Although the SSA （singular spectral analysis） is a potential tool for analysing time series of different physical processes, the processing of large geophysical data set requires more time and is found to be computa...Although the SSA （singular spectral analysis） is a potential tool for analysing time series of different physical processes, the processing of large geophysical data set requires more time and is found to be computationally expansive. In particular for the SVD （singular value decomposition） of large trajectory matrix, the processing units require huge memory and high performance computing system. In the present work, we propose an alternative scheme based on WSSA （windowed singular spectral analysis）, which is robust for analysing long data sets without losing any valuable low-frequency information contained in the data. The underlying scheme reduces the floating point operations in SVD computations as the size of the trajectory matrix is small in windowed processing. In order to test the efficiency, the authors applied the proposed method on two geophysical data sets i.e., the climatic record with 30,000 data points and seismic reflection trace with 8,000 data points. The authors have shown that without distorting any physical information, the low-frequency contents of the data are well preserved after the windowed processing in both the cases.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
为在大数据环境下处理高维矩阵和应用奇异值分解提供更高效的解决方案,从而加速数据分析和处理速度,通过研究随机投影以及Krylov子空间投影理论下关于高维矩阵求解特征值特征向量(奇异值奇异向量)问题,分别总结了6种高效计算方法并对其...为在大数据环境下处理高维矩阵和应用奇异值分解提供更高效的解决方案,从而加速数据分析和处理速度,通过研究随机投影以及Krylov子空间投影理论下关于高维矩阵求解特征值特征向量(奇异值奇异向量)问题,分别总结了6种高效计算方法并对其相关应用研究进行对比分析。结果表明,在谱聚类的应用上,通过降低核心步骤SVD(Singular Value Decomposition)的复杂度,使优化后的算法与原始谱聚类算法的精度相近,但大大缩短了运行时间,在1200维的数据下计算速度相较原算法快了10倍以上。同时,该方法应用于图像压缩领域,能有效地提高原有算法的运行效率,在精度不变的情况下,运行效率得到了1~5倍的提升。展开更多
文摘Although the SSA （singular spectral analysis） is a potential tool for analysing time series of different physical processes, the processing of large geophysical data set requires more time and is found to be computationally expansive. In particular for the SVD （singular value decomposition） of large trajectory matrix, the processing units require huge memory and high performance computing system. In the present work, we propose an alternative scheme based on WSSA （windowed singular spectral analysis）, which is robust for analysing long data sets without losing any valuable low-frequency information contained in the data. The underlying scheme reduces the floating point operations in SVD computations as the size of the trajectory matrix is small in windowed processing. In order to test the efficiency, the authors applied the proposed method on two geophysical data sets i.e., the climatic record with 30,000 data points and seismic reflection trace with 8,000 data points. The authors have shown that without distorting any physical information, the low-frequency contents of the data are well preserved after the windowed processing in both the cases.
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.
文摘为在大数据环境下处理高维矩阵和应用奇异值分解提供更高效的解决方案,从而加速数据分析和处理速度,通过研究随机投影以及Krylov子空间投影理论下关于高维矩阵求解特征值特征向量(奇异值奇异向量)问题,分别总结了6种高效计算方法并对其相关应用研究进行对比分析。结果表明,在谱聚类的应用上,通过降低核心步骤SVD(Singular Value Decomposition)的复杂度,使优化后的算法与原始谱聚类算法的精度相近,但大大缩短了运行时间,在1200维的数据下计算速度相较原算法快了10倍以上。同时,该方法应用于图像压缩领域,能有效地提高原有算法的运行效率,在精度不变的情况下,运行效率得到了1~5倍的提升。
