On the choice of parameters in singular spectrum analysis and related subspace-based methods

Golyandina, Nina

doi:10.4310/sii.2010.v3.n3.a2

Cited by 138 publications

(109 citation statements)

References 34 publications

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“…Let us remark that Case A corresponds to Singular Value Decomposition (SVD) of X, that is, X = ∑ i √ λ i U i V T i , P i = U i are left singular vectors of X, Q i = √ λ i V i , V i are called factor vectors or right singular vectors, λ i are eigenvalues of XX T ; therefore, Note also that Case B is suitable only for the analysis of stationary time series with zero mean [17].…”

Section: First Stage: Decompositionmentioning

confidence: 99%

A Hybrid Method Based on Singular Spectrum Analysis, Firefly Algorithm, and BP Neural Network for Short-Term Wind Speed Forecasting

Gao

Zhang

2016

Energies

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Abstract:With increasing importance being attached to big data mining, analysis, and forecasting in the field of wind energy, how to select an optimization model to improve the forecasting accuracy of the wind speed time series is not only an extremely challenging problem, but also a problem of concern for economic forecasting. The artificial intelligence model is widely used in forecasting and data processing, but the individual back-propagation artificial neural network cannot always satisfy the time series forecasting needs. Thus, a hybrid forecasting approach has been proposed in this study, which consists of data preprocessing, parameter optimization and a neural network for advancing the accuracy of short-term wind speed forecasting. According to the case study, in which the data are collected from Peng Lai, a city located in China, the simulation results indicate that the hybrid forecasting method yields better predictions compared to the individual BP, which indicates that the hybrid method exhibits stronger forecasting ability.

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Section: First Stage: Decompositionmentioning

confidence: 99%

A Hybrid Method Based on Singular Spectrum Analysis, Firefly Algorithm, and BP Neural Network for Short-Term Wind Speed Forecasting

Gao

Zhang

2016

Energies

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“…This almost prevents the use of the optimum window lengths even for time series of moderate length (say, few thousand). The problem is much more severe for 2D-SSA [15] or subspace-based methods [2,8,13], where a window size is typically large.…”

Section: Introductionmentioning

confidence: 99%

Computation- and space-efficient implementation of SSA

Korobeynikov

2010

Statistics and Its Interface

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The computational complexity of different steps of the Basic SSA is discussed. It is shown that the use of the general-purpose "blackbox" routines which can be found in packages like LAPACK leads to a huge waste of time since the Hankel structure of the trajectory matrix is not taken into account.We outline several state-of-the-art algorithms including the Lanczos-based truncated Singular Value Decomposition (SVD) which can be modified to exploit the structure of the trajectory matrix. The key components here are Hankel matrix-vector multiplication and the hankelization operator. We show that both operations can be computed efficiently by means of the Fast Fourier Transform.The use of these methods yields the reduction of the worst-case computational complexity from O(N 3 ) to O(kN log N ), where N is the series length and k is the number of desired eigentriples.

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“…In addition to the clear connection with time series analysis and signal processing, HSLRA has been extensively used in system identification (modeling dynamical systems) [13], in speech and audio processing [11], in modal and spectral analysis [18] and image processing [15]. Some discussion on the relationship of HSLRA with some well known subspace-based methods of time series analysis and signal processing is given in [8].…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…We restrict our attention to the distance function associated with the matrix Frobenuis norm (6), that is, we take W = V in (8).…”

Section: Algorithms Based On the Use Of Alternating Projectionsmentioning

confidence: 99%

Global optimization for structured low rank approximation

Gillard

Zhigljavsky

2016

AIP Conference Proceedings

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Abstract. In this paper, we investigate the complexity of the numerical construction of the Hankel structured low-rank approximation (HSLRA) problem, and develop a family of algorithms to solve this problem. Briefly, HSLRA is the problem of finding the closest (in some pre-defined norm) rank r approximation of a given Hankel matrix, which is also of Hankel structure. Unlike many other methods described in the literature the family of algorithms we propose has the property of guaranteed convergence.

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On the choice of parameters in singular spectrum analysis and related subspace-based methods

Cited by 138 publications

References 34 publications

A Hybrid Method Based on Singular Spectrum Analysis, Firefly Algorithm, and BP Neural Network for Short-Term Wind Speed Forecasting

A Hybrid Method Based on Singular Spectrum Analysis, Firefly Algorithm, and BP Neural Network for Short-Term Wind Speed Forecasting

Computation- and space-efficient implementation of SSA

Global optimization for structured low rank approximation

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