Manifold optimization is ubiquitous in computational and appliedmathematics,statistics,engineering,machine learning,physics,chemistry,etc.One of the main challenges usually is the non-convexity of the manifold constra...Manifold optimization is ubiquitous in computational and appliedmathematics,statistics,engineering,machine learning,physics,chemistry,etc.One of the main challenges usually is the non-convexity of the manifold constraints.By utilizing the geometry of manifold,a large class of constrained optimization problems can be viewed as unconstrained optimization problems on manifold.From this perspective,intrinsic structures,optimality conditions and numerical algorithms for manifold optimization are investigated.Some recent progress on the theoretical results of manifold optimization is also presented.展开更多
Canonical correlation analysis(CCA)describes the relationship between two sets of variables by finding a linear combination that maximizes the correlation coefficient.However,in high-dimensional settings where the num...Canonical correlation analysis(CCA)describes the relationship between two sets of variables by finding a linear combination that maximizes the correlation coefficient.However,in high-dimensional settings where the number of variables exceeds sample size,or in the case that the variables are highly correlated,the traditional CCA is no longer appropriate.In this paper,a new matrix regularization is introduced,which is an extension of the trace Lasso in the vector case.Then we propose an adaptive sparse version of CCA(ASCCA)to overcome these disadvantages by utilizing the trace Lasso regularization.The adaptability of ASCCA is that the sparsity regularization of canonical vectors depends on the sample data,which is more realistic in practical applications.The ASCCA model is further reformulated to an optimization problem on the Riemannian manifold.Then we adopt a manifold inexact augmented Lagrangian method to solve the resulting optimization problem.The performance of the ASCCA model is compared with some existing sparse CCA techniques in different simulation settings and real datasets.展开更多
This paper describes a new design of the neutral beam manifold based on a more optimized support system.A proposed alternative scheme has presented to replace the former complex manifold supports and internal pipe sup...This paper describes a new design of the neutral beam manifold based on a more optimized support system.A proposed alternative scheme has presented to replace the former complex manifold supports and internal pipe supports in the final design phase.Both the structural reliability and feasibility were confirmed with detailed analyses.Comparative analyses between two typical types of manifold support scheme were performed.All relevant results of mechanical analyses for typical operation scenarios and fault conditions are presented.Future optimization activities are described,which will give useful information for a refined setting of components in the next phase.展开更多
In this paper,we investigate the reconfigurable intelligent surface(RIS)-enabled multiple-input-single-output orthogonal frequency division multiplexing(MISO-OFDM)system under frequency-selective channels,and propose ...In this paper,we investigate the reconfigurable intelligent surface(RIS)-enabled multiple-input-single-output orthogonal frequency division multiplexing(MISO-OFDM)system under frequency-selective channels,and propose a low-complexity alternating optimization(AO)based joint beamforming and RIS phase shifts optimization algorithm to maximize the achievable rate.First,with fixed RIS phase shifts,we devise the optimal closedform transmit beamforming vectors corresponding to different subcarriers.Then,with given active beamforming vectors,near-optimal RIS reflection coefficients can be determined efficiently leveraging fractional programming(FP)combined with manifold optimization(MO)or majorization-minimization(MM)framework.Additionally,we also propose a heuristic RIS phase shifts design approach based on the sum of subcarrier gain maximization(SSGM)criterion requiring lower complexity.Numerical results indicate that the proposed MO/MM algorithm can achieve almost the same rate as the upper bound achieved by the semidefinite relaxation(SDR)algorithm,and the proposed SSGM based scheme is only slightly inferior to the upper bound while has much lower complexity.These results demonstrate the effectiveness of the proposed algorithms.展开更多
Intelligent Reflecting Surface (IRS) can offer unprecedented channel capacity gains since it can reconfigure the signal propagation environment. We decide to maximize the channel capacity by jointly optimizing the tra...Intelligent Reflecting Surface (IRS) can offer unprecedented channel capacity gains since it can reconfigure the signal propagation environment. We decide to maximize the channel capacity by jointly optimizing the transmit-power-constrained precoding matrix at the base station and the unit-modulus-constrained phase shift vector at the IRS in IRS-assisted multi-user downlink communication. We first convert the resulting non-convex problem into an equivalent problem, then use the alternate optimization algorithm. While fixing the phase shift vector, we can obtain the optimal precoding matrix directly by adopting standard optimization packages. While fixing the precoding matrix, we propose the Riemannian Trust-Region (RTR) algorithm to solve this optimization problem. And the key of the RTR algorithm is the solution of the trust-region sub-problem. We first adopt the accurate solution based on Newton's (ASNT) method to solve this sub-problem, which can obtain the global solution but cannot guarantee that the solution is optimal since the initial iteration point is difficult to choose. Then, we propose the Improved-Polyline (IPL) method, which can avoid the difficulty of the ASNT method and improve convergence speed and calculation efficiency. The numerical results show that the RTR algorithm has more significant performance gains and faster convergence speed compared with the existing approaches.展开更多
Hybrid beamforming(HBF)has become an attractive and important technology in massive multiple-input multiple-output(MIMO)millimeter-wave(mmWave)systems.There are different hybrid architectures in HBF depending on diffe...Hybrid beamforming(HBF)has become an attractive and important technology in massive multiple-input multiple-output(MIMO)millimeter-wave(mmWave)systems.There are different hybrid architectures in HBF depending on different connection strategies of the phase shifter network between antennas and radio frequency chains.This paper investigates HBF optimization with different hybrid architectures in broadband point-to-point mmWave MIMO systems.The joint hybrid architecture and beamforming optimization problem is divided into two sub-problems.First,we transform the spectral efficiency maximization problem into an equivalent weighted mean squared error minimization problem,and propose an algorithm based on the manifold optimization method for the hybrid beamformer with a fixed hybrid architecture.The overlapped subarray architecture which balances well between hardware costs and system performance is investigated.We further propose an algorithm to dynamically partition antenna subarrays and combine it with the HBF optimization algorithm.Simulation results are presented to demonstrate the performance improvement of our proposed algorithms.展开更多
As the scale of software systems expands,maintaining their stable operation has become an extraordinary challenge.System logs are semi-structured text generated by the recording function in the source code and have im...As the scale of software systems expands,maintaining their stable operation has become an extraordinary challenge.System logs are semi-structured text generated by the recording function in the source code and have important research significance in software service anomaly detection.Existing log anomaly detection methods mainly focus on the statistical characteristics of logs,making it difficult to distinguish the semantic differences between normal and abnormal logs,and performing poorly on real-world industrial log data.In this paper,we propose an unsupervised framework for log anomaly detection based on generative pre-training-2(GPT-2).We apply our approach to two industrial systems.The experimental results on two datasets show that our approach outperforms state-of-the-art approaches for log anomaly detection.展开更多
In this paper,we propose a general algorithmic framework to solve a class of optimization problems on the product of complex Stiefel manifolds based on the matrix polar decomposition.We establish the weak convergence,...In this paper,we propose a general algorithmic framework to solve a class of optimization problems on the product of complex Stiefel manifolds based on the matrix polar decomposition.We establish the weak convergence,global convergence and linear convergence properties,respectively,of this general algorithmic approach using theŁojasiewicz gradient inequality and the Morse–Bott property.This general algorithmic approach and its convergence results are applied to the simultaneous approximate tensor diagonalization problem and the simultaneous approximate tensor compression problem,which include as special cases the low rank orthogonal approximation,best rank-1 approximation and low multilinear rank approximation for higher order complex tensors.We also present a variant of this general algorithmic framework to solve a symmetric version of this class of optimization models,which essentially optimizes over a single Stiefel manifold.We establish its weak convergence,global convergence and linear convergence properties in a similar way.This symmetric variant and its convergence results are applied to the simultaneous approximate symmetric tensor diagonalization,which includes as special cases the low rank symmetric orthogonal approximation and best symmetric rank-1 approximation for higher order complex symmetric tensors.It turns out that well-known algorithms such as LROAT,S-LROAT,HOPM and S-HOPM are all special cases of this general algorithmic framework and its symmetric variant,and our convergence results subsume the results found in the literature designed for those special cases.All the algorithms and convergence results in this paper are straightforwardly applicable to the real case.展开更多
This work investigates the potential of the aerial intelligent reflecting surface(AIRS)in secure communication,where an intelligent reflecting surface(IRS)carried by an unmanned aerial vehicle(UAV)is utilized to help ...This work investigates the potential of the aerial intelligent reflecting surface(AIRS)in secure communication,where an intelligent reflecting surface(IRS)carried by an unmanned aerial vehicle(UAV)is utilized to help the communication between the ground nodes.Specifically,we formulate the joint design of the AIRS’s deployment and the phase shift to maximize the secrecy rate.To solve the non-convex objective,we develop an alternating optimization(AO)approach,where the phase shift optimization is solved by the Riemannian manifold optimization(RMO)method,while the deployment optimization is handled by the successive convex approximation(SCA)technique.Furthermore,to reduce the computational complexity of the RMO method,an element-wise block coordinate descent(EBCD)based method is employed.Simulation results verify the effect of AIRS in improving the communication security,as well as the importance of designing the deployment and phase shift properly.展开更多
基金Xin Liu’s research was supported in part by the National Natural Science Foundation of China(No.11971466)Key Research Program of Frontier Sciences,Chinese Academy of Sciences(No.ZDBS-LY-7022)+1 种基金the National Center for Mathematics and Interdisciplinary Sciences,Chinese Academy of Sciences and the Youth Innovation Promotion Association,CAS.Zai-Wen Wen’s research was supported in part by the the National Natural Science Foundation of China(Nos.11421101 and 11831002)the Beijing Academy of Artificial Intelligence.Ya-Xiang Yuan’s research was supported in part by the National Natural Science Foundation of China(Nos.11331012 and 11461161005).
文摘Manifold optimization is ubiquitous in computational and appliedmathematics,statistics,engineering,machine learning,physics,chemistry,etc.One of the main challenges usually is the non-convexity of the manifold constraints.By utilizing the geometry of manifold,a large class of constrained optimization problems can be viewed as unconstrained optimization problems on manifold.From this perspective,intrinsic structures,optimality conditions and numerical algorithms for manifold optimization are investigated.Some recent progress on the theoretical results of manifold optimization is also presented.
基金supported by the National Science Foundation of China(No.12071398)the Natural Science Foundation of Hunan Province(No.2020JJ4567)the Key Scientific Research Found of Hunan Education Department(Nos.20A097 and 18A351).
文摘Canonical correlation analysis(CCA)describes the relationship between two sets of variables by finding a linear combination that maximizes the correlation coefficient.However,in high-dimensional settings where the number of variables exceeds sample size,or in the case that the variables are highly correlated,the traditional CCA is no longer appropriate.In this paper,a new matrix regularization is introduced,which is an extension of the trace Lasso in the vector case.Then we propose an adaptive sparse version of CCA(ASCCA)to overcome these disadvantages by utilizing the trace Lasso regularization.The adaptability of ASCCA is that the sparsity regularization of canonical vectors depends on the sample data,which is more realistic in practical applications.The ASCCA model is further reformulated to an optimization problem on the Riemannian manifold.Then we adopt a manifold inexact augmented Lagrangian method to solve the resulting optimization problem.The performance of the ASCCA model is compared with some existing sparse CCA techniques in different simulation settings and real datasets.
文摘This paper describes a new design of the neutral beam manifold based on a more optimized support system.A proposed alternative scheme has presented to replace the former complex manifold supports and internal pipe supports in the final design phase.Both the structural reliability and feasibility were confirmed with detailed analyses.Comparative analyses between two typical types of manifold support scheme were performed.All relevant results of mechanical analyses for typical operation scenarios and fault conditions are presented.Future optimization activities are described,which will give useful information for a refined setting of components in the next phase.
基金supported in part by the National Natural Science Foundation of China under Grants 61971126 and 61921004ZTE CorporationState Key Laboratory of Mobile Network and Mobile Multimedia Technology.
文摘In this paper,we investigate the reconfigurable intelligent surface(RIS)-enabled multiple-input-single-output orthogonal frequency division multiplexing(MISO-OFDM)system under frequency-selective channels,and propose a low-complexity alternating optimization(AO)based joint beamforming and RIS phase shifts optimization algorithm to maximize the achievable rate.First,with fixed RIS phase shifts,we devise the optimal closedform transmit beamforming vectors corresponding to different subcarriers.Then,with given active beamforming vectors,near-optimal RIS reflection coefficients can be determined efficiently leveraging fractional programming(FP)combined with manifold optimization(MO)or majorization-minimization(MM)framework.Additionally,we also propose a heuristic RIS phase shifts design approach based on the sum of subcarrier gain maximization(SSGM)criterion requiring lower complexity.Numerical results indicate that the proposed MO/MM algorithm can achieve almost the same rate as the upper bound achieved by the semidefinite relaxation(SDR)algorithm,and the proposed SSGM based scheme is only slightly inferior to the upper bound while has much lower complexity.These results demonstrate the effectiveness of the proposed algorithms.
基金supported by the General Program of Natural Science Foudation of Chongqing Province of China(cstc2021jcyj-msxmX0454)
文摘Intelligent Reflecting Surface (IRS) can offer unprecedented channel capacity gains since it can reconfigure the signal propagation environment. We decide to maximize the channel capacity by jointly optimizing the transmit-power-constrained precoding matrix at the base station and the unit-modulus-constrained phase shift vector at the IRS in IRS-assisted multi-user downlink communication. We first convert the resulting non-convex problem into an equivalent problem, then use the alternate optimization algorithm. While fixing the phase shift vector, we can obtain the optimal precoding matrix directly by adopting standard optimization packages. While fixing the precoding matrix, we propose the Riemannian Trust-Region (RTR) algorithm to solve this optimization problem. And the key of the RTR algorithm is the solution of the trust-region sub-problem. We first adopt the accurate solution based on Newton's (ASNT) method to solve this sub-problem, which can obtain the global solution but cannot guarantee that the solution is optimal since the initial iteration point is difficult to choose. Then, we propose the Improved-Polyline (IPL) method, which can avoid the difficulty of the ASNT method and improve convergence speed and calculation efficiency. The numerical results show that the RTR algorithm has more significant performance gains and faster convergence speed compared with the existing approaches.
基金supported by ZTE Industry-University-Institute Cooperation Funds,the Natural Science Foundation of Shanghai under Grant No.23ZR1407300the National Natural Science Foundation of China un⁃der Grant No.61771147.
文摘Hybrid beamforming(HBF)has become an attractive and important technology in massive multiple-input multiple-output(MIMO)millimeter-wave(mmWave)systems.There are different hybrid architectures in HBF depending on different connection strategies of the phase shifter network between antennas and radio frequency chains.This paper investigates HBF optimization with different hybrid architectures in broadband point-to-point mmWave MIMO systems.The joint hybrid architecture and beamforming optimization problem is divided into two sub-problems.First,we transform the spectral efficiency maximization problem into an equivalent weighted mean squared error minimization problem,and propose an algorithm based on the manifold optimization method for the hybrid beamformer with a fixed hybrid architecture.The overlapped subarray architecture which balances well between hardware costs and system performance is investigated.We further propose an algorithm to dynamically partition antenna subarrays and combine it with the HBF optimization algorithm.Simulation results are presented to demonstrate the performance improvement of our proposed algorithms.
文摘As the scale of software systems expands,maintaining their stable operation has become an extraordinary challenge.System logs are semi-structured text generated by the recording function in the source code and have important research significance in software service anomaly detection.Existing log anomaly detection methods mainly focus on the statistical characteristics of logs,making it difficult to distinguish the semantic differences between normal and abnormal logs,and performing poorly on real-world industrial log data.In this paper,we propose an unsupervised framework for log anomaly detection based on generative pre-training-2(GPT-2).We apply our approach to two industrial systems.The experimental results on two datasets show that our approach outperforms state-of-the-art approaches for log anomaly detection.
基金supported by the National Natural Science Foundation of China(No.11601371)the Guangdong Basic and Applied Basic Research Foundation(No.2021A1515010232).
文摘In this paper,we propose a general algorithmic framework to solve a class of optimization problems on the product of complex Stiefel manifolds based on the matrix polar decomposition.We establish the weak convergence,global convergence and linear convergence properties,respectively,of this general algorithmic approach using theŁojasiewicz gradient inequality and the Morse–Bott property.This general algorithmic approach and its convergence results are applied to the simultaneous approximate tensor diagonalization problem and the simultaneous approximate tensor compression problem,which include as special cases the low rank orthogonal approximation,best rank-1 approximation and low multilinear rank approximation for higher order complex tensors.We also present a variant of this general algorithmic framework to solve a symmetric version of this class of optimization models,which essentially optimizes over a single Stiefel manifold.We establish its weak convergence,global convergence and linear convergence properties in a similar way.This symmetric variant and its convergence results are applied to the simultaneous approximate symmetric tensor diagonalization,which includes as special cases the low rank symmetric orthogonal approximation and best symmetric rank-1 approximation for higher order complex symmetric tensors.It turns out that well-known algorithms such as LROAT,S-LROAT,HOPM and S-HOPM are all special cases of this general algorithmic framework and its symmetric variant,and our convergence results subsume the results found in the literature designed for those special cases.All the algorithms and convergence results in this paper are straightforwardly applicable to the real case.
基金supported in part by the National Natural Science Foundation of China(Nos.61901490,61801434,62071223,and 62031012)the Open Fund of the Shaanxi Key Laboratory of Information Communication Network and Security(No.ICNS201801)+1 种基金the Project funded by China Postdoctoral Science Foundation(No.2020M682345)the Henan Postdoctoral Foundation(No.202001015).
文摘This work investigates the potential of the aerial intelligent reflecting surface(AIRS)in secure communication,where an intelligent reflecting surface(IRS)carried by an unmanned aerial vehicle(UAV)is utilized to help the communication between the ground nodes.Specifically,we formulate the joint design of the AIRS’s deployment and the phase shift to maximize the secrecy rate.To solve the non-convex objective,we develop an alternating optimization(AO)approach,where the phase shift optimization is solved by the Riemannian manifold optimization(RMO)method,while the deployment optimization is handled by the successive convex approximation(SCA)technique.Furthermore,to reduce the computational complexity of the RMO method,an element-wise block coordinate descent(EBCD)based method is employed.Simulation results verify the effect of AIRS in improving the communication security,as well as the importance of designing the deployment and phase shift properly.
