Social networks like LinkedIn, Facebook, and Instagram contribute significantly to the rise of image prevalence in daily life, with numerous images posted in everyday. Detecting image similarity is crucial for many applications. While deep learning methods like Learned Perceptual Image Patch Similarity (LPIPS) are popular, they often overlook image structure. An alternative method involves using pre-trained models ($e.g.$, LeNet-$5$ and VGG-$16$) to extract features and employing classifiers. However, deep learning methods demand substantial computational resources and they also suffer from uncontrolled false alarms. This paper proposes a novel Generalized Likelihood Ratio Test (GLRT) detector based on a hypothesis testing framework to identify the similarity of structural image pairs. The proposed approach minimizes the need for extensive computational resources, and false alarms can be regulated by employing a threshold. The detector is applied to Local Dissimilarity Maps (LDM), with gray-level values modeled by a statistical distribution. Experimental results on simulated and real data confirm its effectiveness for structural similarity detection. Additionally, a Simple Likelihood Ratio Test (SLRT) is tested on simulated data. Comparisons with deep learning and classical measures like Structural Similarity Index (SSIM) and Feature Similarity Index (FSIM) show the proposed detector performs comparably or better in terms of Area Under the Curve (AUC) with less computing time, especially for structural similarity.
{"title":"New Statistic Detector for Structural Image Similarity","authors":"Moustapha Diaw;Florent Retraint;Frédéric Morain-Nicolier;Agnès Delahaies;Jérôme Landré","doi":"10.1109/TSP.2025.3543207","DOIUrl":"10.1109/TSP.2025.3543207","url":null,"abstract":"Social networks like LinkedIn, Facebook, and Instagram contribute significantly to the rise of image prevalence in daily life, with numerous images posted in everyday. Detecting image similarity is crucial for many applications. While deep learning methods like Learned Perceptual Image Patch Similarity (LPIPS) are popular, they often overlook image structure. An alternative method involves using pre-trained models (<inline-formula><tex-math>$e.g.$</tex-math></inline-formula>, LeNet-<inline-formula><tex-math>$5$</tex-math></inline-formula> and VGG-<inline-formula><tex-math>$16$</tex-math></inline-formula>) to extract features and employing classifiers. However, deep learning methods demand substantial computational resources and they also suffer from uncontrolled false alarms. This paper proposes a novel Generalized Likelihood Ratio Test (GLRT) detector based on a hypothesis testing framework to identify the similarity of structural image pairs. The proposed approach minimizes the need for extensive computational resources, and false alarms can be regulated by employing a threshold. The detector is applied to Local Dissimilarity Maps (LDM), with gray-level values modeled by a statistical distribution. Experimental results on simulated and real data confirm its effectiveness for structural similarity detection. Additionally, a Simple Likelihood Ratio Test (SLRT) is tested on simulated data. Comparisons with deep learning and classical measures like Structural Similarity Index (SSIM) and Feature Similarity Index (FSIM) show the proposed detector performs comparably or better in terms of Area Under the Curve (AUC) with less computing time, especially for structural similarity.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"1168-1183"},"PeriodicalIF":4.6,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143443547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-14DOI: 10.1109/TSP.2025.3541872
Yuhan Li;Tianyao Huang;Lei Wang;Yimin Liu;Xiqin Wang
We study the problem of representing a discrete tensor that comes from finite uniform samplings of a multi-dimensional and multiband analog signal. Particularly, we consider two typical cases in which the shape of the subbands is cubic or parallelepipedic. For the cubic case, by examining the spectrum of its corresponding time- and band-limited operators, we obtain a low-dimensional optimal dictionary to represent the original tensor. We further prove that the optimal dictionary can be approximated by the famous discrete prolate spheroidal sequences (DPSSs) with certain modulation, leading to an efficient constructing method. For the parallelepipedic case, we show that there also exists a low-dimensional dictionary to represent the original tensor. We present rigorous proof that the numbers of atoms in both dictionaries are approximately equal to the dot of the total number of samplings and the total volume of the subbands. Our derivations are mainly focused on the 2-dimensional (2-D) scenarios but can be naturally extended to high dimensions.
{"title":"Approximating Multi-Dimensional and Multiband Signals","authors":"Yuhan Li;Tianyao Huang;Lei Wang;Yimin Liu;Xiqin Wang","doi":"10.1109/TSP.2025.3541872","DOIUrl":"10.1109/TSP.2025.3541872","url":null,"abstract":"We study the problem of representing a discrete tensor that comes from finite uniform samplings of a multi-dimensional and multiband analog signal. Particularly, we consider two typical cases in which the shape of the subbands is cubic or parallelepipedic. For the cubic case, by examining the spectrum of its corresponding time- and band-limited operators, we obtain a low-dimensional optimal dictionary to represent the original tensor. We further prove that the optimal dictionary can be approximated by the famous discrete prolate spheroidal sequences (DPSSs) with certain modulation, leading to an efficient constructing method. For the parallelepipedic case, we show that there also exists a low-dimensional dictionary to represent the original tensor. We present rigorous proof that the numbers of atoms in both dictionaries are approximately equal to the dot of the total number of samplings and the total volume of the subbands. Our derivations are mainly focused on the 2-dimensional (2-D) scenarios but can be naturally extended to high dimensions.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"954-969"},"PeriodicalIF":4.6,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143417887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-13DOI: 10.1109/TSP.2025.3541569
Gökhan Gül
Three fundamental problems are addressed for distributed detection networks regarding the maximum of performance/detection loss. The losses obtained are, first, due to the choice of decision rule in parallel sensor networks (general-case vs identical decisions), second, due to the choice of network architecture (serial vs parallel), and third, due to the choice of quantization rule (centralized vs decentralized). Previous results, if available, for all these three problems are restricted to the statement that the loss is “small” over some specific examples. The key principles underlying this study are delineated as follows. First, there is a surjection from all simple hypothesis tests to the receiver operating characteristic (ROC) curve. Second, the ROC can be well modeled with linear splines. Third, considering splines with only a finite number of line segments, in fact, on the order of the total number of sensors, is sufficient to determine the maximum loss. Leveraging these principles, infinite-dimensional optimization problems are reduced to their finite-dimensional equivalent forms. The equivalent problems are then numerically solved to obtain the theoretical bounds.
{"title":"Theoretical Bounds in Decentralized Hypothesis Testing","authors":"Gökhan Gül","doi":"10.1109/TSP.2025.3541569","DOIUrl":"https://doi.org/10.1109/TSP.2025.3541569","url":null,"abstract":"Three fundamental problems are addressed for distributed detection networks regarding the maximum of performance/detection loss. The losses obtained are, first, due to the choice of decision rule in parallel sensor networks (general-case vs identical decisions), second, due to the choice of network architecture (serial vs parallel), and third, due to the choice of quantization rule (centralized vs decentralized). Previous results, if available, for all these three problems are restricted to the statement that the loss is “small” over some specific examples. The key principles underlying this study are delineated as follows. First, there is a surjection from all simple hypothesis tests to the receiver operating characteristic (ROC) curve. Second, the ROC can be well modeled with linear splines. Third, considering splines with only a finite number of line segments, in fact, on the order of the total number of sensors, is sufficient to determine the maximum loss. Leveraging these principles, infinite-dimensional optimization problems are reduced to their finite-dimensional equivalent forms. The equivalent problems are then numerically solved to obtain the theoretical bounds.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"1110-1121"},"PeriodicalIF":4.6,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10884703","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143553368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-12DOI: 10.1109/TSP.2025.3540561
VÍctor Manuel Bautista;Mario Garrido
This paper presents a novel method to obtain non-power-of-two (NP2) fast Fourier transform (FFT) flow graphs based on a new prime factor algorithm (PFA). The FFT flow graph is crucial for designing FFT architectures but previous works only provide systematic approaches to build flow graphs for power-of-two sizes (P2). Thus, the derivation of NP2 flow graphs is an important step towards the design of efficient NP2 FFT architectures. The proposed approach consists of two independent parts. On the one hand, it obtains all the possible index mappings that lead to a flow graph with no rotations between butterflies. On the other hand, it determines the permutations between butterflies in the flow graph. By combining these two parts, the order of the inputs and outputs is derived. As a result, the entire flow graph is obtained systematically. Additionally, the proposed approach generates all the possible flow graphs for a given factorization of the FFT size. The reduction in operations for NP2 FFTs using the proposed approach leads to a significant reduction in area and power consumption concerning P2 FFTs with similar sizes after implementing the proposed flow graphs directly in hardware. Particularly, there is a significant improvement between the proposed 30-point and 60-point FFT and previous efficient P2 FFTs. This remarkable fact sets NP2 at the forefront of FFT research after being in second place behind P2 FFTs for decades.
{"title":"A Method to Obtain Non-Power-of-Two FFT Flow Graphs Based on a New Prime Factor Algorithm","authors":"VÍctor Manuel Bautista;Mario Garrido","doi":"10.1109/TSP.2025.3540561","DOIUrl":"10.1109/TSP.2025.3540561","url":null,"abstract":"This paper presents a novel method to obtain non-power-of-two (NP2) fast Fourier transform (FFT) flow graphs based on a new prime factor algorithm (PFA). The FFT flow graph is crucial for designing FFT architectures but previous works only provide systematic approaches to build flow graphs for power-of-two sizes (P2). Thus, the derivation of NP2 flow graphs is an important step towards the design of efficient NP2 FFT architectures. The proposed approach consists of two independent parts. On the one hand, it obtains all the possible index mappings that lead to a flow graph with no rotations between butterflies. On the other hand, it determines the permutations between butterflies in the flow graph. By combining these two parts, the order of the inputs and outputs is derived. As a result, the entire flow graph is obtained systematically. Additionally, the proposed approach generates all the possible flow graphs for a given factorization of the FFT size. The reduction in operations for NP2 FFTs using the proposed approach leads to a significant reduction in area and power consumption concerning P2 FFTs with similar sizes after implementing the proposed flow graphs directly in hardware. Particularly, there is a significant improvement between the proposed 30-point and 60-point FFT and previous efficient P2 FFTs. This remarkable fact sets NP2 at the forefront of FFT research after being in second place behind P2 FFTs for decades.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"1004-1017"},"PeriodicalIF":4.6,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10883046","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143401804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-12DOI: 10.1109/TSP.2025.3540018
Shanli Chen;Yunfei Zheng;Dongyuan Lin;Peng Cai;Yingying Xiao;Shiyuan Wang
Neural network-assisted (NNA) Kalman filters provide an effective solution to addressing the filtering issues involving partially unknown system information by incorporating neural networks to compute the intermediate values influenced by unknown data, such as the Kalman gain in the filtering process. However, whenever there are slight changes in the state-space model (SSM), previously trained networks used in NNA Kalman filters become outdated, necessitating extensive time and data for retraining. Furthermore, obtaining sufficient labeled data for supervised learning is costly, and the effectiveness of unsupervised learning can be inconsistent. To this end, to address the inflexibility of neural network architecture and the scarcity of training data, we propose a model-agnostic meta-learning based neural network-assisted Kalman filter in this paper, called MAML-KalmanNet, by employing a limited amount of labeled data and training rounds to achieve desirable outcomes comparable to the supervised NNA Kalman filters with sufficient training. MAML-KalmanNet utilizes a pre-training approach based on specifically tailored meta-learning, enabling the network to adapt to model changes with minimal data and time without the requirement of retraining. Simultaneously, by fully leveraging the information from the SSM, MAML-KalmanNet eliminates the requirement of a large amount of labeled data to train the meta-learning initialization network. Simulations show that MAML-KalmanNet can mitigate the shortcomings existing in NNA Kalman filters regarding the requirements of abundant training data and sensitive network architecture, while providing real-time state estimation across a range of noise distributions.
{"title":"MAML-KalmanNet: A Neural Network-Assisted Kalman Filter Based on Model-Agnostic Meta-Learning","authors":"Shanli Chen;Yunfei Zheng;Dongyuan Lin;Peng Cai;Yingying Xiao;Shiyuan Wang","doi":"10.1109/TSP.2025.3540018","DOIUrl":"10.1109/TSP.2025.3540018","url":null,"abstract":"Neural network-assisted (NNA) Kalman filters provide an effective solution to addressing the filtering issues involving partially unknown system information by incorporating neural networks to compute the intermediate values influenced by unknown data, such as the Kalman gain in the filtering process. However, whenever there are slight changes in the state-space model (SSM), previously trained networks used in NNA Kalman filters become outdated, necessitating extensive time and data for retraining. Furthermore, obtaining sufficient labeled data for supervised learning is costly, and the effectiveness of unsupervised learning can be inconsistent. To this end, to address the inflexibility of neural network architecture and the scarcity of training data, we propose a model-agnostic meta-learning based neural network-assisted Kalman filter in this paper, called MAML-KalmanNet, by employing a limited amount of labeled data and training rounds to achieve desirable outcomes comparable to the supervised NNA Kalman filters with sufficient training. MAML-KalmanNet utilizes a pre-training approach based on specifically tailored meta-learning, enabling the network to adapt to model changes with minimal data and time without the requirement of retraining. Simultaneously, by fully leveraging the information from the SSM, MAML-KalmanNet eliminates the requirement of a large amount of labeled data to train the meta-learning initialization network. Simulations show that MAML-KalmanNet can mitigate the shortcomings existing in NNA Kalman filters regarding the requirements of abundant training data and sensitive network architecture, while providing real-time state estimation across a range of noise distributions.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"988-1003"},"PeriodicalIF":4.6,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143401957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-11DOI: 10.1109/TSP.2025.3540655
Pedro Valdeira;João Xavier;Cláudia Soares;Yuejie Chi
Communication overhead is a known bottleneck in federated learning (FL). To address this, lossy compression is commonly used on the information communicated between the server and clients during training. In horizontal FL, where each client holds a subset of the samples, such communication-compressed training methods have recently seen significant progress. However, in their vertical FL counterparts, where each client holds a subset of the features, our understanding remains limited. To address this, we propose an error feedback compressed vertical federated learning (EF-VFL) method to train split neural networks. In contrast to previous communication-compressed methods for vertical FL, EF-VFL does not require a vanishing compression error for the gradient norm to converge to zero for smooth nonconvex problems. By leveraging error feedback, our method can achieve a $mathcal{O}({1}/{T})$ convergence rate for a sufficiently large batch size, improving over the state-of-the-art $mathcal{O}({1}/{sqrt{T}})$ rate under $mathcal{O}({1}/{sqrt{T}})$ compression error, and matching the rate of uncompressed methods. Further, when the objective function satisfies the Polyak-Łojasiewicz inequality, our method converges linearly. In addition to improving convergence, our method also supports the use of private labels. Numerical experiments show that EF-VFL significantly improves over the prior art, confirming our theoretical results.
{"title":"Communication-Efficient Vertical Federated Learning via Compressed Error Feedback","authors":"Pedro Valdeira;João Xavier;Cláudia Soares;Yuejie Chi","doi":"10.1109/TSP.2025.3540655","DOIUrl":"10.1109/TSP.2025.3540655","url":null,"abstract":"Communication overhead is a known bottleneck in federated learning (FL). To address this, lossy compression is commonly used on the information communicated between the server and clients during training. In horizontal FL, where each client holds a subset of the samples, such communication-compressed training methods have recently seen significant progress. However, in their vertical FL counterparts, where each client holds a subset of the features, our understanding remains limited. To address this, we propose an error feedback compressed vertical federated learning (<monospace>EF-VFL</monospace>) method to train split neural networks. In contrast to previous communication-compressed methods for vertical FL, <monospace>EF-VFL</monospace> does not require a vanishing compression error for the gradient norm to converge to zero for smooth nonconvex problems. By leveraging error feedback, our method can achieve a <inline-formula><tex-math>$mathcal{O}({1}/{T})$</tex-math></inline-formula> convergence rate for a sufficiently large batch size, improving over the state-of-the-art <inline-formula><tex-math>$mathcal{O}({1}/{sqrt{T}})$</tex-math></inline-formula> rate under <inline-formula><tex-math>$mathcal{O}({1}/{sqrt{T}})$</tex-math></inline-formula> compression error, and matching the rate of uncompressed methods. Further, when the objective function satisfies the Polyak-Łojasiewicz inequality, our method converges linearly. In addition to improving convergence, our method also supports the use of private labels. Numerical experiments show that <monospace>EF-VFL</monospace> significantly improves over the prior art, confirming our theoretical results.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"1065-1080"},"PeriodicalIF":4.6,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143392952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-11DOI: 10.1109/TSP.2025.3540798
Juan Hu;Lei Zuo;Pramod K. Varshney;Zhengyu Lan;Yongchan Gao
In this paper, an effective collaborative trajectory optimization (CTO) strategy is proposed for multitarget tracking in airborne radar networks with missing data. Missing data may occur during data exchange between radar nodes and a fusion center (FC) due to unreliability of communication channels. The CTO strategy aims to enhance the overall multi-target tracking performance by collaboratively optimizing the trajectories of airborne radars and the FC. In this paper, we derive the posterior Cramér-Rao lower bound (PCRLB) with missing data to evaluate the target tracking performance. On this basis, to maximize the target tracking performance while considering dynamics, collision avoidance, and communication distance constraints, we formulate the CTO optimization problem. The formulated problem is non-convex and internally coupled, which is challenging to solve directly. We decompose the CTO problem into two subproblems and devise an alternating optimization method. Specifically, approximation, and successive convex approximation are applied to make the subproblems solvable. Then, the two subproblems are solved alternately to realize the collaborative trajectory optimization of radars and the FC. Simulation results demonstrate that the proposed CTO strategy achieves better target tracking performance as compared with other benchmark strategies.
{"title":"Collaborative Trajectory Optimization for Multitarget Tracking in Airborne Radar Network With Missing Data","authors":"Juan Hu;Lei Zuo;Pramod K. Varshney;Zhengyu Lan;Yongchan Gao","doi":"10.1109/TSP.2025.3540798","DOIUrl":"10.1109/TSP.2025.3540798","url":null,"abstract":"In this paper, an effective collaborative trajectory optimization (CTO) strategy is proposed for multitarget tracking in airborne radar networks with missing data. Missing data may occur during data exchange between radar nodes and a fusion center (FC) due to unreliability of communication channels. The CTO strategy aims to enhance the overall multi-target tracking performance by collaboratively optimizing the trajectories of airborne radars and the FC. In this paper, we derive the posterior Cramér-Rao lower bound (PCRLB) with missing data to evaluate the target tracking performance. On this basis, to maximize the target tracking performance while considering dynamics, collision avoidance, and communication distance constraints, we formulate the CTO optimization problem. The formulated problem is non-convex and internally coupled, which is challenging to solve directly. We decompose the CTO problem into two subproblems and devise an alternating optimization method. Specifically, approximation, and successive convex approximation are applied to make the subproblems solvable. Then, the two subproblems are solved alternately to realize the collaborative trajectory optimization of radars and the FC. Simulation results demonstrate that the proposed CTO strategy achieves better target tracking performance as compared with other benchmark strategies.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"1048-1064"},"PeriodicalIF":4.6,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143392950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Many real-world time series, such as electricity demand data, biomedical signals, and mechanical vibration signals, exhibit complex trends, encompass multiple seasonal (or periodic) components, and are prone to noise contamination. Existing decomposition methods encounter difficulties when confronted with unknown periods and the presence of multiple nonlinear seasonal components. To address these challenges, we propose a novel nonparametric approach based on periodic Gaussian process models, called sequential seasonal-trend decomposition (SSTD). This model is capable of extracting multiple seasonal components sequentially while estimating the component periods. A spectrum-regularized periodic Gaussian process is proposed to sequentially extract each of the seasonal components, leveraging Fourier basis functions to represent the remaining components. The unknown periods are estimated through a tailored two-step parameter estimation technique from the non-convex likelihood. To mitigate the computational complexity of the proposed method, we propose a circulant acceleration approach. By enabling the sequential extraction of multiple seasonal components and the estimation of unknown periods, SSTD bridges a gap in existing methodologies, yielding improved accuracy and efficiency. Empirical studies on synthetic and real-world data demonstrate its outperformance over current methods.
{"title":"Sequential Decomposition of Multiple Seasonal Components Using Spectrum-Regularized Periodic Gaussian Process","authors":"Yongxiang Li;Wuyang Zhang;Matthias Hwai Yong Tan;Peter Chien","doi":"10.1109/TSP.2025.3540720","DOIUrl":"10.1109/TSP.2025.3540720","url":null,"abstract":"Many real-world time series, such as electricity demand data, biomedical signals, and mechanical vibration signals, exhibit complex trends, encompass multiple seasonal (or periodic) components, and are prone to noise contamination. Existing decomposition methods encounter difficulties when confronted with unknown periods and the presence of multiple nonlinear seasonal components. To address these challenges, we propose a novel nonparametric approach based on periodic Gaussian process models, called sequential seasonal-trend decomposition (SSTD). This model is capable of extracting multiple seasonal components sequentially while estimating the component periods. A spectrum-regularized periodic Gaussian process is proposed to sequentially extract each of the seasonal components, leveraging Fourier basis functions to represent the remaining components. The unknown periods are estimated through a tailored two-step parameter estimation technique from the non-convex likelihood. To mitigate the computational complexity of the proposed method, we propose a circulant acceleration approach. By enabling the sequential extraction of multiple seasonal components and the estimation of unknown periods, SSTD bridges a gap in existing methodologies, yielding improved accuracy and efficiency. Empirical studies on synthetic and real-world data demonstrate its outperformance over current methods.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"1034-1047"},"PeriodicalIF":4.6,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143392949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-07DOI: 10.1109/TSP.2025.3539883
Shuche Wang;Vincent Y. F. Tan
Distributed gradient descent algorithms have come to the fore in modern machine learning, especially in parallelizing the handling of large datasets that are distributed across several workers. However, scant attention has been paid to analyzing the behavior of distributed gradient descent algorithms in the presence of adversarial corruptions instead of random noise. In this paper, we formulate a novel problem in which adversarial corruptions are present in a distributed learning system. We show how to use ideas from (lazy) mirror descent to design a corruption-tolerant distributed optimization algorithm. Extensive convergence analysis for (strongly) convex loss functions is provided for different choices of the stepsize. We carefully optimize the stepsize schedule to accelerate the convergence of the algorithm, while at the same time amortizing the effect of the corruption over time. Experiments based on linear regression, support vector classification, and softmax classification on the MNIST dataset corroborate our theoretical findings.
{"title":"A Mirror Descent-Based Algorithm for Corruption-Tolerant Distributed Gradient Descent","authors":"Shuche Wang;Vincent Y. F. Tan","doi":"10.1109/TSP.2025.3539883","DOIUrl":"10.1109/TSP.2025.3539883","url":null,"abstract":"Distributed gradient descent algorithms have come to the fore in modern machine learning, especially in parallelizing the handling of large datasets that are distributed across several workers. However, scant attention has been paid to analyzing the behavior of distributed gradient descent algorithms in the presence of adversarial corruptions instead of random noise. In this paper, we formulate a novel problem in which adversarial corruptions are present in a distributed learning system. We show how to use ideas from (lazy) mirror descent to design a corruption-tolerant distributed optimization algorithm. Extensive convergence analysis for (strongly) convex loss functions is provided for different choices of the stepsize. We carefully optimize the stepsize schedule to accelerate the convergence of the algorithm, while at the same time amortizing the effect of the corruption over time. Experiments based on linear regression, support vector classification, and softmax classification on the MNIST dataset corroborate our theoretical findings.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"827-842"},"PeriodicalIF":4.6,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143367350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-07DOI: 10.1109/TSP.2025.3539605
Qinchen Wu;Jinping Sun;Bin Yang;Tao Shan;Yanping Wang
The standard multi-target transition density assumes that, conditional on the current multi-target state, targets survive and move independently of each other. Although this assumption is followed by most multi-target tracking (MTT) algorithms, it may not be applicable for tracking group targets exhibiting coordinated motion. This paper presents a principled Bayesian solution to tracking multiple resolvable group targets in the labeled random finite set framework. The transition densities of group targets with collective behavior are derived both for single-group and multi-group. For single-group, the transition density is characterized by a general labeled multi-target density and then approximated by the closest general labeled multi-Bernoulli (GLMB) density in terms of Kullback-Leibler divergence. For multi-group, we augment the group structure to multi-target states and propose a multiple group structure transition model (MGSTM) to recursively infer it. Additionally, the conjugation of the structure augmented multi-group multi-target density is also proved. An efficient implementation of multi-group multi-target tracker, named MGSTM-LMB filter, and its Gaussian mixture form are devised which preserves the first-order moment of multi-group multi-target density in recursive propagation. Numerical simulation results demonstrate the capability of the proposed MGSTM-LMB filter in multi-group scenes.
{"title":"Tracking Multiple Resolvable Group Targets With Coordinated Motion via Labeled Random Finite Sets","authors":"Qinchen Wu;Jinping Sun;Bin Yang;Tao Shan;Yanping Wang","doi":"10.1109/TSP.2025.3539605","DOIUrl":"10.1109/TSP.2025.3539605","url":null,"abstract":"The standard multi-target transition density assumes that, conditional on the current multi-target state, targets survive and move independently of each other. Although this assumption is followed by most multi-target tracking (MTT) algorithms, it may not be applicable for tracking group targets exhibiting coordinated motion. This paper presents a principled Bayesian solution to tracking multiple resolvable group targets in the labeled random finite set framework. The transition densities of group targets with collective behavior are derived both for single-group and multi-group. For single-group, the transition density is characterized by a general labeled multi-target density and then approximated by the closest general labeled multi-Bernoulli (GLMB) density in terms of Kullback-Leibler divergence. For multi-group, we augment the group structure to multi-target states and propose a multiple group structure transition model (MGSTM) to recursively infer it. Additionally, the conjugation of the structure augmented multi-group multi-target density is also proved. An efficient implementation of multi-group multi-target tracker, named MGSTM-LMB filter, and its Gaussian mixture form are devised which preserves the first-order moment of multi-group multi-target density in recursive propagation. Numerical simulation results demonstrate the capability of the proposed MGSTM-LMB filter in multi-group scenes.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"1018-1033"},"PeriodicalIF":4.6,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143367351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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