
Contemporary visual assistive devices often lack immersive user experience due to passive control systems. This study introduces a neuronally controlled visual assistive device (NCVAD) that aims to assist visually impaired users in performing reach tasks with active, intuitive control. The developed NCVAD integrates [...] Read more.
Contemporary visual assistive devices often lack immersive user experience due to passive control systems. This study introduces a neuronally controlled visual assistive device (NCVAD) that aims to assist visually impaired users in performing reach tasks with active, intuitive control. The developed NCVAD integrates computer vision, electroencephalogram (EEG) signal processing, and robotic manipulation to facilitate object detection, selection, and assistive guidance. The monocular vision-based subsystem implements the YOLOv8n algorithm to detect objects of daily use. Then, audio prompting conveys the detected objects’ information to the user, who selects their targeted object using a voluntary trigger decoded through real-time EEG classification. The target’s physical coordinates are extracted using ArUco markers, and a gradient descent-based path optimization algorithm (POA) guides a 3-DoF robotic arm to reach the target. The classification algorithm achieves over 85% precision and recall in decoding EEG data, even with coexisting physiological artifacts. Similarly, the POA achieves approximately 650 ms of actuation time with a 0.001 learning rate and 0.1 cm2 error threshold settings. In conclusion, the study also validates the preliminary analysis results on a working physical model and benchmarks the robotic arm’s performance against human users, establishing the proof-of-concept for future assistive technologies integrating EEG and computer vision paradigms. Full article
(This article belongs to the Section Intelligent Sensors)
Show Figures

Figure 1

20 pages, 2661 KB  
Article
Cooperative Jamming for RIS-Assisted UAV-WSN Against Aerial Malicious Eavesdropping
by Juan Li, Gang Wang, Weijia Wu, Jing Zhou, Yingkun Liu, Yangqin Wei and Wei Li
Drones 2025, 9(6), 431; https://doi.org/10.3390/drones9060431 - 13 Jun 2025
Viewed by 655
Abstract
As the low-altitude economy undergoes rapid growth, unmanned aerial vehicles (UAVs) have served as mobile sink nodes in wireless sensor networks (WSNs), significantly enhancing data collection efficiency. However, the open nature of wireless channels and spectrum scarcity pose severe challenges to data security, [...] Read more.
As the low-altitude economy undergoes rapid growth, unmanned aerial vehicles (UAVs) have served as mobile sink nodes in wireless sensor networks (WSNs), significantly enhancing data collection efficiency. However, the open nature of wireless channels and spectrum scarcity pose severe challenges to data security, particularly when legitimate UAVs (UAV-L) receive confidential information from ground sensor nodes (SNs), which is vulnerable to interception by eavesdropping UAVs (UAV-E). In response to this challenge, this study presents a cooperative jamming (CJ) scheme for Reconfigurable Intelligent Surfaces (RIS)-assisted UAV-WSN to combat aerial malicious eavesdropping. The multi-dimensional optimization problem (MDOP) of system security under quality of service (QoS) constraints is addressed by collaboratively optimizing the transmit power (TP) of SNs, the flight trajectories (FT) of the UAV-L, the frame length (FL) of time slots, and the phase shift matrix (PSM) of the RIS. To address the challenge, we put forward a Cooperative Jamming Joint Optimization Algorithm (CJJOA) scheme. Specifically, we first apply the block coordinate descent (BCD) to decompose the original MDOP into several subproblems. Then, each subproblem is convexified by successive convex approximation (SCA). The numerical results demonstrate that the designed algorithm demonstrates extremely strong stability and reliability during the convergence process. At the same time, it shows remarkable advantages compared with traditional benchmark testing methods, effectively and practically enhancing security. Full article
(This article belongs to the Special Issue UAV-Assisted Mobile Wireless Networks and Applications)
Show Figures

Figure 1

27 pages, 2165 KB  
Article
Load Frequency Control via Multi-Agent Reinforcement Learning and Consistency Model for Diverse Demand-Side Flexible Resources
by Guangzheng Yu, Xiangshuai Li, Tiantian Chen and Jing Liu
Processes 2025, 13(6), 1752; https://doi.org/10.3390/pr13061752 - 2 Jun 2025
Viewed by 758
Abstract
With the high-proportion integration of renewable energy into the power grid, the fast-response capabilities of demand-side flexible resources (DSFRs), such as electric vehicles (EVs) and thermostatic loads, have become critical for frequency stability. However, the diverse dynamic characteristics of heterogeneous resources lead to [...] Read more.
With the high-proportion integration of renewable energy into the power grid, the fast-response capabilities of demand-side flexible resources (DSFRs), such as electric vehicles (EVs) and thermostatic loads, have become critical for frequency stability. However, the diverse dynamic characteristics of heterogeneous resources lead to high modeling complexity. Traditional reinforcement learning methods, which rely on neural networks to approximate value functions, often suffer from training instability and lack the effective quantification of resource regulation costs. To address these challenges, this paper proposes a multi-agent reinforcement learning frequency control method based on a Consistency Model (CM). This model incorporates power, energy, and first-order inertia characteristics to uniformly characterize the response delays and dynamic behaviors of EVs and air conditioners (ACs), providing a reduced-order analytical foundation for large-scale coordinated control. On this basis, a policy gradient controller is designed. By using projected gradient descent, it ensures that control actions satisfy physical boundaries. A reward function including state deviation penalties and regulation costs is constructed, dynamically adjusting penalty factors according to resource states to achieve priority configuration for frequency regulation. Simulations on the IEEE 39-node system demonstrate that the proposed method significantly outperforms traditional approaches in terms of frequency deviation, algorithm training efficiency, and frequency regulation economy. Full article
Show Figures

Figure 1

31 pages, 1200 KB  
Article
Power-Efficient UAV Positioning and Resource Allocation in UAV-Assisted Wireless Networks for Video Streaming with Fairness Consideration
by Zaheer Ahmed, Ayaz Ahmad, Muhammad Altaf and Mohammed Ahmed Hassan
Drones 2025, 9(5), 356; https://doi.org/10.3390/drones9050356 - 7 May 2025
Viewed by 1057
Abstract
This work proposes a power-efficient framework for adaptive video streaming in UAV-assisted wireless networks specially designed for disaster-hit areas where existing base stations are nonfunctional. Delivering high-quality videos requires higher video rates and more resources, which leads to increased power consumption. With the [...] Read more.
This work proposes a power-efficient framework for adaptive video streaming in UAV-assisted wireless networks specially designed for disaster-hit areas where existing base stations are nonfunctional. Delivering high-quality videos requires higher video rates and more resources, which leads to increased power consumption. With the increasing demand of mobile video, efficient bandwidth allocation becomes essential. In shared networks, users with lower bitrates experience poor video quality when high-bitrate users occupy most of the bandwidth, leading to a degraded and unfair user experience. Additionally, frequent video rate switching can significantly impact user experience, making the video rates’ smooth transition essential. The aim of this research is to maximize the overall users’ quality of experience in terms of power-efficient adaptive video streaming by fair distribution and smooth transition of video rates. The joint optimization includes power minimization, efficient resource allocation, i.e., transmit power and bandwidth, and efficient two-dimensional positioning of the UAV while meeting system constraints. The formulated problem is non-convex and difficult to solve with conventional methods. Therefore, to avoid the curse of complexity, the block coordinate descent method, successive convex approximation technique, and efficient iterative algorithm are applied. Extensive simulations are performed to verify the effectiveness of the proposed solution method. The simulation results reveal that the proposed method outperforms 95–97% over equal allocation, 77–89% over random allocation, and 17–40% over joint allocation schemes. Full article
Show Figures

Figure 1

23 pages, 1976 KB  
Article
Joint Optimization Algorithm for UAV-Assisted Caching and Charging Based on Wireless Energy Harvesting
by Yumeng Zhu and Qi Zhu
Appl. Sci. 2025, 15(7), 3908; https://doi.org/10.3390/app15073908 - 2 Apr 2025
Viewed by 440
Abstract
The proliferation of mobile terminal applications and the increasing energy consumption of chips have raised concerns about insufficient power in mobile user terminals. In response to this issue, this paper proposes a joint optimization algorithm for UAV-assisted caching and charging based on non-orthogonal [...] Read more.
The proliferation of mobile terminal applications and the increasing energy consumption of chips have raised concerns about insufficient power in mobile user terminals. In response to this issue, this paper proposes a joint optimization algorithm for UAV-assisted caching and charging based on non-orthogonal multiple access (NOMA) within the context of mobile edge caching scenarios. The proposed algorithm considers the revenue generated from UAVs providing caching and charging services to users, as well as the cost associated with leasing cache files and the UAV energy consumption. The optimization problem aimed at maximizing UAV utility is established under constraints related to power and cache capacity. To address this mixed-integer programming problem, we divided it into two parts. The first part uses the Stackelberg–Bertrand game to optimize file pricing and the UAV cache strategy. In the second part, the block coordinate descent (BCD) method is used to optimize the UAV transmission power distribution, positioning, and user pairing. The joint optimization problem is divided into three subproblems, which use the Lagrange multiplier method, a simulated annealing algorithm, and a particle swarm optimization algorithm. Simulation results demonstrate that the proposed algorithm effectively reduces user transmission delay while also improving overall revenue generated by UAVs. Full article
(This article belongs to the Special Issue Wireless Networking: Application and Development)
Show Figures

Figure 1

22 pages, 491 KB  
Article
Enhancing Physical-Layer Security in UAV-Assisted Communications: A UAV-Mounted Reconfigurable Intelligent Surface Scheme for Secrecy Rate Optimization
by Mengqiu Chai, Yuan Liu, Shengjie Zhao and Hao Deng
Drones 2025, 9(3), 208; https://doi.org/10.3390/drones9030208 - 14 Mar 2025
Cited by 1 | Viewed by 1427
Abstract
With the wide application of unmanned aerial vehicles (UAVs) in the military and civilian fields, the physical layer security of UAV-assisted communication has attracted more and more attention in recent years. Reconfigurable intelligent surface (RIS) is a revolutionizing and promising technology that can [...] Read more.
With the wide application of unmanned aerial vehicles (UAVs) in the military and civilian fields, the physical layer security of UAV-assisted communication has attracted more and more attention in recent years. Reconfigurable intelligent surface (RIS) is a revolutionizing and promising technology that can improve spectrum efficiency through intelligent reconfiguration of the propagation environment. In this paper, we investigate the physical layer security of RIS and UAV-assisted communication systems. Specifically, we consider the scenario of multiple eavesdroppers wiretapping the communication between the base station and the legitimate user and propose a secure mechanism that deploys the RIS on a dynamic UAV for security assistance. In order to maximize the average secrecy rate of the system, we propose a joint optimization problem of joint UAV flight trajectory, RIS transmit phase shift, and base station transmit power. Since the proposed problem is non-convex, it is difficult to solve it directly, so we propose a joint optimization algorithm based on block coordinate descent and successive convex optimization techniques. Simulation results verify the effectiveness of our proposed design in improving the secrecy performance of the considered system. Full article
(This article belongs to the Special Issue Physical-Layer Security in Drone Communications)
Show Figures

Figure 1

19 pages, 534 KB  
Article
Sum-Throughput Maximization in an IRS-Enhanced Multi-Cell NOMA Wireless-Powered Communication Network
by Jiaqian Liang, Yi Mo, Xingquan Li and Chunlong He
Symmetry 2025, 17(3), 413; https://doi.org/10.3390/sym17030413 - 10 Mar 2025
Viewed by 839
Abstract
A wireless-powered communication network (WPCN) provides sustainable power solutions for energy-intensive Internet of Things (IoT) devices in remote or inaccessible locations. This technology is particularly beneficial for applications in smart transportation and smart cities. Nevertheless, WPCN experiences performance degradation due to severe path [...] Read more.
A wireless-powered communication network (WPCN) provides sustainable power solutions for energy-intensive Internet of Things (IoT) devices in remote or inaccessible locations. This technology is particularly beneficial for applications in smart transportation and smart cities. Nevertheless, WPCN experiences performance degradation due to severe path loss and inefficient long-range energy and information transmission. To address the limitation, this paper investigates an intelligent reflecting surface (IRS)-enhanced multi-cell WPCN integrated with non-orthogonal multiple access (NOMA). The emerging IRS technology mitigates propagation losses through precise phase shift adjustments with symmetric reflective components. Asymmetric resource utilization in symmetric downlink and uplink transmissions is crucial for optimal throughput and quality of service. Alternative iterations are employed to optimize time allocation and IRS phase shifts in both downlink and uplink transmissions. This approach allows for the attainment of maximum sum throughput. Specifically, the phase shifts are optimized using two algorithms called semidefinite relaxation (SDR) and block coordinate descent (BCD). Our simulations reveal that integrating the IRS into multi-cell NOMA-WPCN enhances user throughput. This surpasses the performance of traditional multi-cell WPCN. In addition, the coordinated deployment of multiple hybrid access points (HAPs) and IRS equipment can expand communications coverage and network capacity. Full article
(This article belongs to the Section Computer)
Show Figures

Figure 1

22 pages, 1895 KB  
Article
The Influencing Factors and Emission Reduction Pathways for Carbon Emissions from Private Cars: A Scenario Simulation Based on Fuzzy Cognitive Maps
by Wenjie Chen, Xiaogang Wu and Zhu Xiao
Sustainability 2025, 17(5), 2268; https://doi.org/10.3390/su17052268 - 5 Mar 2025
Cited by 1 | Viewed by 833
Abstract
The promotion of carbon reduction in the private car sector is crucial for advancing sustainable transportation development and addressing global climate change. This study utilizes vehicle trajectory big data from Guangdong Province, China, and employs machine learning, an LDA topic model, a gradient [...] Read more.
The promotion of carbon reduction in the private car sector is crucial for advancing sustainable transportation development and addressing global climate change. This study utilizes vehicle trajectory big data from Guangdong Province, China, and employs machine learning, an LDA topic model, a gradient descent-based fuzzy cognitive map model, and grey correlation analysis to investigate the influencing factors and emission reduction pathways of carbon emissions from private cars. The findings indicate that (1) population density exhibits the strongest correlation with private car carbon emissions, with a coefficient of 0.85, rendering it a key factor influencing emissions, (2) the development of public transportation emerges as the primary pathway for carbon reduction in the private car sector under a single-factor scenario, and (3) coordinating public transport with road network density and fuel prices with traffic congestion are both viable pathways as well for reducing carbon emissions in the private car sector. This study attempts to integrate multiple factors and private car carbon emissions within a unified research framework, exploring and elucidating carbon reduction pathways for private cars with the objective of providing valuable insights into the green and low-carbon transition of the transportation sector. Full article
Show Figures

Figure 1

24 pages, 30044 KB  
Article
Minimum-Fuel Trajectories and Near-Optimal Explicit Guidance for Pinpoint Landing from Low Lunar Orbit
by Matteo Caruso, Giulio De Angelis, Edoardo Maria Leonardi and Mauro Pontani
Aerospace 2025, 12(3), 183; https://doi.org/10.3390/aerospace12030183 - 25 Feb 2025
Viewed by 817
Abstract
This research addresses minimum-fuel pinpoint lunar landing at the South Pole, focusing on trajectory design and near-optimal guidance aimed at driving a spacecraft from a circular low lunar orbit (LLO) to an instantaneous hovering state above the lunar surface. Orbit dynamics is propagated [...] Read more.
This research addresses minimum-fuel pinpoint lunar landing at the South Pole, focusing on trajectory design and near-optimal guidance aimed at driving a spacecraft from a circular low lunar orbit (LLO) to an instantaneous hovering state above the lunar surface. Orbit dynamics is propagated in a high-fidelity ephemeris-based framework, which employs spherical coordinates as the state variables and includes several harmonics of the selenopotential, as well as third-body gravitational perturbations due to the Earth and Sun. Minimum-fuel two-impulse descent transfers are identified using Lambert problem solutions as initial guesses, followed by refinement in the high-fidelity model, for a range of initial LLO inclinations. Then, a feedback Lambert-based impulsive guidance algorithm is designed and tested through a Monte Carlo campaign to assess the effectiveness under non-nominal conditions related to injection and actuation errors. Because the last braking maneuver is relatively large, a finite-thrust, locally flat, near-optimal guidance is introduced and applied. Simplified dynamics is assumed for the purpose of defining a minimum-time optimal control problem along the last thrust arc. This admits a closed-form solution, which is iteratively used until the desired instantaneous hovering condition is reached. The numerical results in non-nominal flight conditions testify to the effectiveness of the guidance approach at hand in terms of propellant consumption and precision at landing. Full article
(This article belongs to the Special Issue Advances in Lunar Exploration)
Show Figures

Figure 1

21 pages, 2425 KB  
Article
Resource and Trajectory Optimization in RIS-Assisted Cognitive UAV Networks with Multiple Users Under Malicious Eavesdropping
by Juan Li, Gang Wang, Hengzhou Jin, Jing Zhou, Wei Li and Hang Hu
Electronics 2025, 14(3), 541; https://doi.org/10.3390/electronics14030541 - 29 Jan 2025
Viewed by 1029
Abstract
Unmanned aerial vehicles (UAVs) have shown significant advantages in disaster relief, emergency communication, and Integrated Sensing and Communication (ISAC). However, the escalating demand for UAV spectrum is severely restricted by the scarcity of available spectrum, which in turn significantly limits communication performance. Additionally, [...] Read more.
Unmanned aerial vehicles (UAVs) have shown significant advantages in disaster relief, emergency communication, and Integrated Sensing and Communication (ISAC). However, the escalating demand for UAV spectrum is severely restricted by the scarcity of available spectrum, which in turn significantly limits communication performance. Additionally, the openness of the wireless channel poses a serious threat, such as wiretapping and jamming. Therefore, it is necessary to improve the security performance of the system. Recently, Reconfigurable Intelligent Surfaces (RIS), as a highly promising technology, has been integrated into Cognitive UAV Network. This integration enhances the legitimate signal while suppressing the eavesdropping signal. This paper investigates a RIS-assisted Cognitive UAV Network with multiple corresponding receiving users as cognitive users (CUs) in the presence of malicious eavesdroppers (Eav), in which the Cognitive UAV functions as the mobile aerial Base Station (BS) to transmit confidential messages for the users on the ground. Our primary aim is to attain the maximum secrecy bits by means of jointly optimizing the transmit power, access scheme of the CUs, the RIS phase shift matrix, and the trajectory. In light of the fact that the access scheme is an integer, the original problem proves to be a mixed integer non-convex one, which falls into the NP-hard category. To solve this problem, we propose block coordinate descent and successive convex approximation (BCD-SCA) algorithms. Firstly, we introduce the BCD algorithm to decouple the coupled variables and convert the original problem into four sub-problems for the non-convex subproblems to solve by the SCA algorithm. The results of our simulations indicate that the joint optimization scheme we have put forward not only achieves robust convergence but also outperforms conventional benchmark approaches. Full article
(This article belongs to the Special Issue Unmanned Aerial Vehicles (UAVs) Communication and Networking)
Show Figures

Graphical abstract

17 pages, 573 KB  
Article
Fitting Penalized Estimator for Sparse Covariance Matrix with Left-Censored Data by the EM Algorithm
by Shanyi Lin, Qian-Zhen Zheng, Laixu Shang, Ping-Feng Xu and Man-Lai Tang
Mathematics 2025, 13(3), 423; https://doi.org/10.3390/math13030423 - 27 Jan 2025
Cited by 1 | Viewed by 874
Abstract
Estimating the sparse covariance matrix can effectively identify important features and patterns, and traditional estimation methods require complete data vectors on all subjects. When data are left-censored due to detection limits, common strategies such as excluding censored individuals or replacing censored values with [...] Read more.
Estimating the sparse covariance matrix can effectively identify important features and patterns, and traditional estimation methods require complete data vectors on all subjects. When data are left-censored due to detection limits, common strategies such as excluding censored individuals or replacing censored values with suitable constants may result in large biases. In this paper, we propose two penalized log-likelihood estimators, incorporating the L1 penalty and SCAD penalty, for estimating the sparse covariance matrix of a multivariate normal distribution in the presence of left-censored data. However, the fitting of these penalized estimators poses challenges due to the observed log-likelihood involving high-dimensional integration over the censored variables. To address this issue, we treat censored data as a special case of incomplete data and employ the Expectation Maximization algorithm combined with the coordinate descent algorithm to efficiently fit the two penalized estimators. Through simulation studies, we demonstrate that both penalized estimators achieve greater estimation accuracy compared to methods that replace censored values with constants. Moreover, the SCAD penalized estimator generally outperforms the L1 penalized estimator. Our method is used to analyze the proteomic datasets. Full article
(This article belongs to the Special Issue Multivariate Statistical Analysis and Application)
Show Figures

Figure 1

36 pages, 2057 KB  
Article
Incorporating Symmetric Smooth Regularizations into Sparse Logistic Regression for Classification and Feature Extraction
by Jing Wang, Xiao Xie, Pengwei Wang, Jian Sun, Yaochen Liu and Li Zhang
Symmetry 2025, 17(2), 151; https://doi.org/10.3390/sym17020151 - 21 Jan 2025
Cited by 3 | Viewed by 1215
Abstract
This paper introduces logistic regression with sparse and smooth regularizations (LR-SS), a novel framework that simultaneously enhances both classification and feature extraction capabilities of standard logistic regression. By incorporating a family of symmetric smoothness constraints into sparse logistic regression, LR-SS uniquely preserves underlying [...] Read more.
This paper introduces logistic regression with sparse and smooth regularizations (LR-SS), a novel framework that simultaneously enhances both classification and feature extraction capabilities of standard logistic regression. By incorporating a family of symmetric smoothness constraints into sparse logistic regression, LR-SS uniquely preserves underlying structures inherent in structured data, distinguishing it from existing approaches. Within the minorization–maximization (MM) framework, we develop an efficient optimization algorithm that combines coordinate descent with soft-thresholding techniques. Through extensive experiments on both simulated and real-world datasets, including time series and image data, we demonstrate that LR-SS significantly outperforms conventional sparse logistic regression in classification tasks while providing more interpretable feature extraction. The results highlight LR-SS’s ability to leverage sparse and symmetric smooth regularizations for capturing intrinsic data structures, making it particularly valuable for machine learning applications requiring both predictive accuracy and model interpretability. Full article
Show Figures

Figure 1

17 pages, 2496 KB  
Article
Fair Spectral Clustering Based on Coordinate Descent
by Ruixin Feng, Caiming Zhong and Tiejun Pan
Symmetry 2025, 17(1), 12; https://doi.org/10.3390/sym17010012 - 25 Dec 2024
Viewed by 804
Abstract
Research on the fairness of spectral clustering has gradually increased attention. Normally, existing methods of fair spectral clustering add a fairness constraint to the original objective function so that fairness is guaranteed. However, similar to the solver of traditional spectral clustering, that of [...] Read more.
Research on the fairness of spectral clustering has gradually increased attention. Normally, existing methods of fair spectral clustering add a fairness constraint to the original objective function so that fairness is guaranteed. However, similar to the solver of traditional spectral clustering, that of fairness spectral clustering has to relax a discrete value condition into an arbitrary one, which leads to the deterioration of both fairness and clustering quality. Moreover, the eigen-problem is inevitable in the solver, which takes O(n3) time complexity and is not available for large-scale data. In this paper, we propose a fair spectral clustering algorithm by employing the coordinate descent method to find the solution. As the relaxation of the discreteness condition is discarded, the fairness is improved. Furthermore, we refine the process of coordinate descent by avoiding redundant calculations, and as a result, the time complexity is reduced from O(n3) to O(n2). Additionally, the importance of clustering quality and fairness is symmetric; hence, we achieve a trade-off between them by adjusting the parameters. The experimental findings, obtained from both real-world and synthetic datasets, clearly illustrate that our proposal delivers superior fairness and clustering quality with the best BAL compared to other fair clustering methods. In addition, our method is more efficient than existing fair spectral clustering algorithms. Full article
(This article belongs to the Section Mathematics)
Show Figures

Figure 1

Back to TopTop