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group sparse optimization for inpainting of random fields on the sphere

IMA JOURNAL OF NUMERICAL ANALYSIS 2023年第5期44卷 3028-3058页

作者： Li, Chao Chen, Xiaojun Taiyuan Normal Univ Sch Math & Stat Jinzhong 030619 Shanxi Peoples R China Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong 999077 Peoples R China

We propose a group sparse optimization model for inpainting of a square-integrable isotropic random field on the unit sphere, where the field is represented by spherical harmonics with random complex coefficients. In the proposed optimization model, the variable is an infinite-dimensional complex vector and the objective function is a real-valued function defined by a hybrid of the $\ell _2$ norm and non-Lipschitz $\ell _p (0group structure of the random complex coefficients. We show that the infinite-dimensional optimization problem is equivalent to a convexly-constrained finite-dimensional optimization problem. Moreover, we propose a smoothing penalty algorithm to solve the finite-dimensional problem via unconstrained optimization problems. We provide an approximation error bound of the inpainted random field defined by a scaled Karush-Kuhn-Tucker (KKT) point of the constrained optimization problem in the square-integrable space on the sphere with probability measure. Finally, we conduct numerical experiments on band-limited random fields on the sphere and images from Cosmic Microwave Background (CMB) data to show the promising performance of the smoothing penalty algorithm for inpainting of random fields on the sphere.

关键词： group sparse optimization exact penalty smoothing method random field

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Compressive sensing of wireless sensors based on group sparse optimization for structural health monitoring

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STRUCTURAL HEALTH MONITORING-AN INTERNATIONAL JOURNAL 2018年第4期17卷 823-836页

作者： Bao, Yuequan Shi, Zuoqiang Wang, Xiaoyu Li, Hui Harbin Inst Technol Minist Educ Key Lab Struct Dynam Behav & Control Harbin 150090 Heilongjiang Peoples R China Harbin Inst Technol Sch Civil Engn Harbin Heilongjiang Peoples R China Tsinghua Univ Yau Math Sci Ctr Beijing Peoples R China

Vibration signals of most civil infrastructures have sparse characteristics (i.e. only a few modes contribute to the vibration of the structures). Therefore, the vibration data usually have sparse representation. Additionally, the vibration data measured by the sensors placed on different locations of structure have almost the same sparse structure in the frequency domain. On basis of the group sparsity of the structural vibration data, we proposed a group sparse optimization algorithm based on compressive sensing for wireless sensors. Different from the Nyquist sampling theorem, the data are first acquired by a nonuniform low-rate random sampling method according to compressive sensing theory. We then developed the group sparse optimization algorithm to reconstruct the original data from incomplete measurements. By conducting a field test on Xiamen Haicang Bridge with wireless sensors, we illustrate the effectiveness of the proposed approach. The results show that smaller reconstruction errors can be achieved using data from multiple sensors with the group sparse optimization method than using data from only single sensor. Even using only 10% random sampling data, the original data can be reconstructed using the group sparse optimization method with a small reconstruction error. In addition, the modal parameters can also be identified from the reconstruction data with small identification errors.

关键词： Structural health monitoring compressive sensing data reconstruction group sparse optimization wireless sensor

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Wideband Millimeter Wave Communication With Lens Antenna Array: Joint Beamforming and Antenna Selection With group sparse optimization

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2018年第10期17卷 6575-6589页

作者： Huang, Wei Huang, Yongming Zeng, Yong Yang, Luxi Southeast Univ Sch Informat Sci & Engn Natl Mobile Commun Res Lab Nanjing 210096 Jiangsu Peoples R China Univ Sydney Sch Elect & Informat Engn Sydney NSW 2006 Australia

For millimeter wave (mm-wave) communication systems, a lens antenna array with single-carrier transmission and path delay compensation is a promising technique for realizing cost-effective large multiple-input multiple-output communications with limited number of radio frequency chains. In this paper, we study the multi-user mm-wave downlink lens antenna array system for the general frequency-selective channels. By leveraging the angle-dependent energy focusing property of the lens antenna array and the angular sparsity of mm-wave channels, we investigate the low-complexity single-carrier transmission scheme with path delay pre-compensation applied at the base station (BS). The resulting signal-to-interference-plusnoise ratio (SINR) is derived by taking into account both the residual inter-symbol interference and inter-user interference. Based on the derived SINR expression, we propose an effective joint antenna selection and beamforming scheme by utilizing the group sparse optimization to accommodate for the limited number of RF chains at the BS. Thus, the proposed scheme can obtain the approximate performance with the fully digital case and has a better performance than the conventional orthogonal frequency-division multiplexing mode for the frequency-selectivity channels. Numerical results are provided to verify the effectiveness of the proposed schemes.

关键词： Lens antenna array millimeter wave communications group sparse optimization single-carrier transmission path delay pre-compensation

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Computation of second-order directional stationary points for group sparse optimization

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optimization METHODS & SOFTWARE 2020年第2期35卷 348-376页

作者： Peng, Dingtao Chen, Xiaojun Guizhou Univ Sch Math & Stat Guiyang Guizhou Peoples R China Hong Kong Polytech Univ Dept Appl Math Hong Kong Peoples R China

We consider a nonconvex and nonsmooth group sparse optimization problem where the penalty function is the sum of compositions of a folded concave function and the vector norm for each group variable. We show that under some mild conditions a first-order directional stationary point is a strict local minimizer that fulfils the first-order growth condition, and a second-order directional stationary point is a strong local minimizer that fulfils the second-order growth condition. In order to compute second-order directional stationary points, we construct a twice continuously differentiable smoothing problem and show that any accumulation point of the sequence of second-order stationary points of the smoothing problem is a second-order directional stationary point of the original problem. We give numerical examples to illustrate how to compute a second-order directional stationary point by the smoothing method.

关键词： group sparse optimization nonconvex and nonsmooth optimization composite folded concave penalty directional stationary point smoothing method

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group sparse optimization via lp,q regularization

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2017年第1期18卷

作者： Yaohua Hu Chong Li Kaiwen Meng Jing Qin Xiaoqi Yang College of Mathematics and Statistics Shenzhen University Shenzhen P. R. China School of Mathematical Sciences Zhejiang University Hangzhou P. R. China School of Economics and Management Southwest Jiaotong University Chengdu P. R. China School of Life Sciences The Chinese University of Hong Kong and Shenzhen Research Institute The Chinese University of Hong Kong Shenzhen P. R. China Department of Applied Mathematics The Hong Kong Polytechnic University Kowloon Hong Kong

In this paper, we investigate a group sparse optimization problem via lp,q regularization in three aspects: theory, algorithm and application. In the theoretical aspect, by introducing a notion of group restricted eigenvalue condition, we establish an oracle property and a global recovery bound of order O(λ2/2-q) for any point in a level set of the lp,q regularization problem, and by virtue of modern variational analysis techniques, we also provide a local analysis of recovery bound of order O(λ2) for a path of local minima. In the algorithmic aspect, we apply the well-known proximal gradient method to solve the p,q regularization problems, either by analytically solving some specific lp,q regularization subproblems, or by using the Newton method to solve general lp,q regularization subproblems. In particular, we establish a local linear convergence rate of the proximal gradient method for solving the l1,q regularization problem under some mild conditions and by first proving a second-order growth condition. As a consequence, the local linear convergence rate of proximal gradient method for solving the usual lq regularization problem (0 < q < 1) is obtained. Finally in the aspect of application, we present some numerical results on both the simulated data and the real data in gene transcriptional regulation.

关键词： gene regulation network group sparse optimization iterative thresholding algorithm lower-order regularization nonconvex optimization proximal gradient method restricted eigenvalue condition

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Application of second-order differential optimisation group sparse algorithm in fault diagnosis

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ENGINEERING RESEARCH EXPRESS 2025年第2期7卷 025206-025206页

作者： Ding, Yi Kunming Univ Sci & Technol Fac Mech & Elect Engn 727 South Jingming Rd Kunming 650500 Peoples R China

Vibration monitoring and feature extraction are critical factors in determining the fault frequency. However, strong background noise can seriously affect the accuracy of fault information extraction and bring challenges to fault diagnosis. In order to enhance the fault information on the spectrum, this paper proposes a non-convex group sparse optimisation algorithm based on the second-order difference structure. It can distinguish the noise and the main fault components in the signal by computational properties of the second-order difference structure. Firstly, the structure of second order difference is used to replace the original signal term in the penalty function and to reconstruct the noisy signal. Then, the signals from the differentiation process are grouped in the form of non-overlapping manner and construct an objective function with a group sparse structure. The Generalized Minimax-Concave (GMC) penalty is also introduced as the penalty function to improve the amplitude preserving ability of the algorithm, and the result shows that it can keep the cost function convex. Additionally, the criteria for setting the relevant parameters are also investigated to ensure that the algorithm has some degree of adaptive capability. Finally, the validation results of the public data and the industrial field data show that the algorithm has excellent performance in both background noise suppression and fault feature extraction. It can extract the fault information accurately, which is more advantageous than the traditional group sparse optimisation algorithm. And it is a reliable and efficient algorithm for fault diagnosis.

关键词： fault diagnosis group sparse optimization second-order difference parameter optimization

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SINR Balancing via Base Station Association, Beamforming, and Power Control in Downlink Multicell MISO Systems

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2018年第3期17卷 1811-1821页

作者： Xie, Mengjie Lok, Tat-Ming Chinese Univ Hong Kong Dept Informat Engn Hong Kong Hong Kong Peoples R China

This paper considers the downlink channel of multicell multiuser multiple-input single-output systems with arbitrary architecture. We aim to maximize the minimum weighted signal-to-interference-plus-noise ratio (SINR) through user-base station (BS) association, coordinated beamforming among BSs, and power control subject to per BS power constraints. The problem is known to be NP-hard. In the high-SNR regime, where the performance is interference-limited, we globally optimize the upper bound, which is achieved asymptotically, of the balanced SINR. In the low-SNR regime, where the performance is restricted by the tightest per BS power constraint, we balance the transmit power using relaxed integer programming and group sparse optimization techniques. The two goals can be integrated to achieve a universally better performance. From the perspective of optimization methods, the corresponding algorithms are based on Lagrangian relaxation and are guaranteed to converge. Simulation results show that the proposed algorithms outperform the existing algorithms designed for the downlink single-input single-output systems.

关键词： Downlink multicell MISO SINR balancing max-min SINR base station association relaxed integer programming group sparse optimization

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MUSIC RECOMMENDATION USING HYPERGRAPHS AND group SPARSITY

MUSIC RECOMMENDATION USING HYPERGRAPHS AND GROUP SPARSITY

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IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Theodoridis, Antonis Kotropoulos, Constantine Panagakis, Yannis Aristotle Univ Thessaloniki Dept Informat Thessaloniki 54124 Greece

ISBN: (纸本)9781479903566

A challenging problem in multimedia recommendation is to model a variety of relations, such as social, friend, listening, or tagging ones in a unified framework and to exploit all these sources of information. In this paper, music recommendation problem is expressed as a hypergraph ranking problem, introducing group sparsity constraints. By doing so, one can control how the different data groups (i.e., sets of hypergraph vertices) affect the recommendation process. Experiments on a dataset collected from Last. fm demonstrate that the accuracy is significantly increased by exploiting the group structure of the data. Preliminary results are also presented for Greek folk music recommendation.

关键词： music recommendation social media information hypergraph group sparse optimization music signal processing

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PERSONALIZED MUSIC TAGGING USING RANKING ON HYPERGRAPHS

PERSONALIZED MUSIC TAGGING USING RANKING ON HYPERGRAPHS

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6th International Symposium on Communications, Control and Signal Processing (ISCCSP)

作者： Pliakos, Konstantinos Kotropoulos, Constantine Aristotle Univ Thessaloniki Dept Informat Thessaloniki 54124 Greece

ISBN: (纸本)9781479928903

Social tagging enables users of social media sharing platforms to annotate multimedia items by employing arbitrary keywords (i.e., tags), which describe better the multimedia content. Several applications, such as personalized multimedia recommendation or music genre classification, to name a few, benefit from tagging. Clearly, tagging aims at bridging the semantic gap between human concepts and content retrieval exploiting low-level features extracted from the multimedia. Here, the problem of personalized tag recommendation is addressed in a "query and ranking" manner on hypergraphs. This way, the relationships between the different object types, such as user friendships, user groups, music tracks and tags are captured and tags are recommended for a certain track to a user. Ranking on hypergraphs is studied by enforcing either l(2) norm regularization or group sparsity. Experiments on a dataset collected from Last. fm demonstrate a promising tag recommendation accuracy.

关键词： Music Signal Processing Tagging Hypergraph group sparse optimization

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sparse Learning for Neural Networks with A Generalized sparse Regularization

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Procedia Computer Science 2022年 214卷 747-754页

作者： Anda Tang Tongsheng Yao Lingfeng Niu Yong Shi School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100190 China Key Laboratory of Big Data Mining and Knowledge Management Chinese Academy of Sciences Beijing 100190 China

Deep neural networks (DNNs) is very important and have achieved remarkable accuracies in tasks such as image processing. However, the success of DNNs heavily relies on excessive computation and parameter storage costs. To cut down the overheads, a wide range of regularization terms are proposed on netwok compression, which have their own scope of application though. To further reduce computation, structural sparsity learning is a matter of great concern where group sparse regularizations are blossoming in radiant splendour. However, the group sparse regularizations used in network compression is relatively scarce. A majority of structural compression only stem from ℓ 2,1 regularization. In addition, sparse regularization in structural network compression lacks unified form and theoretical guidance. Therefore, we focus our attention on a generalized sparse regularization in sparse learning of deep learning. We put a series of sparse regularization into a framework where some group sparse regularizations with different properties are introduced. The transformation of regularizations can be completed through the selection of hyper-parameters. In this case, we can use the optimization strategy for unification and theoretical guidance, and transform different sparse regularizations to adapt to different tasks. To our knowledge, it is the first work applying the generalized sparse regularization with novel group sparsity in compression of DNNs. The proposed ℓ p , q , r regularization can achieve both neuron-level and connection-level sparsity. And we give the analytical solutions for some specific ( p,q, r ) thus the compression can be achieved throughout the standard optimization process. We perform extensive experiments to illustrate the advantages and characteristics of our new method for further applications.

关键词： Deep neural networks Model compression group sparse optimization Regularization sparse Learning

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