Tensor robust principal component analysis has received a substantial amount of attention in various fields.Most existing methods,normally relying on tensor nuclear norm minimization,need to pay an expensive computati...Tensor robust principal component analysis has received a substantial amount of attention in various fields.Most existing methods,normally relying on tensor nuclear norm minimization,need to pay an expensive computational cost due to multiple singular value decompositions at each iteration.To overcome the drawback,we propose a scalable and efficient method,named parallel active subspace decomposition,which divides the unfolding along each mode of the tensor into a columnwise orthonormal matrix(active subspace)and another small-size matrix in parallel.Such a transformation leads to a nonconvex optimization problem in which the scale of nuclear norm minimization is generally much smaller than that in the original problem.We solve the optimization problem by an alternating direction method of multipliers and show that the iterates can be convergent within the given stopping criterion and the convergent solution is close to the global optimum solution within the prescribed bound.Experimental results are given to demonstrate that the performance of the proposed model is better than the state-of-the-art methods.展开更多
To avoid drawbacks of classic discrete Fourier transform(DFT)method,modern spectral estimation theory was introduced into harmonics and inter-harmonics analysis in electric power system.Idea of the subspace-based root...To avoid drawbacks of classic discrete Fourier transform(DFT)method,modern spectral estimation theory was introduced into harmonics and inter-harmonics analysis in electric power system.Idea of the subspace-based root-min-norm algorithm was described,but it is susceptive to noises with unstable performance in different SNRs.So the modified root-min-norm algorithm based on cross-spectral estimation was proposed,utilizing cross-correlation matrix and independence of different Gaussian noise series.Lots of simulation experiments were carried out to test performance of the algorithm in different conditions,and its statistical characteristics was presented.Simulation results show that the modified algorithm can efficiently suppress influence of the noises,and has high frequency resolution,high precision and high stability,and it is much superior to the classic DFT method.展开更多
基金the HKRGC GRF 12306616,12200317,12300218 and 12300519,and HKU Grant 104005583.
文摘Tensor robust principal component analysis has received a substantial amount of attention in various fields.Most existing methods,normally relying on tensor nuclear norm minimization,need to pay an expensive computational cost due to multiple singular value decompositions at each iteration.To overcome the drawback,we propose a scalable and efficient method,named parallel active subspace decomposition,which divides the unfolding along each mode of the tensor into a columnwise orthonormal matrix(active subspace)and another small-size matrix in parallel.Such a transformation leads to a nonconvex optimization problem in which the scale of nuclear norm minimization is generally much smaller than that in the original problem.We solve the optimization problem by an alternating direction method of multipliers and show that the iterates can be convergent within the given stopping criterion and the convergent solution is close to the global optimum solution within the prescribed bound.Experimental results are given to demonstrate that the performance of the proposed model is better than the state-of-the-art methods.
基金Shandong University of Science and Technology Research Fund(No.2010KYTD101)
文摘To avoid drawbacks of classic discrete Fourier transform(DFT)method,modern spectral estimation theory was introduced into harmonics and inter-harmonics analysis in electric power system.Idea of the subspace-based root-min-norm algorithm was described,but it is susceptive to noises with unstable performance in different SNRs.So the modified root-min-norm algorithm based on cross-spectral estimation was proposed,utilizing cross-correlation matrix and independence of different Gaussian noise series.Lots of simulation experiments were carried out to test performance of the algorithm in different conditions,and its statistical characteristics was presented.Simulation results show that the modified algorithm can efficiently suppress influence of the noises,and has high frequency resolution,high precision and high stability,and it is much superior to the classic DFT method.
